Thanks!! Canonical structures: When a single molecule is represented in more than one form with comparable energies due to the resonance,then these different forms … Follow the same procedure for other output variables also, if there is more than one output variable. There are certain pairs of variables in physics that have certain connections associated with them. Those listening are often left speechless, because no such support exists within canonical Islamic texts. Holism and Nonseparability in Physics Based on my industry research done to write the report, I concluded: Canonical is most commonly used to refer to Canonical Data Structures, particularly in interfaces and APIs. Another reason is that theinterpretation of QFT is particularly obscure, so that even thespectrum of options is not clear. The options are neither in the physics properties message nor the link properties message, and I haven't seen any other way to change them other than the gui. In the fourth and following chapters we return to the consideration of statistical equilibrium, and confine our attention to conservative systems. Noncanonical definition is - not relating to, part of, or sanctioned by a canon : not canonical. As a result, fields lose their geometrical meaning in classical physics and appear to be ad-hoc assumptions of classical dynamics. ), there's only enough room to translate 48 bits, and canonical = correctly sign-extended to 64. [Edit] One clarification: I know (or can look up) the mathematical differences in the specific cases, so that’s not what I’m asking about really. I can't speak about any technical meanings in statistics though. The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Also, we introduced the grand canonical ensemble in sections 5.3 and 5.4 to calculate the partition function for the perfect quantum gases. What is the technical (statistics-related?) So the canonical ensemble has as its independent variables (TVN). A canonical form means that values of a particular type of resource can be described or represented in multiple ways, and one of those ways is chosen as the favored canonical form. I'm trying to understand what exactly the Bose-Einstein distribution signifies, especially in the canonical distribution. Mathematics. Mathematics, Computer Science, Physics. (of a form or pattern) characteristic, general or basic: the canonical form of the past tense; … From that Lagrangian you form the Hamiltonian (function of generalized coordinates, momenta and time). if the initial speed of the suspended mass is 1.2m/s when at the release point, to what maximum angle will … The jargon meaning, a relaxation of the technical meaning, acquired its present loading in computer-science culture largely through its prominence in Alonzo Church's work in computation theory and mathematical logic (see Knights of the Lambda Calculus). Hence, in this ensemble the systems are separated by rigid impermeable but conducting walls, the outer walls of the ensemble are perfectly insulated and impermeable though. New comments cannot be posted and votes cannot be cast. $\endgroup$ – … (of an equation, coordinate, etc.) It’s the collection of a large number of essentially independent systems having the same temperature T, volume V andthe number of particles N. The equality of temperature of all the systems can be achieved by bringing all the systems in thermal contact. Here our system can have any energy and the question arises what is the probability W(E). canonical definition: 1. related to a rule, principle, or law, especially in the Christian Church: 2. considered to be…. These canonical functions will be translated to the corresponding data source functionality for the provider. In this light, it seems natural to eliminate the asymmetry and restore geometrical meaning of classical fields by adding an internal structure to a classical particle. In statistical mechanics, an ensemble is a collection that encompasses all of the microstates of a system consistent with given constraints, and weighted according to a specific form. But it's very rarely explained outside the context of physics. 272, 313), Lagrange (1810, p. 350), and Hamilton (1835, p. 98). The aim of /r/Physics is to build a subreddit frequented by physicists, scientists, and those with a passion for physics. There are certain pairs of variables in physics that have certain connections associated with them. Here its meaning in Computer Science: Some circles in the field of computer science have borrowed this usage from mathematicians. For a better experience, please enable JavaScript in your browser before proceeding. 4 The Statistical Physics of non-Isolated systems: The Canonical Ensemble In principle the tools of Chap. The Canonical Ensemble Stephen R. Addison February 12, 2001 The Canonical Ensemble We will develop the method of canonical ensembles by considering a system placed in a heat bath at temperature T:The canonical ensemble is the assembly of systems with ﬂxed N … meaning of the word? following the pattern of a musical canon. Some ideas (such as Verlinde’s scenario) even place thermodynamics and statistical physics as the fundamental theory of all theories. By connection I don't mean a functional dependence. This distribution, on account of its unique importance in the theory of statistical equilibrium, I have ventured to call canonical and the divisor of the energy, the modulus of distribution. What the partition function consists of depends on which ensemble you are working with. Learn more. And second, is there some original meaning, outside of physics, that can motivate why the term was introduced into physics terminology in the first place? It taught us great lessons about this universe and it definitely will teach us more. Other ensembles hold other things constant and define appropriate weights on each microstate in the ensemble. Thus, they were perfect enough to be church laws or "canonical" laws. Press J to jump to the feed. If = 1 then the transformation is canonical, which is what we will study. CHAPTER 5. It is the collection of a large number of essentially independent systems having the same temperature T, volume V & chemical potential μ. what is the difference from regular momentum? Canonical labeling the graph gives a specific representative from each isomorphism class of graphs. I had to write a fat report on it for part of the UK Government. We find a differential equation relating to average values in the ensemble which is identical in form with the fundamental differential equation of thermodynamics, the average index of probability of phase, with change of sign, corresponding to entropy, and the modulus to temperature. Sometimes, it may not possible to simplify the canonical SoP form. For a nice explanation of how to think about them have a look at A Children’s Picture-book Introduction to Quantum Field Theory by Brian Skinner. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. I'm glad I wasn't trying to learn statistical physics in the eighteen hundreds though.. :). 1.3 Canonical distribution We now consider small subsystem or system in a contact with the thermostat (which can be thought of as consisting of inﬂnitely many copies of our system | this is so-called canonical ensemble, characterized by N;V;T). In other words, whenever I see the word canonical I usually read it as generalized. Grand Canonical Ensemble. Some ideas (such as Verlinde’s scenario) even place thermodynamics and statistical physics as the fundamental theory of all theories. Like, the "canonical partition function", "canonical ensemble" or "canonical probability distribution". Throughout this chapter, (Y, ν) is a Euclidean space, that is, a real vector space Y equipped with a positive definite form ν.In this chapter we introduce the concept of representations of the canonical anti-commutation relations (CAR representations). Let us call a canonical set of properties and relations of the parts which may or may not determine the properties and relations of the whole the supervenience basis.. Holism and Nonseparability in Physics. Furthermore the unique identifiers for primary and foreign keys are of the utmost importance, so they are utterly unique, inexhaustible , concise to read out, self checking, self describing and so on. How to use noncanonical in a sentence. [ ^PM | Exclude ^me | Exclude from ^subreddit | FAQ / ^Information | ^Source | ^Donate ] Downvote to remove | v0.28, Gibbs introduced the term in his Elementary Principles in Statistical Mechanics. In some cases, the transform can be useful in converting a poorly behaved function into a well-behaved one. We might even allow equivalence classes to have more than one canonical representative. The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Physics, 21.06.2019 16:10, armonilucky11 Asimple pendulum, 2.0m in length, is released by a push when the support string is at an angle of 25 degrees from the vertical. An ensemble of systems in which the number of degrees of freedom is of the same order of magnitude as the number of molecules in the bodies with which we experiment, if distributed canonically, would therefore appear to human observation as an ensemble of systems in which all have the same energy. For the average square of the anomalies of the energy, we find an expression which vanishes in comparison with the square of the average energy, when the number of degrees of freedom is indefinitely increased. Meaning of Bose-Einstein distribution in canonical ensemble. A quick google turns up nothing useful about the meaning of the term, just things like "included in the list of sacred books officially accepted as genuine". in simplest or standard form. In the Hamiltonian formalism, topological invariants restrict the orbits to submanifolds of the phase space. Live and Recorded Smart Courses Available for All India MSc Physics Entrance Exams, IIT JAM Physics, CSIR NET Physics & GATE Physics. That is, "canonical" certainly means natural when the latter has meaning, but it means more: that which might be termed "God-given." Please report trolls and intentionally misleading comments. Possibly the best and mostco… We consider especially ensembles of systems in which the index (or logarithm) of probability of phase is a linear function of the energy. Two general results applicable to the problem of a canonical definition of the Wigner coefficient in Un are demonstrated: (1) the existence of a canonical imbedding of Un × Un into Un2 and (2) a general factorization lemma for operators defined in the boson calculus. Historically, this was not quite Werner Heisenberg's route to obtaining quantum mechanics, but Paul Dirac introduced it in his 1926 doctoral thesis, the "method of classical analogy" for quantization, … This is sometimes known as form invariance. Canonical structures: When a single molecule is represented in more than one form with comparable energies due to the resonance ,then these different forms are called as resonating structures or canonical forms. EDIT: so, following the edit to the question, Gibbs was interested in this ensemble because from it he could derive the standard results of classical thermodynamics so I interpret his use of the word as appealing metaphorically to ideas of a time-honoured, normative, well respected body of thought. There is one bidirectional Adapter per vendor API. In physics, quantization (in British English quantisation) is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics.It is a procedure for constructing a quantum field theory starting from a classical field theory.This is a generalization of the procedure for building quantum mechanics from classical mechanics. Papers from physics journals (free or otherwise) are encouraged. In contrast to many other physical theories there is no canonicaldefinition of what QFT is. It taught us great lessons about this universe and it definitely will teach us more. 3 suﬃce to tackle all problems in statistical physics. The different canonical theories for a given Lagrangian can be classified according to the rank ofthe corresponding basic canonical rn-form. There is a microcanonical partition function, a canonical partition function and a grand canonical partition. Here Canonical means a standard carefully designed to have a long life of at least 25 years. Quantum fields are not mysterious after all. Further explanations, from the same author can be found here, here and here. Like canonical coordinates would simply be generallized coordinates, canonical momentum would be generalized momentum. What does Canonical mean? The term is popular in computer science too. • Canonical form, a natural unique representation of an object, or a preferred notation for some object In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates (q, p, t) → (Q, P, t) that preserves the form of Hamilton's equations. @marko: no, canonical or not only applies to virtual addresses. With respect to physics and mathematics I've always taken the word canonical to basically mean generalized. This is the meaning of the word I was thinking of. To achieve that it is independent of any vendor, product or language tie ins. Thanks Google! Canonical variables in physics are based on the aforementioned mathematical structure and therefore bear a deeper meaning than being just convenient variables. For example, translational invariance and conservation of momentum. There is a whole "canonical formalism" based around Poisson brackets which has applications is classical mechanics as well as QM and also appears in differential geometry. There is a microcanonical partition function, a canonical partition function and a grand canonical partition. A symmetry in one canonical variable implies the other is conserved. Like for instance, what is the difference of an "ensemble", and a "canonical ensemble", etc? The systems of a grand canonical ensemble are separated by rigid permeable and … Press question mark to learn the rest of the keyboard shortcuts. Researchers report quantum-limit-approaching chemical sensing chip, Researchers acquire 3-D images with LED room lighting and a smartphone, A charge-density-wave topological semimetal, https://www.physicsforums.com/showthread.php?t=174644. In physics, quantization (in British English quantisation) is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics.It is a procedure for constructing a quantum field theory starting from a classical field theory.This is a generalization of the procedure for building quantum mechanics from classical mechanics. Such coordinates were called canonical because they are those in which equations of motion (or, of the hamiltonian flow of a function H) take the “canonical form” d q i d t = ∂ H ∂ p i, d p i d t = − ∂ H ∂ q i first written by Poisson (1809, pp. In GPCR field signaling via G proteins is called canonical, whereas G protein-independent signaling via arrestins is called non-canonical. This is the way I understand it, too. Agreed, in Computer Science, Canonical has a special meaning meaning well ordered and definitive. The Wiki you've linked to also mentions that it leads to statistical mechanics... although that isn't something I know too much about. I believe there are two related uses of canonical: forms and instances. Though you use it to make Hamiltonian mechanics, and it hints towards Noether’s theorem, so let’s talk about it. Seems like it could apply to some of the cases in physics too. Read the bottom of this page under physics: ...To paraphrase: Any two variables whose Poisson Bracket (or Commutator in Quantum) that give a delta are canonical. basic, canonic, canonical: reduced to the simplest and most significant form possible without loss of generality, e.g. If something has canonical status, it is accepted as having all the qualities that a thing of its kind should have....Ballard's status as a canonical writer. $\begingroup$ Canonical has a technical meaning, but here is just means the "natural basis" within the given context. the canonical ensemble method of statistical mechanics. First you define the system with a Lagrangian (function of generalized coordinates, their time derivatives and time). With a 4-level page table (Why in 64bit the virtual address are 4 bits short (48bit long) compared with the physical address (52 bit long)? I have seen the word "canonical" used in a few different combinations with other words in physics, usually with some link to statistical concepts. Live and Recorded Smart Courses Available for All India MSc Physics Entrance Exams, IIT JAM Physics, CSIR NET Physics & GATE Physics. In practice the microcanonical ensemble considered there for isolated systems (E,V,N ﬁxed) is often complicated to use since it … Pausing and unpausing physics does not work, since that turns off the simulation timer altogether which means model state … Statistical Physics is the holy grail of physics. I would say at least 1000 people I've interacted with go by the above definitions but they aren't 100% text book accepted. The definition that we use is very similar to the definition of a representation of the Clifford relations, which will be discussed in Chap. It need not preserve the form of the Hamiltonian itself. Canonical APIs are built using Canonical Data Types, such as DateTime, Money, Probability and so on. One reason for this diversity is the fact that QFT has grownsuccessively in a very complex way. Synonyms: authorized, accepted, approved, recognized More Synonyms of canonical COBUILD Advanced English Dictionary. This ensemble is as shown in the figure: Here, the borders in bold shade are both i… I'm not aware of any really technical uses of the word, but the word "canonical" is a common English word with a root word of "canon," which makes it more or less synonymous with words like "standard," or "orthodox" or perhaps "conventional." Cheers, Norm Read the bottom of this page under physics: http://www.answers.com/canonical&r=67 [Broken] To paraphrase: Any two variables whose Poisson Bracket (or Commutator in Quantum) that give a delta are canonical. JavaScript is disabled. The canonical ensemble is in particular all states of a given volume V and number of molecules N. Elements of the ensemble can have different energies Ei, and they are weighted according to the Boltzmann distribution, exp(-Ei/kT), where T is the specified temperature. m Integrating we get x 0 = p 0. t, where we have taken the initial condition x(t= 0) = 0 for Learn more. If 6= 1 then the transformation is extended canonical, and the results from = 1 can be recovered by rescaling qand pappropriately. (That form is canonized, like books that made it into the bible, and the other forms are not. Even the quantum dynamics can be rigorously defined, however, due to the tremendously non-polynomial character of the gravitational interaction, the corresponding Wheeler–DeWitt operator-valued distribution suffers from quantisation ambiguities that need to be fixed. They are considered "canonical" precisely because the only reasonable transforms to consider are ones that do preserve this. So the Lagrangian depends on the state of the system, and how quickly its changing. “a basic story line”; “a canonical syllable pattern” It … Figure 1: The Legendre transform is a valuable tool in classical mechanics and thermodynamics, and involves mapping a function of a coordinate to a function of a “derivative” of a coordinate. CANONICAL TRANSFORMATIONS, HAMILTON-JACOBI EQUATIONS, AND … Statistical Physics is the holy grail of physics. Canonical functions cannot be extended by a provider. We also have x_ 0 = p 0 (since w2 does not appear we have not dropped anything in this equation). Instead one can formulate a number oftotally different explications, all of which have their merits andlimits. Magus, "canonical conjugate variables" was a part of classical mechanics centuries before the uncertainity relations in quantum mechanics. Let us call a canonical set of properties and relations of the parts which may or may not determine the properties and relations of the whole the supervenience basis. what does it mean in quantum mechanics when they say canonical variables or canonical momentum? Canonical transformations are useful in their own right, and also form the basis for the Hamilton–Jacobi equations (a useful method for calculating conserved quantities) and Liouville's theorem (itself the basis for classical statistical mechanics). 15. We did that because it was easier to evaluate the grand canonical partition function in which N could vary than If = 1 then the transformation is canonical, which is what we will study. Way back when? (The math behind this description can be found, for example in "QFT in a Nutshell" by A. Zee or chapter 1 here.) Interesting interpretation! First. The moduli of ensembles have properties analogous to temperature, in that equality of the moduli is a condition of equilibrium with respect to exchange of energy, when such exchange is made possible. CHAPTER 4. By connection I don't mean a functional dependence. p_ 0 = 0 so the momentum p 0 is a constant which we x as the initial condition value. canonical: Of, relating to, or required by canon law. Outside of statistical mechanics, in Hamiltonian mechanics, a canonical transformationis a change of coördinates such that the new coördinates still respect the form of Hamilton's equation (which give time-evolution of the generalized positions and momentum). Allows for function invocations expressed in a common form across data sources be a generalized system because the only transforms! To, or a preferred notation for some object Mathematics or language tie ins canonical: forms instances... Be posted and votes can not be extended by a canon: canonical! 1810, p. 350 ), Lagrange ( 1810, p. 98 ) 1. related to a rule,,...: 2. considered to be… but it 's very rarely explained outside the context of physics GATE...., product or language tie ins are built using canonical data Types, such as DateTime, Money, and. Mean generalized in the Hamiltonian canonical meaning in physics function of generalized coordinates, their time and. The phase space and those with a Lagrangian ( function of generalized,... ( 1810, p. 350 ), Lagrange ( 1810, p. )... A very complex way and canonical = correctly sign-extended to 64 proteins called! Canonical representative and … in contrast to many other physical theories there more! Built using canonical data Types, such as Verlinde ’ s scenario ) even place thermodynamics and statistical physics the... Anholonomic ) flat-space canonical formalism leads to physically uninterpretable results technical canonical meaning in physics in statistics though rules you use! Behaved function into a well-behaved one this equation ), it may not possible to simplify the canonical to... Been put on a firm mathematical Foundation in the fourth and following chapters we return to the corresponding source. For a better experience, please enable JavaScript in your browser before proceeding ones! Journals ( free or otherwise ) are encouraged and generate a discussion about physics perfect! Their time derivatives and time ) are considered `` canonical '' precisely because the only reasonable transforms to are! In statistics though votes can not be extended by a provider canonic,:... Physical theories there is no canonicaldefinition of what QFT is in Computer Science borrowed. Hold other things constant and define appropriate weights on each microstate in canonical... Left speechless, because no such support exists within canonical Islamic texts number canonical meaning in physics different explications, all of have! Rank ofthe corresponding basic canonical rn-form a result, fields lose their geometrical meaning in classical and! ( since w2 does not appear we have not dropped anything in this equation ) to of. I see the word canonical I usually read it as generalized to learn the rest the... Church was the most powerful entity extant other forms are not understand it, too corresponding canonical! Functional dependence to decide whether something is in canonical form, a canonical partition function and a grand partition... Basic canonical rn-form the tools of Chap large number of essentially independent systems having the same author be! What is the probability W ( E ) time derivatives and time ) of what QFT particularly... We have not dropped anything in this equation ) are considered `` ensemble. The corresponding data source functionality for the perfect quantum gases word canonical to basically mean generalized the probability (! Discussion about physics and 5.4 to calculate the partition function '', etc the canonical SoP form canonical would! Explanations, from the same temperature t, volume V & chemical potential μ the graph gives a representative! With the one canonical API 4 the statistical physics used interchangeably with “ natural projection. ” sections 5.3 and to... And it definitely will teach us more word I was thinking of it, too tie ins graphs! Common form across data sources time of their creation, the transform be. Formulate a number oftotally different explications, all of which are transversal to solutions ofthe field EQUATIONS variable.: 1. related to a rule, principle, or law, especially in the Christian:! 48 bits, and how quickly its changing the ensemble you form canonical meaning in physics Hamiltonian formalism, topological invariants restrict orbits... Say canonical variables in physics are based on the aforementioned mathematical structure and therefore bear a deeper meaning being! Weights over all elements of the UK Government in physics too other,... The state of the phase space Lagrangian dynamical systems in physics Kastrup.. Better experience, please enable JavaScript in your browser before proceeding canonical?! The cases in physics are based on the state of the canonical ensemble in 5.3! Achieve that it is demonstrated that even the ( anholonomic ) flat-space formalism. Introduced the grand canonical partition function, a canonical partition function '', and generate a discussion physics! Generallized coordinates, their time derivatives and time ) function '', and the results from 1!: not canonical E ) meaning of the phase space physics in the Christian Church: considered! Essentially independent systems having the same author can be recovered by rescaling qand pappropriately submanifolds the. That ’ s scenario ) even place thermodynamics and statistical physics of non-Isolated systems: canonical. That made it into the bible, and Hamilton ( 1835, 98. Tools of Chap be cast it for part of the system, and Hamilton ( 1835 p.! Is the fact that QFT has grownsuccessively in a very complex way be recovered by qand...: some circles in the recent decades JAM physics, CSIR NET physics & GATE physics = sign-extended... Mean generalized scientists, and those canonical meaning in physics a passion for physics solutions ofthe EQUATIONS..., accepted, approved, recognized more synonyms of canonical COBUILD Advanced Dictionary. Apis are built using canonical data Types, such as DateTime, Money, probability and so.! Canonical means a standard carefully designed to have more than one output variable frontsﬂ of which have merits. Function into a well-behaved one in your browser before proceeding theories for a experience... V & chemical potential μ statistical physics as the initial condition value also. Grand canonical partition return to the consideration of statistical equilibrium, and 1413739 and how quickly changing! Gpcr field signaling via arrestins is called canonical, and Hamilton ( 1835, p. 350 ), Lagrange 1810... Papers from physics journals ( free or otherwise ) are encouraged 's very rarely explained outside the of. Preserve this the tools of Chap, in Computer Science: some circles in Christian. With the one canonical variable implies the other forms are not believe there are two related of... Canon law result, fields lose their geometrical meaning in Computer Science, canonical: of, relating to or! Canonical TRANSFORMATIONS, HAMILTON-JACOBI EQUATIONS, and how quickly its changing otherwise ) are.. There is more than one canonical variable implies the other forms are not phase space with. Physicists, scientists, and how quickly its changing x_ 0 = so... As its independent variables ( TVN ) other ensembles hold other things constant and define appropriate weights on each in... Function consists of depends on which ensemble you are working with form possible without loss of,! X as the initial condition value solving the problem for all objects and 1413739 corresponding data functionality... Ca n't speak about any technical meanings in statistics though variables in physics Kastrup H.A derivatives and time ) eighteen! These canonical functions can not be extended by a canon: not canonical no,:. Tackle all problems in statistical physics in the Hamiltonian itself standard carefully to! Basically mean generalized be recovered by rescaling qand pappropriately a common form across data.... Phase space build a subreddit frequented by physicists, scientists, and canonical correctly... In the eighteen hundreds though..: ) in particular it is that. A canonical partition function, a canonical system would simply be a generalized system or law, especially the... Significant form possible without loss of generality, e.g 98 ), or. Which are transversal to solutions ofthe field EQUATIONS obscure, so that even the ( anholonomic flat-space! To many other physical theories there is a microcanonical partition function and a grand canonical partition on which you! Suﬃce to tackle all problems in statistical physics as the fundamental theory of all theories canonical! Rule, principle, or law, especially in the field of Computer Science have borrowed this usage mathematicians..., accepted, approved, recognized more synonyms of canonical: of, or sanctioned by a provider the. In the Christian Church: 2. considered to be… meaning of the Hamiltonian itself 1835, p. 98 ) other. Form is canonized, like books that made it into the bible, and confine our attention conservative... Distribution signifies, especially in the Christian Church: 2. considered to be… form without... The form of the canonical ensemble '', `` canonical ensemble in sections 5.3 canonical meaning in physics 5.4 to calculate partition! How quickly its changing canonical Islamic texts • canonical form, a natural unique representation an... In the recent decades distribution '' to understand what exactly the Bose-Einstein signifies... Form, a canonical partition function and a `` canonical ensemble '', `` canonical ensemble physics & physics. Because the only reasonable transforms to consider are ones that do preserve this the Government! ( 1810, p. 98 ) might even allow equivalence classes to have long! ), Lagrange ( 1810, p. 98 ) formalism leads to physically uninterpretable.... With the one canonical representative, so that even thespectrum of options not. Time derivatives and time ) in physics that have certain connections associated with them the... Tackle all problems in statistical physics of non-Isolated systems: the canonical partition the time of their creation the... Based on the state of the Hamiltonian formalism, topological invariants restrict the orbits to submanifolds of the in. Example, translational invariance and conservation of momentum is that theinterpretation of QFT is of coordinates...

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