# Questions tagged [deformation-quantization]

A description of quantum mechanics in phase space a common ambit with classical mechanics, through the Wigner map from Hilbert space. May be used to address Quantum Mechanics in phase space, the star product binary operation controlling composition of observables, and Wigner, Husimi, and other distribution functions in phase space.

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### Quantization of $x$ and $p$ through the Weyl transformation

I have a question about the development of the integral for calculating the quantization of the classical variables $x$ and $p$ using the Weyl transformation method. The notation that the textbook I'm ...
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### Weyl Quantization Integral

I have some doubts when calculating the integral for Weyl Quantization symbol. If I understand correctly, quantization using the Weyl symbol takes a function in phase space and takes it to an operator ...
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### Uncertainty principle in deformation quantization

Deformation quantization procedure is a well-known way to quantize a classical phase space (at least formally for Poisson manifolds which is known as formal deformation quantization). Although it is a ...
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### A Hamiltonian with a potential depending on the momentum

Imagine we have a Hamiltonian, whose potential depends on velocities (and hence on the momentum), like, for example, $$H= \frac{p^{2}}{2m}+ V(x,p)$$ then how can I quantize that?
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### Quantum corrections in the phase space formulation

I'm trying to reconcile the following two statements: Quantum Mechanics gives physical predictions which are different than the predictions that are obtained in the $\hbar \rightarrow 0$ limit, that ...
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### Poisson algebra and the origin of canonical quantization [duplicate]

Professor Achim Kempf in his lecture note mentioned that non-commutativity of quantum observables in the associated Poisson algebra to the system, impose CCR It was Dirac who first realized that all ...
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### Wigner transform & convolution

I'm trying to understand the gradient expansion within the Keldysh formalism. In particular, I am reading "Quantum Field Theory of Non-equilibrium States" by J. Rammer, section 7.2, ...
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### Is it possible to minimize the number of axioms/rules of the canonical quantization?

In the standard canonical quantization procedure there are two rules. Transform all quantities to operators. Transform the Poisson bracket to a commutator. Of course it will be nicer to minimize the ...
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### Can Friedlander Equations be used to Model Buried Explosive

To quote from WIKIPEDIA The simplest form of a blast wave has been described and termed the Friedlander waveform.[11] It occurs when a high explosive detonates in a free field, that is, with no ...
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### Time Evolution of Wigner Function

The Wigner Function is defined as: $$W(x,p,t)=\frac{1}{2\pi\hbar}\int dy \rho(x+y/2, x-y/2, t)e^{-ipy/\hbar}\tag{1}$$ Where $\rho(x, y, t)=\langle x|\hat{\rho}|y\rangle$. I am supposed to find the ...
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### Operator traces in Kontsevich quantization

In quantization, one studies maps from functions on the phase space to operators acting on the Hilbert space. Let's fix one such map and call it $Q$. Deformation quantization is based on the idea that ...
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### Quantum mechanics in phase space - what are coordinate components?

I'm trying to understand the answer provided by Qmechanic to this question: What's the intuitive reason that phase space flow is incompressible in Classical Mechanics but compressible in Quantum ...
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### Symplectic reduction to moduli space in Chern-Simons theory

In QFT and the Jones polynomial, Witten claims that it is possible to perform symplectic reduction from the distributional Poisson bracket on the unconstrained phase space to a symplectic structure on ...
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### Constructing Quantum Theories without Semiclassical Quantization

This question builds off of this previous question particularly the excellent answer by @Cosmas Zachos and the this document which he attached. Quantization whatever form it takes always seeks to ...
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### On Groenewold's Theorem and Classical and Quantum Hamiltonians

I recently encountered Groenewold's Theorem or the Groenewold-Van Hove Theorem which shows that there is no function which can satisfy the following mapping $$\{A,B\} \to \frac{1}{i\hbar}[A,B].$$ ...
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