# 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.

65 questions
Filter by
Sorted by
Tagged with
1 vote
101 views

### 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 ...
117 views

173 views

### Does geometric quantization work for arbitrary "particle with constraint + potential" systems?

I was struck by the following line in Hall's Quantum Theory for Mathematicians (Ch. 23, p. 484): In the case $N = T^*M$, for example, with the natural “vertical” polarization, geometric quantization ...
68 views

### Is there a relationship between the phase space path integral and phase space quantum mechanics?

I understand that they're, in the end, related because they're the same theory. But is there a closer relationship because both are theories of probability distributions on phase space? I also ...
188 views

### Commutator Constant

I have seen a lot of commutators in quantum mechanics having a constant factor $i\hbar$. I have read about Dirac supplanting Poisson Brackets with commutators having a constant $i\hbar$. I want to ...
188 views

### Wigner transform, convolution, and poles

Let \begin{equation} \int\mathrm{d}z~ A(x,z) B(z,y) = \delta(x - y). \end{equation} Taking Wigner transform of both sides we readily obtain \begin{equation} A^W(X,p) \star B^W(X,p) = 1, \end{equation} ...
92 views

### Do we lose information about the state when we obtain the Wigner function by solving the eigenvalue equation?

It can be shown that $$H(q,p)\star W_{\psi}(q,p)=EW_{\psi}(q,p)$$ where $H(q,p)$ is the classicaly Hamiltonian function, $\star$ is the Moyal/Groenewold star product and $W_{\psi}(q,p)$ is the Wigner ...
1 vote
94 views

121 views

### Commutators as contour integrals in 2D CFT, and classical limits

In a 2D CFT, the commutator of two operators $$A_i=\oint a_i(z)dz$$ can be given by $$[A_1,A_2]=\oint_0dw\oint_wdza_1(z)a_2(w)$$ where the $z$ integral is taken over a contour around $w$ and the $w$ ...
71 views

### Basic question in similarities and difference on quantizations

In physics, usually quantization means canonical quantization. i.e., which we treat classical objects to quantum operators. i.e., For the association $Q:f \mapsto \hat{f}$ from functions on the ...
5k views

### How can Planck's constant take different values?

I have seen books and papers mentioning "In the semiclassical limit, $\hbar$ tends to zero", "the scaled Planck's constant goes as $1/N$ where $N$ is the Hilbert space dimension" ...
192 views

### Physical motivation of quantization

I am a mathematics student recently looking into (geometric and deformation) quantization. I'd like to know more about their physical motivations. Here by "quantization" I mean any process ...
36 views

### How to obtain a star product of a pair of functionals in matter sector?

In lecture notes D-branes, Tachyons and String field theory by Washington Taylor and Barton Zwiebach in the topic "Witten's cubic bosonic SFT" there they define a star product and when star ...
1 vote
202 views

238 views

### Geometric Intuition for the Moyal Product

I've recently been reading into deformation quantization as another formulation of quantum mechanics. I have focused on understanding the Moyal product in particular, as it contains the seeds for the ...
1 vote
376 views