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Questions tagged [moyal-product]

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1 answer
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Exact calculations with Moyal product by "Bopp Shift"

I'm now working on my Phd thesis on the area of deformation quantization and field theory. After doing all the "ground work" (definitions, motivations, basics of the theory etc) I have now ...
Diego Santos's user avatar
0 votes
0 answers
131 views

Integral expression for the Poisson bracket

I already asked this in the physics forum but without much attention, so I thought it might attract more attention here. Is there an integral expression for the Poisson bracket that can be derived ...
Nicolas Medina Sanchez's user avatar
1 vote
0 answers
68 views

Moyal products of exponentials

I have trouble verifying a claim made by Sharan in his paper: https://doi.org/10.1103/PhysRevD.20.414. What he essentially claims is that the sequence of Moyal $*$-products $$\underbrace{\exp(-itH/n)*\...
Kostas's user avatar
  • 11
3 votes
0 answers
276 views

Resource request: Moyal $\star$-product based calculations

I already asked two questions about the Moyal $\star$-product here and here but I think I'll have a lot more similar questions, so I'm wondering if anyone can help me with finding some good resources. ...
lel's user avatar
  • 314
5 votes
1 answer
370 views

Moyal $\star$-product of $\star$-exponentials

Definitions and assumptions On a 2n-dimensional phase-space with coordinates $x$ and $p$, the Moyal product can be written explicitly as $$g(x,p) \star h(x,p) = g(x,p) e^{\frac{i}{2}\left( \...
lel's user avatar
  • 314
8 votes
1 answer
416 views

Moyal $\star$-product inverse?

On a 2n-dimensional phase-space with coordinates $x$ and $p$, the Moyal product can be written explicitly as $$g(x,p) \star h(x,p) = g(x,p) e^{\frac{i}{2}\left( \overleftarrow{\partial_x} \cdot \...
lel's user avatar
  • 314
4 votes
0 answers
325 views

The Moyal action of a planar vector field

Let $X=P\frac{\partial}{\partial x}+Q\frac{\partial}{\partial y}$ be a polynomial vector field on $\mathbb{R}^{2}$. Consider the following (Moyal) operator on $\mathbb{C}[x,y]$: $\tilde{D}_{X}(f)=...
Ali Taghavi's user avatar