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Results tagged with quantization
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user 24965
Questions on various methods and aspects of quantization
7
votes
0
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Could we extend the star product on a Poisson manifold from its ring of smooth functions to ...
Kontsevich proved that there exists a deformation quantization of $M$, i.e. let $C^{\infty}(M)[[\hbar]]=C^{\infty}(M)\otimes_{\mathbb{R}}\mathbb{R}[[\hbar]]$ be the formal power series of smooth functions …
- 9,009
6
votes
1
answer
400
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Does the vanishing of the Poisson bracket on $S(\mathfrak{g})^{\mathfrak{g}}$ inspire the di...
For any finite dimensional Lie algebra $\mathfrak{g}$, we know that the universal enveloping algebra $U(\mathfrak{g})$ is a deformation of the symmetric algebra $S(\mathfrak{g})$. In fact let's define …
- 9,009
3
votes
1
answer
217
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What is the definition of "the $L_\infty$ part of a $G_\infty$ morphism"?
We know that in Tamarkin's proof of Kontsevich's formality theorem, he defined the $G_\infty$ structure on the Hochschild cochain complex $C^\cdot(A,A)$ and constructed a $G_\infty$ morphism from $HH^ …
- 9,009