All Questions
Tagged with quantization sg.symplectic-geometry
7 questions with no upvoted or accepted answers
9
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544
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From classical to quantum mechanics
Let ($X,\omega$) be a symplectic manifold (phase space of some physical system). Consider the algebra $\mathcal{C}^{\infty}(X,\mathbb{R})$ of smooth functions on $X$ and $[\omega]\in \textrm{H}^{2}_{\...
- 1,629
7
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139
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Could we extend the star product on a Poisson manifold from its ring of smooth functions to its de Rham complex?
Let $M$ be a smooth manifold with a Poisson bracket $\{-,-\}$. Kontsevich proved that there exists a deformation quantization of $M$, i.e. let $C^{\infty}(M)[[\hbar]]=C^{\infty}(M)\otimes_{\mathbb{R}}\...
- 9,019
5
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Isn't the quantomorphism group really just the "WKB-quantomorphism" group?
Introduction
In his second-most upvoted post, called "Why quantum mechanics?" (second only to his post on fibre bundles & gauge theory) in the physics SE community, Urs Schreiber, in the setting ...
- 215
5
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Deformation quantization of Poisson bracket without star-product
Kontsevich's formality theorem implies in particular that star-products on a $C^\infty$-manifold $M$,
$$f\star g = fg + \sum_{k\geq1} \hbar^k B_k(f,g),\qquad f,g\in C^\infty(M),$$ where $B_k$ are ...
- 654
2
votes
0
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540
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Polarizations in algebraic and symplectic geometry
In context of Abelian varieties there are a couple of equivalent ways to
introduce the polarization of a algebraic variety. One way is to
choose a line bundle $\mathcal{L}$ which satisfies certain ...
- 5,966
1
vote
0
answers
662
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On prequantization bundles over integral symplectic manifolds
I am trying to clarify certain subtleties regarding prequantization bundles over symplectic manifolds, for which I haven't found any clear explanation so far.
Let me fix some definitions first.
...
- 1,227
1
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0
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On different definitions of a prequantization space
Geometric quantization associates to a symplectic manifold $(M,\omega)$ a hermitian line bundle $L \to M$ with connection $\nabla$ whose curvature is $\omega$ (up to some constant).
Without talking ...
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