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Feb
24
awarded  Yearling
Feb
18
comment Physical intuition for deformation quantization of Poisson manifolds
@user40276 - 1)I have added a few examples of explicitly known star products. 2) Consider for example vector fields which can be realized as differential operators on each chart, but not every set of differential operators defined on each chart is a vector field. Only the cases in which these differential operators satisfy the correct transformation properties on the overlaps make them vector fields, i.e., when they are global sections of $TM$.
Feb
18
comment Physical intuition for deformation quantization of Poisson manifolds
@Alex Nelson - Corrected. Thank you.
Feb
18
revised Physical intuition for deformation quantization of Poisson manifolds
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Feb
17
answered Physical intuition for deformation quantization of Poisson manifolds
Feb
13
answered Why do we assume local conformal transformations are symmetries in 2D CFT
Jan
18
answered What is the Weyl algebra of a confined bosonic particle?
Jan
9
comment Topological ground state degeneracy of SU(N), SO(N), Sp(N) Chern-Simons theory
@Idear For the case of $SO(N)$ You can use equation (1b) together with the coefficients given in sections 3.B and 3.D of Gannon's article arxiv.org/abs/hep-th/0106123 to compute the integrable highest weights. I'll correct and update my answer soon. I used the symbol # for the cardinality of the set. Yes, the rank is the dimension of the Cartan matrix, it is also the dimension of the maximal torus $T$.
Jan
8
revised Topological ground state degeneracy of SU(N), SO(N), Sp(N) Chern-Simons theory
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Jan
8
answered Topological ground state degeneracy of SU(N), SO(N), Sp(N) Chern-Simons theory
Jan
7
comment Vector potential $A$ on a 2-sphere $S^2$ of radius $R$ with some points removed
@Hamurabi I have corrected the answer
Jan
7
revised Vector potential $A$ on a 2-sphere $S^2$ of radius $R$ with some points removed
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Jan
6
comment Vector potential $A$ on a 2-sphere $S^2$ of radius $R$ with some points removed
@Hamurabi Sorry that it is taking more time than I thought. I'll try to finish as soon as possible.
Jan
4
answered Large-N factorization of single-trace operators
Dec
30
comment Braiding statistics of anyons from a Non-Abelian Chern-Simon theory
@Hamurabi There exist generalizations of the Knizhnik-Zamolodchikov, for example arXiv:arXiv:hep-th/9510143, hep-th/9410091, for elliptic curves and Riemann surfaces.
Dec
30
answered Fundamental group of Calabi-Yau 3-fold in string theory
Dec
26
revised Supersymmetric generalisation of the bosonic $\sigma$ model in QM
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Dec
25
answered Supersymmetric generalisation of the bosonic $\sigma$ model in QM
Dec
19
comment Braiding statistics of anyons from a Non-Abelian Chern-Simon theory
@Ideat cont. Witten's approach is more "thermodynamical" and he prefers to see the traces of the non-Abelian statistics in the partition function. To be more precise,(and this fact was also written in not so much words in Witten's paper): A non-Abelian Wilson loop can be thought of as a particle moving on a group or a flag manifold stuck to the boundary in the limit where its mass vanishes. Then its dynamics restricts upon quantization to the lowest Landau level producing the correct Wilson loop insertion.
Dec
19
comment Braiding statistics of anyons from a Non-Abelian Chern-Simon theory
@Idear These two approaches are very similar (but not exactly equivalent). Actually, Witten in his Jones polynomial paper (on page 365) refers to this similarity and asserts that the Wilson loop can be "thought of" as the trajectory of a particle in 2+1 dimensions. Witten refers to a famous paper by Polyakov adopting the strategy that Lee and Oh used later. This is only one of the numerous issues that Witten only talked about in his Jones polynomial paper (even without giving a single formula), which proved to be very fruitful for subsequent research.