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Feb
27
comment Conservation of phase space volume in Rindler space-time
@V. Moretti Thank you very much for the information
Feb
26
comment Conservation of phase space volume in Rindler space-time
@V. Moretti I am referring to the canonical quantization of the Hamiltonian (Last equation in the text) $ H = gx \sqrt{p^2+m^2}$ on $L^2(\mathbb{R}, dx)$. Operator ordering will be needed to reach a self adjoint operator. I think that no solution is available to this problem because of the geodesic incompleteness of the Rindler space.
Feb
25
comment Conservation of phase space volume in Rindler space-time
@Nathaniel cont. In the field case, you are talking about an infinite dimensional Hamiltonian system. It is not straightforward to define a volume in infinite dimensions. (It must be regularized). Although, there are some results on regularized volumes in general, I think that there is only little work, if any, on Liouville's theorem in infinite dimensions.
Feb
25
comment Conservation of phase space volume in Rindler space-time
@Nathaniel In general, the phase space of a system of several particles, even in interaction, is the Cartesian product of their individual phase spaces. The phase space is the space of initial data and one needs two initial conditions per particle. Thus, the same result should be valid.
Feb
25
answered Conservation of phase space volume in Rindler space-time
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.