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Mar
16
answered Significance of magnetic translation operator defined in fractional QHE's description
Mar
13
awarded  Nice Answer
Mar
13
comment Which symmetric pure qudit states can be reached within local operations?
@Piotr Migdal Thank you very much
Mar
13
awarded  Nice Answer
Mar
9
comment Lie algebra of axial charges
@gian_25 The matrix representation is just the 4-dimensional fundamental representation of $SO(4) = SU(2) \times SU(2)$, denoting the indices of the 4-space corresponding to $(\sigma, \pi_1, \pi_2, \pi_3)$ by $0,1,2,3$. Then$ (T^{V}_i)_{jk} = i \epsilon_{ijk}, (T^{(A)}_i)_{jk} = i (\delta_{ji}\delta_{k0}+ \delta_{ki}\delta_{i0})$. Please observe that the commutator of two axial generators is a vector generator.
Mar
9
answered Lie algebra of axial charges
Mar
6
comment How to prove the covariant derivative cannot be written as an eigendecomposition of the partial derivative?
@MBN there are partial results, for example Ellis meghnad.iucaa.ernet.in/~tarun/pprnt/topology/… mentions a result by Clarke that every 3+1 noncompact space-time can be isometrically embedded into a flat $\mathbb{R}^{87,3}$.
Mar
6
comment How to prove the covariant derivative cannot be written as an eigendecomposition of the partial derivative?
@linuxfreebird. In the case when the transformation is invertible, then your analysis is correct, but this special case is not really interesting in general relativity. I updated my answer with a detailed explanation.
Mar
6
revised How to prove the covariant derivative cannot be written as an eigendecomposition of the partial derivative?
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Mar
6
comment Quantization of electrostatic $\vec E$ field?
@webb corrected and cited. But this does not change the argument: a nonvanishing commutation relation between any component of the electric and magnetic fields imply nonzero uncertainty.
Mar
6
revised Quantization of electrostatic $\vec E$ field?
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Mar
5
revised Quantization of electrostatic $\vec E$ field?
added 34 characters in body
Mar
5
answered Quantization of electrostatic $\vec E$ field?
Mar
5
answered How to prove the covariant derivative cannot be written as an eigendecomposition of the partial derivative?
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