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May
22
comment The derivation of the Belinfante-Rosenfeld tensor
@ramanujan_dirac: The energy momentum tensor constitutes of the source term in Einstein equations: $R_{\mu\nu}-g_{\mu\nu}R = \frac{8\pi G}{c^4}T_{\mu\nu}$, and both the Ricci curvature and the metric tensor are symmetric.
May
4
answered The properity of $\mathbb{R}^4$ that has infinitely many differential structures is related to Yang-Mills field?
May
1
comment The curvature of the space of commuting hermitian matrices
@vesofilev: Sorry for not understanding you. The following reference arxiv.org/abs/0801.2913 contains a parameterization of the matrix $U$ for the flag manifold $\frac{SU(3)}{U(1)\times U(1)}$ on page 9, the third paragraph. (The authors call it the dressing matrix).
Apr
30
comment The curvature of the space of commuting hermitian matrices
@vesofilev: The $SU(2)$ case is a special case. Take for example the space of one commuting matrix in $SU(3)$, the spaces obtained from the adjoint action on $diag(0,0,1)$ and $diag(0,1,1)$ are disconnected.
Apr
30
comment The curvature of the space of commuting hermitian matrices
The space of $p$ commuting $n\times n$ matrices is not connected, since a unitary transformation does not change the rank of a matrix. Each connected component corresponds to a specific choice of the ranks of the commuting matrices. The connected components are generalized flag manifolds. Since they are homogeneous spaces, they are of constant curvature and there are many ways to calculate their curvatures.The following lecture notes may be of help to you uregina.ca/~mareal/flag-coh.pdf
Apr
29
revised Anyons only in 2+1 spacetime dimensions - better explanation
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Apr
29
answered Anyons only in 2+1 spacetime dimensions - better explanation
Apr
7
revised Allowed interactions in bosonic string theory
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Apr
7
answered Allowed interactions in bosonic string theory
Mar
31
answered The Lagrangian as a metric
Mar
25
comment Soliton Moduli Spaces and Homotopy Theory
@jamalS cont. There are more applications besides anomalies such as spinc quantization, charge quantization and fractionalization, Brane charges, supersymmetric quantum mechanics, Berezin-Toeplitz quantization and may be more. I don’t know of a single review comprising all these applications.
Mar
25
comment Soliton Moduli Spaces and Homotopy Theory
@jamalS There are analogous computations for the monopole moduli space dimension in the following review arxiv.org/abs/hep-th/0609055v2 by Weinberg and Yi, and for nonAbelian vortices in arxiv.org/abs/hep-th/0306150v1 by Hannay and Tong. There is a more mathematical review of the instanton and Seiberg-Witten moduli spaces dimension computation by David Bleecker milne.ruc.dk/~Booss/A-S-Index-Book/BlckBss_2012_04_25.pdf.
Mar
24
revised Soliton Moduli Spaces and Homotopy Theory
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Mar
24
revised Soliton Moduli Spaces and Homotopy Theory
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Mar
24
answered Soliton Moduli Spaces and Homotopy Theory
Mar
24
answered Galilean, SE(3), Poincare groups - Central Extension
Mar
20
comment Lie group of Schrodinger Wave equation
@user35952 I'll try to answer your new question soon, I'll try to clarify the previous "Poincare group vs Galilean group" answer
Mar
19
revised Lie group of Schrodinger Wave equation
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Mar
19
revised Lie group of Schrodinger Wave equation
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Mar
19
answered Lie group of Schrodinger Wave equation