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Feb
26
awarded  Good Question
Feb
24
awarded  Yearling
Jan
20
awarded  Nice Answer
Jan
8
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Dec
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Nov
26
comment What are orbifolds and why are they useful and interesting for physics?
@Siva This observation is based on the solution of Schrödinger equation on a two dimensional cone where the energy eigenfunctions become more concentrated around the tip as the cone's half angle becomes smaller.
Nov
22
awarded  Good Answer
Oct
30
comment Aharonov-Bohm Effect and Flux Quantization in superconductors
They showed that the Shrödinger wave function of a single particle acquires a phase under a translation and a boost and this is alright, but, under a sequence of transformations: translation, boost, reverse translation, reverse boost, the overall phase does not vanish even though we returned to the initial frame of reference. This is a multivalued function related to the nontrivial central extension of the Galilean group.
Oct
30
comment Aharonov-Bohm Effect and Flux Quantization in superconductors
@jinawee Wigner worked on the representations of the Galilean group together with Inönü in their article "Representations of the Galilei Group". Please see the article on page 359 of Wigner's collected work: books.google.co.il/….
Oct
8
comment Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory
Sorry, the first sentence in my comments should be: The scalar and Dirac field examples were not given for the purpose of showing how to couple torsion to classical fields, they were given as examples of matter.
Oct
8
comment Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory
The answer to your second comment is that nothing was added by hand, the coupling term is obtained according to the rules of the minimal coupling. The only manipulation done is to separate the symmetric part of the affine connection and include it in the spin connection, and writing the antisymmetrical components separately giving the interaction term. In summary, the coupling of the matter fields to Einstein-Cartan theory can be viewed as a stage in the determination of its spin tensor.
Oct
8
comment Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory
This is given in equation (2.20) in Shapiro. The spin tensor is also analogous to the energy momentum tensor being a Noether current of the Lorentz symmetry as the energy momentum tensor is the Noether current of the translation symmetry. (Together they generate the Poincare symmetry).
Oct
8
comment Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory
This is exactly analogous to the energy momentum tensor: In order to obtain the energy momentum tensor, first one minimally couples the matter theory to gravity, and then varies the Lagrangian with respect to the metric. The analogy for the spin tensor: first one couples the matter theory to gravity with torsion (i.e., with a nonsymmetrical affine connection), then varies the Lagrangian with respect to the contorsion.
Oct
8
comment Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory
The scalar and Dirac field examples were given for the purpose of showing how to couple torsion to classical fields, they were given as examples of matter, please see that these examples are given in Shapiro's review in section 2.3 titled as "Interaction of torsion with matter". The interaction appears as a term of the form: Spin tensor $\times$ contorsion tensor as can be seen in the Dirac example.
Oct
2
revised Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory
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Oct
2
answered Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory
Aug
4
comment What does it mean to renormalize an effective field theory?
@ New_new_newbie It may happen that some process (like photon-photon scattering in QED) does not exist at the tree level approximation, then you can say that radiative corrections predict new physics. But apart from that, the control of the quantum corrections is mainly required to ensure that these corrections will not spoil the leading order.
Jul
31
revised Instantons in Witten's supersymmetry and Morse theory
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Jul
31
answered Instantons in Witten's supersymmetry and Morse theory
Jul
17
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