All Questions
5
questions
1
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0
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81
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Why can't we gauge the Lorentz group? (Or can we?)
One of the (many different, somewhat independent) routes to gauge theory is to start from a global symmetry of some kind and "gauge" it, which involves promoting it to a local symmetry and ...
- 858
9
votes
1
answer
1k
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General relativity as a gauge theory of the Poincaré algebra
Let the Poincaré algebra be given without any factors of i as
$[P_\mu,P_\nu]=0$,
$[M_{\rho \sigma},P_\mu]=\eta_{\sigma\mu}P_\rho-\eta_{\rho\mu}P_\sigma$,
$[M_{\mu\nu},M_{\rho\sigma}]=\eta_{\nu\rho}...
- 1,031
10
votes
2
answers
596
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GR as a gauge theory: there's a Lorentz-valued spin connection, but what about a translation-valued connection?
Given an internal symmetry group, we gauge it by promoting the exterior derivative to its covariant version:
$$
D = d+A,
$$
where $A=A^a T_a$ is a Lie algebra valued one-form known as the connection ...
- 281
23
votes
3
answers
3k
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Which global symmetry of Minkowski space (if any) gets gauged to the diffeomorphism invariance of general relativity?
Minkowski space has both translational and Lorentz symmetry, which together give Poincare symmetry. (It also has some discrete symmetries like parity and time-reversal that I won't be concerned with.) ...
- 48.3k
8
votes
1
answer
464
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What gauge field can be constructed from Lorentz symmetry?
You can take a global symmetry and promote it to a local gauge symmetry by introducing an appropriate gauge field and upgrading the partial derivative to a covariant derivative. The photon field ...
- 325