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When dealing with quantum field theory in curved spacetime, a spin connection field is introduced as a result of the Lorentz symmetry. I'm wondering what would be intuitively considered as "charge" in this case? For other gauge symmetries one has a corresponding charge (like color for $SU(3)$ in QCD,...). So, is it conceivable to also think about some "charge" in the case of Lorentz gauge symmetry?

Qmechanic
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physics_2015
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1 Answers1

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  1. The spin connection is not really an object unique to quantum field theory, it's perfectly possible to phrase classical GR in terms of it. It - together with the vielbein - is merely a different representation of the information we usually encode in the Christoffel symbols. See this answer of mine for the classical geometric meaning of the spin connection.

  2. The equivalent to "charge", for both the Christoffel symbols or the spin connection, is simply whether something is a scalar, vector, tensor, etc. If you insist on using the language of colors and charges, a scalar field is "uncharged" under the spin connection, the vector transforms in the fundamental representation ("has color" in the color terminology), etc.

ACuriousMind
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