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When dealing with the Dirac equation in curved spacetime one has to replace the partial derivative with the following covariant derivative:

${\partial_{\mu}}-\frac{i}{4}\omega_{\mu}^{\alpha\beta}\sigma_{\alpha\beta}$

where $\omega_{\mu}^{\alpha\beta}$ is the spin connection. What type of physical field this spin connection corresponds to? In the case of the electroweak theory the gauge fields in the covariant derivative correspond to the weak gauge bosons but what actual physical field does the spin connection correspond to?

Qmechanic
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physics_2015
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  • Simple and straightforward interpretation: $\sigma_{\alpha\beta}$ is the generator of Lorentz group $SO(1,3)$, and spin connection $\omega_{\mu}^{\alpha\beta}$ is the corresponding gauge field. What else do you want to know? – MadMax May 17 '23 at 17:14
  • My question was: what is the physical manifestation of this field? In other words, how is it observed and measured? – physics_2015 May 22 '23 at 01:40
  • Then you are asking a different question. Please raise a new question for that. – MadMax May 23 '23 at 13:55

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