What is the graviton propagator in the first order formalism?

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SUMMARY

The graviton propagator in the first order formalism can be derived using the harmonic gauge condition and weak field expansion around the flat Minkowski metric, assuming a zero cosmological constant. In this framework, gravitation theory utilizes the vierbein field (e) and spin connection (w) instead of the metric. The discussion seeks to identify the propagators for both the vierbein and spin connection under weak field conditions, specifically when e is constant and w equals zero. References on the graviton propagator in this formalism are also requested.

PREREQUISITES
  • Understanding of harmonic gauge condition
  • Familiarity with weak field expansion in general relativity
  • Knowledge of vierbein and spin connection in the first order formalism
  • Basic concepts of propagators in quantum field theory
NEXT STEPS
  • Research the derivation of the graviton propagator in the first order formalism
  • Study the implications of the harmonic gauge condition in quantum gravity
  • Explore the role of vierbein and spin connection in general relativity
  • Investigate existing literature on graviton propagators in various gauge conditions
USEFUL FOR

The discussion is beneficial for theoretical physicists, researchers in quantum gravity, and students studying advanced general relativity concepts.

Max
With the help of harmonic gauge condition, graviton propagator can be
obtained by weak field expansion around the flat Minkowski metric
(assuming cosmological constant is zero).

Gravitation theory can also be written in the first order (Palatini)
formalism. In stead of the metric, the basic fields are vierbein e and
spin connection w. For weak field expansion around the flat space-time
(e = e0 = constant, w = 0), what are the propagators for vierbein and
spin connection respectively? Are there any references on the graviton
propagator in the first order formalism? Thanks!

Max
 
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