Graduate What is the Spin Connection Equation for Gauging the Poincare Group?

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SUMMARY

The discussion focuses on deriving the equation of motion for the spin connection \( w_\mu^{ab} \) while gauging the Poincaré group using the Euler-Lagrange equation. The user seeks assistance in obtaining the correct terms, acknowledging the equivalence of this equation to the torsionless condition. Key references include Eqn. (25) and Appendix A from the provided link, as well as the paper "Actions for Gravity" by Peldan for additional insights.

PREREQUISITES
  • Understanding of the Poincaré group in theoretical physics
  • Familiarity with the Euler-Lagrange equation
  • Knowledge of spin connections in differential geometry
  • Basic concepts of torsion in the context of general relativity
NEXT STEPS
  • Study the derivation of the spin connection from the action principle
  • Review Eqn. (25) and Appendix A from the referenced document
  • Examine the paper "Actions for Gravity" by Peldan for further context
  • Explore the implications of torsionless conditions in gauge theories
USEFUL FOR

The discussion is beneficial for theoretical physicists, particularly those specializing in gauge theories, general relativity, and differential geometry, as well as graduate students seeking to deepen their understanding of spin connections and the Poincaré group.

shereen1
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Dear All
in the idea of gauging Poincare group i am trying to find the equation of motion of the spin connection w_mu^ab using Euler Lagrange equation. but it seems that i am not getting the same terms
can i have a help. I know that this equation is equivalent to the torsionless condition, but i want to get it in the other way starting from the action and applying euler lagrange.
thank you
 
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The appendix of the paper `Actions for Gravity ...' by Peldan may can help you.
 
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