BRST Symmetry and unphysical polarizations

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SUMMARY

The discussion centers on the BRST symmetry as outlined in Peskin and Schroeder's text, specifically the transformation for the gauge vector, \(\delta A_\mu^a = \varepsilon \partial_\mu c^a\). It is established that this transformation leads to the conclusion that only forward polarized states can create ghosts through the application of the BRST charge \(Q\), defined by \(\delta \phi = \varepsilon Q \phi\). The confusion arises regarding the treatment of the covariant derivative \(D^{ab}\) in the context of Peskin and Schroeder's analysis, particularly in the limit where the coupling constant \(g\) approaches zero.

PREREQUISITES
  • Understanding of BRST symmetry in quantum field theory
  • Familiarity with gauge theories and vector fields
  • Knowledge of Peskin and Schroeder's "An Introduction to Quantum Field Theory"
  • Basic concepts of momentum space analysis in quantum mechanics
NEXT STEPS
  • Study the implications of BRST transformations in gauge theories
  • Explore the role of ghost states in quantum field theory
  • Review the concept of covariant derivatives in the context of gauge groups
  • Investigate the limit of coupling constants in quantum field theories
USEFUL FOR

This discussion is beneficial for theoretical physicists, graduate students studying quantum field theory, and researchers focusing on gauge symmetries and BRST formalism.

lornstone
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Hi,

I am reading the BRST Symmetry section of Peskin and Schroeder but I can't find anywhere
why the BRST transformation for the gauge vector,
[tex]\delta A_\mu^a = \varepsilon \partial_\mu c^a[/tex]
implies that only forward polarized states can create ghosts by applying Q, Q being define by
[tex]\delta \phi = \varepsilon Q \phi[/tex]
I saw in a paper that it's obvious when we go to momentum space, but unfortunately it's not for me...

Thank you!
 
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I'm afraid I can't help, but one point about your post confuses me- why have you taken the [itex]D^{ab}[/itex] from Peskin and Schroeder's treatment to be diagonal? Isn't it the covariant derivative in the adjoint of the gauge group?
 
Yes it is. But Peskin is considering the limit case where g is equal to zero
 

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