BRST Symmetry and unphysical polarizations

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In summary, the BRST transformation for the gauge vector, \delta A_\mu^a = \varepsilon \partial_\mu c^a, implies that only forward polarized states can create ghosts through the application of Q, defined as \delta \phi = \varepsilon Q \phi. This becomes obvious when looking at the transformation in momentum space, but may not be clear in the original treatment. Additionally, the discussion of the covariant derivative in Peskin and Schroeder's treatment assumes the limit where g is equal to zero.
  • #1
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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  • #2
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?
 
  • #3
Yes it is. But Peskin is considering the limit case where g is equal to zero
 

FAQ: BRST Symmetry and unphysical polarizations

What is BRST symmetry in physics?

BRST symmetry is a symmetry that is used in quantum field theory to handle systems with gauge invariance. It is named after the physicists Becchi, Rouet, Stora, and Tyutin who first introduced it in the 1970s. BRST symmetry allows for the quantization of gauge theories, which are important in understanding the fundamental forces of nature.

How does BRST symmetry relate to unphysical polarizations?

Unphysical polarizations are states in a quantum field theory that do not correspond to any physical particles. BRST symmetry is used to eliminate these unphysical polarizations, making the theory more consistent and physically meaningful.

What is the purpose of using BRST symmetry?

The main purpose of using BRST symmetry is to quantize gauge theories, which are important in understanding the fundamental forces of nature. BRST symmetry also helps to eliminate unphysical polarizations and ensure the consistency of the theory.

How is BRST symmetry applied in practice?

In practice, BRST symmetry is applied by introducing a new symmetry transformation, called the BRST transformation, into the Lagrangian of the theory. This transformation is then used to construct a BRST charge, which is a conserved operator that generates the BRST symmetry. The BRST charge is used to eliminate unphysical states and ensure the consistency of the theory.

Are there any limitations to using BRST symmetry?

While BRST symmetry is a powerful tool in quantizing gauge theories, it does have its limitations. In some cases, the BRST charge may not be well-defined, making it difficult to apply the symmetry transformation. Additionally, the implementation of BRST symmetry can be mathematically complex and may require advanced techniques for certain systems.

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