All Questions
29
questions
6
votes
2
answers
358
views
Introduce Ghost Field to eliminate unphysical degrees of freedom in case of Photon Field
In wikipedia's article about ghost fields is stated the following which requires a bit more clarification:
An example of the need of ghost fields is the photon, which is usually described by a four ...
- 1,395
1
vote
1
answer
159
views
Calculating a Gaussian-like path integrals with Grassmann variables and real variables
I want to compute the following path integral
$$Z[w] = \frac{1}{(2\pi)^{n/2}}\int d^n x \: \prod_{i=1}^{n}d\overline{\theta}_id\theta \: \exp{\left(-\overline{\theta}_i \partial_j w_i(x)\theta_j -\...
- 298
2
votes
0
answers
56
views
Typo of P&S' QFT eq.(16.40)
First, begin with P&S's QFT eq.(16.39):
$$ \frac{1}{2}\left[\left(i \mathcal{M}^{\mu \nu} \epsilon_\mu^{-*} \epsilon_\nu^{+*}\right)\left(i \mathcal{M}^{\prime \rho \sigma} \epsilon_\rho^{+} \...
- 1,421
3
votes
2
answers
147
views
Motivation of Grassmann fields in the Faddeev-Popov method for free Gluon fields
The Faddeev-Popov approach to make the generating functional corresponding to free gluon fields well defined, introduces two independent Grassmann fields. Since these are scalar, their quanta can be ...
- 311
3
votes
2
answers
556
views
BRST Symmetry and Single Particle States
I am studying about BRST symmetry from the book of P&S (Peskin's and Schroeder's "An Introduction to QFT", Chapter 16.4). The authors construct a nilpotent charge operator and then they ...
- 3,992
2
votes
1
answer
251
views
Applying the Optical Theorem in Non-Abelian Gauge Theories
I am reading P&S (Peskin's and Schroeder's book on QFT), Chapter 16.3 entitled Ghosts and Unitarity. The authors employ the optical theorem to calculate the imaginary part of a $f\bar{f}\...
- 3,992
3
votes
1
answer
504
views
How does the BRST transformation act on ghost fields?
I understand the general idea behind constructing the BRST symmetry: take a generic gauge transformation
$$\begin{equation}
e^\omega,
\end{equation}\tag{1}$$
where $\omega$ is Lie-algebra valued, and ...
- 71
1
vote
0
answers
73
views
Is there still a Gribov ambiguity when the Faddeev-Popov determinant is treated without ghosts?
In this document (Gribov Ambiguity by Thitipat Sainapha) the setup leading to the equation $3.77$ seems to strongly depend on the treatment of the Faddeev-Popov determinants with ghosts. Indeed the ...
- 2,613
2
votes
1
answer
121
views
Do Faddeev-Popov ghost contribute to vacuum polarisation?
I can imagine how one can draw a Feynman diagram for a boson self-energy with a ghost loop. My question is, shouldnt't the amplitude of that process be 0 as the ghosts are merely a mathematical tool?
- 41
5
votes
4
answers
504
views
Gauge ghosts & unphysical states in gauge theory
I have a general question about a statement from Wikipedia about ghost states as occuring in gauge theory:
"In the terminology of quantum field theory, a ghost, ghost field, or gauge ghost is an ...
- 1,395
7
votes
1
answer
819
views
Why can't Faddeev-Popov ghosts be replaced with bosons?
Faddeev-Popov ghosts are introduced in the quantization of Yang-Mills theory to absorb the Faddeev-Popov determinant into the action,
$$\det \Delta_{\text{FP}} = \int \mathcal{D} \bar{c} \mathcal{D} c ...
- 103k
9
votes
2
answers
1k
views
Why don't high-energy experimentalists ever include Faddeev-Popov ghosts in their Feynman diagrams?
To correctly calculate scattering amplitudes in nonabelian gauge theory, one must include Feynman diagrams with internal Faddeev-Popov ghosts (fictitious fermionic scalars that only appear internally ...
- 48.4k
2
votes
3
answers
829
views
How to prove that Faddeev-Popov ghosts are unnecessary for Yang-Mills theory with axial gauge?
In the book it says that in Yang-Mills theory with axial gauge: $n_{\mu}A^{\mu}=0$ using Faddeev-Popov ghosts are needless. Does anyone know how to prove this?
user178466
1
vote
1
answer
272
views
Anti-ghost translation invariance$.$
The Faddeev-Popov gauge-fixed Yang-Mills Lagrangian is invariant under
$$
\bar c\to\bar c+\chi
$$
for any odd constant $\chi$. What is the physical interpretation of this invariance? What does this ...
5
votes
1
answer
350
views
How does Faddeev-Popov work for higher-spin fields? (or does it?)
Take for example a spin $2$ field $h_{\mu\nu}$ and some gauge-invariant Lagrangian.
Does the Faddeev-Popov trick work here? by work I mean: does it lead to a consistent and unitary theory? is the ...