Questions tagged [ghosts]
Ghosts are unphysical states that arise when quantizing gauge theories. Do not use this tag for 'ghosts' in the paranormal sense.
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questions
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Picture Number Operator in String Theory
My question concerns the ghost picture charge/picture number operator in the RNS formalism of Superstring theory.
In particular I refer to page 403 of "Basic Concepts of String Theory" by R. ...
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vote
3answers
63 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 ...
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0answers
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Missing factor in Dimensionally reduced Yang Mills Ghost Field
I'm trying to calculate the ghost field in the background field gauge for the dimensionally reduced Yang Mills action in this paper. I am using the expression from Srednicki's book, chapter 78. The ...
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1answer
87 views
Finding ghost terms for super Yang-Mills theory in background field gauge
I want to find the ghost terms (2.16) for the action in this paper. The gauge field action is given by
$$ \begin{align}S_{A} =& i \int d\tau \Big(\frac{1}{2}A_{1}(\partial_{\tau}^2 - r^2)A_{1} + \...
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4th polarization in the massive vector boson field propagator
We can build propagators (in this case, for massive vector fields) with at least two approaches:
(1) from canonical quantization (or exact solutions, if you like)
$$\left[[(i\partial)^2-m^2]\delta_{...
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1answer
52 views
Ghost exorcisms of fields?
In Mack's paper "D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes", he makes the following statement ...
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0answers
50 views
Critical dimension from the symmetries of the string action
(Related: This post and this post.)
In this thesis it is said (on page 13) that just by assuming that we have some general action with the same symmetries as the Polyakov action (Poincare invariance, ...
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0answers
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Time reversal symmetry of the Faddeev-Popov determinant
I am studying the Faddeev-Popov procedure to quantize a non-Abelian gauge theory, and I got confused by the status of the time reversal symmetry. People have different definitions of the time reversal ...
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78 views
$bc$-system energy momentum tensor
I have a (maybe silly) question regarding the expression of the energy momentum tensor of the $bc$-system in equations $(2.5.11a)$ and $(2.5.11b)$ in Polchinski's String Theory, page 50. I know that ...
3
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1answer
85 views
Supercurrent of the $bc$-$\beta\gamma$ SCFT
In Polchinksi's Sec. 10.1, the $bc$-$\beta\gamma$ SCFT is introduced with action
$$S_{BC} = \frac{1}{2\pi} \int d^2z (b \bar \partial c + \beta \bar \partial \gamma)$$
and supercurrent
$$T_F = -\...
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1answer
72 views
Longitudinal polarization of gluons in loop
I have a short question about the possible gluon polarization in loop diagrams. For external gluons, we only want the 2 transverse polarizations.
In Peskin-Schroeder it is explained that in Feynman-...
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1answer
85 views
Quantum field theory with only 3-point vertexes
Given an arbitrary quantum field theory, can I always write it in terms of another (different) quantum field theory containing only operators with 3 fields? (i.e. vertexes with 3 legs)
I guess that ...
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52 views
References to understand BRST Quantization
I'm looking for good, rigorous references that discuss BRST quantization in relation to how it leads to dealing with anomalies and ghost fields. I'm looking at high level references (i.e., assume ...
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140 views
Ghosts use in the calculus of the scattering matrix
When you perform the calculus of $S$ matrix in, for instance, QCD maybe you need to add ghosts in external legs or internal loops. E.g.: $q\bar{q} \rightarrow gg$ needs 2 ghosts diagrams with ghosts ...
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1answer
77 views
Fermionic ghost path integral results in $\delta$ function?
This is related to a statement in pg 20 of hep-th/9408074 formula (2.39).
Suppose $$\mathcal{L}\sim\frac{i}{\lambda^{\prime}}\bar{\eta}^xg_{ij}U_x{}^i\psi^j+\cdots \tag{2.35}$$where $\bar{\eta}$ to ...
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1answer
98 views
Gauge fixing while preserving supersymmetry
In supersymmetric gauge theories, the vector potential is a part of a vector supermultiplet which is represented by a real superfield $V$. Expanded out in components, the Lagrangian for such a field ...
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Do longitudinal and scalar have anything to do with Faddeev-Popov ghosts?
In his this book, Hatfield calls ghosts the negative states appearing in the covariant (Gupta-Bleuler) quantization prescription of the electromagnetic field (page 89). When discussing Yang-Mills ...
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0answers
129 views
One-loop correction to triple gluon vertex in QCD
I'm trying to calculate a one loop correction to the 3 gluon vertex, which is given by a circular correction, and another that's due to the 4 gluon vertex.
However I'm unsure how the ghost fields ...
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1answer
85 views
How to integrate by parts ghost fields in electrodynamics?
When applying Faddeev-Popov method to electrodynamics in the Lorenz gauge we obtain the ghost action
$$S=\int d^4xd^4y\bar\eta(x)\left(\partial^2\delta(x-y)\right)\eta(y),\tag{0}$$
where $\partial^2$ ...
4
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0answers
74 views
Ghost in quantum many body systems
Since we know the gauge theory can be emergent from local tensor product Hilbert space of quantum many body systems, such as solid state or condensed matter, etc.
How do we understand the ghosts in ...
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0answers
103 views
Fixing coordinates, Fadeev-popov, gravity
When you fix the coordinates in every patch in General Relativity, you are fixing all the gauge, globally & locally. Does that kind of gauge fixing makes needed a Fadeev-Popov ghost action term to ...
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1answer
260 views
Why can't Faddeev-Popov ghosts be replaced with bosons?
Faddeev-Popov ghosts are introduced in the quantization of Yang-Mills theory to absorb the Faddeev-Popov determinant into the action,
$$\det \Delta_{\text{FP}} = \int \mathcal{D} \bar{c} \mathcal{D} c ...
2
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1answer
117 views
Equivalence between ghosts?
Ok. I'm trying to get the terminology right about the term ghost in physics. Is there any equivalence between these terms?
Faddeev-Popov ghosts
Paul-Villars ghosts
Landau ghost
The vanishing ...
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1answer
85 views
Stuckelberg Formalism for Spin-2 - Metric Signature and Ghost Fields
Caution: This question may be trivial to experts, since I am looking at the consequence of metric conventions on the nature of fields in the calculation. My aim is to spot an error in either my ...
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2answers
570 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 ...
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2answers
235 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?
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1answer
251 views
Calculating $S$-matrix in string theory
To calculate string $S$-matrix, we mainly use Faddeev-Popov gauge fixing method, as in chapter 6 of Polchinsky's book 《string theory》. But in section 6.2, 'tree level amplitude', I didn't find ...
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1answer
194 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 ...
asked Aug 8 '17 at 12:23
AccidentalFourierTransform
32.9k14 gold badges81 silver badges150 bronze badges
8
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1answer
235 views
How do we know that renormalization doesn't change the form of the ghost action in Yang-Mills theory?
In field theory, we typically construct a Lagrangian by only specifying its (global or gauge) symmetries, then writing down all renormalizable terms that respect those symmetries with arbitrary ...
5
votes
1answer
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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 ...
asked May 24 '17 at 20:27
AccidentalFourierTransform
32.9k14 gold badges81 silver badges150 bronze badges
2
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0answers
270 views
Ghost Fields in Abelian and Non-Abelian gauge theories
I have some questions about ghost fields in QED and in a non Abelian gauge theory:
Does the fact that ghosts and photons are decoupled depend on the choice of the gauge-fixing function? In the Lorenz ...
2
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1answer
275 views
BRST Quantization of the Bosonic String: Nilpotence of BRST transformation (Polchinski)
Currently I am studying string theory and I encountered a bunch of interrelated problems in the context of BRST quantization which I can't solve for myself although I tried hard for some days.
My ...
2
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1answer
209 views
BRST Quantization of the Point Particle: Sign of Structure Functions (Polchinski)
Currently I am studying string theory and I encountered a bunch of interrelated problems in the context of BRST quantization which I can't solve for myself although I tried hard for some days.
The ...
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2answers
706 views
Why Faddeev-Popov ghost cannot exist in external line?
I was studying the path integral quantization of non-abelian gauge field. After the path integral quantization, the action becomes
$$\mathcal{L}=-\frac{1}{4}F^a_{\mu\nu}F^{a\mu\nu}-\frac{1}{2\zeta}(\...
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1answer
79 views
Beginner question on ghost system
I have read about $bc$ ant $\beta\gamma$ system. These are the fermionic and bosonic ghost system respectively. My question is
Why these systems are called ghost system?
What is the spin for these ...
2
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2answers
90 views
Diagonalizing Faddeev-Popov Lagrangian $U(1)$
How can we diagonalize the U(1) Faddeev-Popov Lagrangian in a consistent manner.
I can't seem to find any papers on this but I can't believe that they don't exist.
Any pointers would be greatly ...
2
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1answer
240 views
$U(1)$ Faddeev-Popov formalism
What is the correct series expansion for the $U(1)$ Faddeev-Popov ghosts?
I know that the $U(1)$ ghosts are only a phase such that they can be neglected in most cases but it turns out that this is ...
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3answers
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Why do negative norm states break unitarity?
I often hear my teachers say that the negative norm states break unitarity. And I can also read this elsewhere, such as at this place
In this gauge the relation between unitarity and gauge ...
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0answers
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Can a vector boson carry cosmic acceleration?
Clifton, Ferreira, Padilla and Skordis discuss ghosts arising from dark energy:
To get cosmic acceleration we need an additional repulsive force to
act between massive objects at large distances. ...
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2answers
2k views
How do Faddeev-Popov (FP) ghosts help path integrals?
How does the inclusion of Faddeev-Popov ghosts in a path integral help to fix the problem of over counting due to gauge symmetries?
So, after exponentiating the determinant for the inclusion of ...
2
votes
1answer
466 views
Gauge anomalies ruin the unitarity - the explanation involving ghosts
An outline
As is known, the presence of gauge anomalies leads to breakdown of the unitarity of the gauge theory.
One way to understand this is to involve the BRST quantization of the gauge field ...
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1answer
175 views
String Theory, Ghost SCFTs
In the section on free SCFTs in chapter 10, in equation (10.1.19) of Polchinski's volume 2, it isn't clear to me how he writes down the fermionic stress tensor. Shouldn't that correspond to a world ...
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0answers
184 views
Anticommutator BRST charge and $c$-ghost mode
My goal is to compute the anticommutator $\{Q_B, c_m\}$ where $Q_B$ is the BRST charge in string theory and $c_m$ is the $m$th mode of the $c$ ghost field
$$
c(z) = \sum_m \frac{c_m}{z^{m-1}}
$$
(...
3
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1answer
381 views
Why do Faddeev-Popov ghost anti-commute?
I'm trying to understand why the Faddeev-Popov ghost that appear in the quantization of non-abelian gauge theories are anti-commuting fields.
I've seen a number of books (chapters), lecture notes and ...
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0answers
80 views
Determinants in path integrals in gauge theories and geometry
I know that in the formalism of path integral it is easy to show how determinants, corresponding to gauge fixing condition and FP ghosts, appear. But there is strict explanation of these determinants ...
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1answer
1k views
What is the relationship between BRST symmetry and gauge symmetry?
As far as i know the BRST symmetry is an infinitesimal (and expanded) version of gauge symmetry. Recently I read the following:
"when QFT was reformulated in fiber bundle language for application to ...
3
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1answer
434 views
BRST quantization (Green, Schwarz, Witten)
In Green, Schwarz, Witten Volume 1, section 3.2, BRST quantization is introduced in a general way. A Lie algebra $G$ is defined with elements
$$ [K_i,K_j] = f_{ij}{}^k K_k \tag{3.2.1}$$
where $f_{ij}{}...
2
votes
1answer
162 views
Topological susceptibility in QCD and corresponding pole
The topological susceptibility in QCD (here I've used path integral approach, and hence I will neglect all contact terms) is defined as
$$
\kappa (p) \equiv \lim_{y \to 0}\int d^{4}x e^{ip(x-y)}Q(x)Q(...
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0answers
222 views
Unitarity of the S-matrix and Feynman Diagrams
There are several questions on the unitarity of the S matrix, but unfortunately non of them answers directly the following question.
The S matrix is unitary and that can be proven by the fact that ...
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1answer
304 views
Modified gauge fixing condition in Faddeev-Popov approach
Which gauge fixing conditions are allowed to choose for this approach?
For example (following the steps of Peskin in 9.4) I can choose a "modified" lorenz gauge ( for a abelian theory):
$$ (\...
