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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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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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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21 views

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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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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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 ...
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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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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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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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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 $\partial^2$ ...
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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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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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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 ...
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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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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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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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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 ...
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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 ...
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185 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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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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 ...
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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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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 $$ c(z) = \sum_m \frac{c_m}{z^{m-1}} $$ (...
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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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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 ...
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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}{}...
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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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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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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): $$ (\...