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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Accounting for ghosts in calculation of massless closed string emission
I've been trying to do problem 5.8 from String Theory in a Nutshell by Kiritsis, which is think, also related to problem 8.10 in Polchinski. My question is this: how do we account for ghosts in the ...
3
votes
1answer
80 views
Absence of negative-norm states in old covariant quantization of the bosonic string
This question is about the discussion about the absence of negative-norm states in the old covariant quantization of the bosonic string as presented e.g. in Becker Becker & Schwarz (BBS). Their ...
3
votes
0answers
79 views
Free field realisation for Vertex Operators
I wanted to know if for a generic CFT (in weak coupling limit) there exists free field realisation of the vertex operators. This seems like it should exist but I want to know a generic algorithm to ...
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0answers
42 views
Why can we not observe Faddeev-Popov ghost fields? [duplicate]
I know that ghost fields de-couple from the gauge fields in abelian QED. But my question is how does decoupling prove that we cannot observe ghost fields?
5
votes
1answer
140 views
Bosonization of $\beta \gamma$ system
I am studying the bosonization of the $\beta \gamma$ ghost system, also called as the symplectic boson (See for example, section 2.3 of this paper. These have OPE,
\begin{equation}
\beta(z) \gamma(w) \...
2
votes
1answer
54 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?
3
votes
4answers
164 views
Various Definitions of 'Ghosts'
I have seen various different definitions of a ghost field in the literature. For example, one can find many examples where ghosts are simply defined as any field with a negative sign in the kinetic ...
0
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0answers
34 views
Standard model lagrangian density, ghosts-Goldstone bosons part
I have a hard time to find the correct expression for the ghosts-Goldstone bosons part of the standard model lagrangian density. From Peskin & Schroeder it comes from the term $\xi \overline{c}^a ...
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vote
0answers
50 views
Diagonalisation of a ghost Lagrangian
I have a ghost Lagrangian of the form
$\mathcal{L}= \bar{c}M_{11}c + \bar{c}M_{12}b + \bar{b}M_{21}c + \bar{b}M_{22}b$
where $c,b$ are the ghosts and $\bar{c}, \bar{b}$ the anti ghost fields, $M_{...
5
votes
1answer
94 views
What's a minisuperspace in quantum cosmology?
I read this paper on Lorentzian Quantum Cosmology. But I couldn't understand the term minisuperspace which is used to define the path integral $$\int\mathcal{D}N \mathcal{D}\pi\mathcal{D}a\mathcal{D}...
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votes
1answer
47 views
Amplitude of quark$+$antiquark $\rightarrow$ ghost$+$antighost in QCD
Since the BRST charge operator commutes with the Hamiltonian of QCD, a physical state such as $q+\bar q$ should not be allowed to evolve into an unphysical one like $\chi+\bar\chi$, where these two ...
2
votes
1answer
67 views
Nilpotency of BRST operator in gravity
I am going through the BRST quantisation in Perturbative quantum gravity and looked at the papers of Nishijima and Ojima. I am confused about the closure of the BRST operator; I.e $s^2=0$, ...
3
votes
1answer
95 views
BRST as gauge symmetry or global symmetry or the generalization (e.g. in Peskin and Schroeder 16.4)
In Peskin and Schroeder (PS) Chap 16.4, such as after eq.16.45, in p.518, PS said:
"local gauge transformation parameter $\alpha$ is proportional to the ghost field and the anti-commuting ...
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0answers
42 views
Yang-Mills massive ghosts
Is there any procedure to add a mass to Faddeev-Popov Lagrangian density of a pure Yang-Mills theory, other than just add it from nowhere?
2
votes
1answer
135 views
Physical States has ghost number 1 in String Theory
We know by no-ghost theorem (Polchinski I, section 4.4) that the physical Hilbert space have no longitudinal excitations ($X^0, X^1, b, c$). This is obvious by light-cone gauge quantization and in ...
5
votes
2answers
275 views
Questions about BRST formalism and BV formalism
This is from Pierre J. Clavier and Viet Dang Nguyen's paper Batalin-Vilkovisky formalism as a theory of integration for polyvectors.
In section 2.3, it states:
A symmetry is said to be open when it ...
0
votes
0answers
64 views
Understanding the gauge condition in light-cone gauge
When going over Cambridge String Theory Notes (page 38) I came across the following gauge conditions:
$$X^+ (t, \sigma) = x^+(t)\hspace{5mm}, \hspace{5mm} P_−(t, \sigma) = p_−(t) \tag{1} $$
which is ...
3
votes
1answer
134 views
Ghost Theory energy-momentum tensor CFT
Given the action
$$
\mathcal{S_g}=\frac{1}{2\pi}\int{d^2x\left(b\bar{\partial}c+\bar{b}{\partial}\bar{c}\right)}
$$
where $b$ and $c$ are ghosts. How can I calculate the energy-momentum tensor$$
T=...
4
votes
0answers
71 views
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. ...
2
votes
3answers
106 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 ...
2
votes
1answer
125 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
$$ \begin{align}S_{A} =& i \int d\tau \Big(\frac{1}{2}A_{1}(\partial_{\tau}^2 - r^2)A_{1} + \...
0
votes
0answers
67 views
4th polarization in the massive vector boson field propagator
We can build propagators (in this case, for massive vector fields) with at least two approaches:
(1) from canonical quantization (or exact solutions, if you like)
$$\left[[(i\partial)^2-m^2]\delta_{...
1
vote
1answer
57 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
53 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, ...
2
votes
0answers
27 views
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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vote
0answers
139 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
votes
1answer
102 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
$$T_F = -\...
2
votes
1answer
116 views
Longitudinal polarization of gluons in loop
I have a short question about the possible gluon polarization in loop diagrams. For external gluons, we only want the 2 transverse polarizations.
In Peskin-Schroeder it is explained that in Feynman-...
4
votes
1answer
93 views
Quantum field theory with only 3-point vertexes
Given an arbitrary quantum field theory, can I always write it in terms of another (different) quantum field theory containing only operators with 3 fields? (i.e. vertexes with 3 legs)
I guess that ...
4
votes
0answers
178 views
Ghosts use in the calculus of the scattering matrix
When you perform the calculus of $S$ matrix in, for instance, QCD maybe you need to add ghosts in external legs or internal loops. E.g.: $q\bar{q} \rightarrow gg$ needs 2 ghosts diagrams with ghosts ...
2
votes
1answer
123 views
Fermionic ghost path integral results in $\delta$ function?
This is related to a statement in pg 20 of hep-th/9408074 formula (2.39).
Suppose $$\mathcal{L}\sim\frac{i}{\lambda^{\prime}}\bar{\eta}^xg_{ij}U_x{}^i\psi^j+\cdots \tag{2.35}$$where $\bar{\eta}$ to ...
2
votes
1answer
147 views
Gauge fixing while preserving supersymmetry
In supersymmetric gauge theories, the vector potential is a part of a vector supermultiplet which is represented by a real superfield $V$. Expanded out in components, the Lagrangian for such a field ...
4
votes
0answers
63 views
Do longitudinal and scalar have anything to do with Faddeev-Popov ghosts?
In his this book, Hatfield calls ghosts the negative states appearing in the covariant (Gupta-Bleuler) quantization prescription of the electromagnetic field (page 89). When discussing Yang-Mills ...
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0answers
213 views
One-loop correction to triple gluon vertex in QCD
I'm trying to calculate a one loop correction to the 3 gluon vertex, which is given by a circular correction, and another that's due to the 4 gluon vertex.
However I'm unsure how the ghost fields ...
0
votes
1answer
110 views
How to integrate by parts ghost fields in electrodynamics?
When applying Faddeev-Popov method to electrodynamics in the Lorenz gauge we obtain the ghost action
$$S=\int d^4xd^4y\bar\eta(x)\left(\partial^2\delta(x-y)\right)\eta(y),\tag{0}$$
where $\partial^2$ ...
4
votes
0answers
83 views
Ghost in quantum many body systems
Since we know the gauge theory can be emergent from local tensor product Hilbert space of quantum many body systems, such as solid state or condensed matter, etc.
How do we understand the ghosts in ...
5
votes
1answer
382 views
Why can't Faddeev-Popov ghosts be replaced with bosons?
Faddeev-Popov ghosts are introduced in the quantization of Yang-Mills theory to absorb the Faddeev-Popov determinant into the action,
$$\det \Delta_{\text{FP}} = \int \mathcal{D} \bar{c} \mathcal{D} c ...
2
votes
1answer
136 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 ...
1
vote
1answer
110 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 ...
9
votes
2answers
734 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 ...
2
votes
3answers
397 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?
0
votes
1answer
342 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
214 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
42.3k20 gold badges92 silver badges186 bronze badges
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votes
1answer
324 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
257 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 ...
asked May 24 '17 at 20:27
AccidentalFourierTransform
42.3k20 gold badges92 silver badges186 bronze badges
2
votes
0answers
367 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
votes
1answer
352 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 ...
3
votes
2answers
304 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 ...
7
votes
2answers
877 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}(\...
0
votes
1answer
89 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 ...
