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50 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
69 views

Is the standard model a quantized gauge theory?

I have studied some quantum field theory and gauge theory but I am definitely not an expert. I am aware that in quantizing electrodynamics one has to fix a gauge. I have read that for general gauge ...
4
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1answer
132 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
votes
1answer
92 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 ...
2
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0answers
62 views

Correlation function for ghosts in 2D CFT

In Di Fracenso, page 117, it is explained that the correlation function for two primary fields $\phi_1,\phi_2$ of weights $h_1,h_2$ is constrained to be of the form ...
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1answer
39 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 ...
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0answers
36 views

Feynman diagrams with ghosts and symmetry breaking

Let us think of an abelian gauge theory, precisely a scalar QED with 3 complex components of the scalar field and a 4-degree auto-interaction mixing components. Let us consider a spontaneously ...
4
votes
0answers
98 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 ...
1
vote
1answer
90 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): $$ ...
4
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1answer
157 views

BRST quantization and norm

States with definite ghost number have zero norm (since ghost number is anti-hermitian and has real eigenvalues). E.G. when quantizing relativistic point particle, physical spectrum turns out to ...
2
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1answer
296 views

What is a ghost number?

I am currently studying CFT chapter of Becker,Becker,Schwarz and am trying to understand what the ghost number is in BRST Quantization. From what I gather BRST Quantization is used to add an extra ...
2
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0answers
166 views

Ghost in the quantization of relativistic particle

It is well known that in the quantization of certain relativistic theories such electromagnetism or relativistic string negative norm states could arise when quantizing covariantly. Acting with ...
0
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1answer
88 views

Special OPE in $\beta\gamma$ system

I would like to find the OPE $$\beta(z)\gamma(w)^{-1}\tag{1}$$ given $$\beta(z)\gamma(w)~\sim~\frac{1}{z-w}\tag{2}$$ from the $\beta\gamma$-system in CFT. Is it possible?
4
votes
1answer
593 views

Clarifications needed on Gauge Fixing and Ghosts [closed]

The first time some kind of gauge fixing appears is during the Gupta-Bleuler procedure, which is used to be able to quantize the photon field: The basic gauge invariant Lagrangian leads to $\Pi_0=0$ ...
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0answers
38 views

Equations of motion with replacing the Lagrangian by irrep diagrams generating functional

I have read that equations of motion of ghosts is equal to $$ \tag 1 \frac{\delta \Gamma}{\delta \bar{c}^{a}(x)} = -\partial^{\mu}_{x}\frac{\delta \Gamma}{\delta K^{\mu , a}(x)}, $$ where $\Gamma = W ...
7
votes
2answers
943 views

Faddeev-Popov Ghosts

When quantizing Yang-Mills theory, we introduce the ghosts as a way to gauge-fix the path integral and make sure that we "count" only one contribution from each gauge-orbit of the gauge field ...
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0answers
77 views

Ghosts in theories of gravity and holographic theories

I want to understand when a theory leads to ghosts in gravity. Is there any relation between ghosts and non-linear higher order theories? Ghost is a clasical or quantum field concept?
3
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0answers
79 views

Old covariant quantization of open string at level N=1

I have a question regarding an equation in Polchinski's "String Theory, Volume 1, An introduction to the bosonic string". The equation is (4.3.27) on p.135. This section is about the brst-cohomology ...
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0answers
59 views

Non-trivial components of the stress-energy tensor of the bosonic string ghost action

The stress-energy tensor derived from the ghost action of a bosonic string is: $$ T_{\alpha \beta} = \frac{i}{4 \pi} \left ( b_{\alpha \gamma} \nabla_{\beta} c^{\gamma} + b_{\beta \gamma} ...
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1answer
330 views

Ghost fields in particle physics

In my particle physics lecture, ghost fields were briefly mentioned. As far as I understand, these come up when computing cross sections by the path integral method, to compensate for equivalent ...
3
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1answer
78 views

What constrains ghost fields $c^+$ and $b_{++}$ as $z$ going to infinity

In Green's superstring theory, Chapter 3, from equation 3.3.13 to 3.3.18, the author says that the singularity behavior of the ghost field $c^+$ must be no faster than $z^2$ as $z$ goes to infinity. ...
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vote
1answer
86 views

Ghosts on Torus worldsheet

Why after the expansion, only 0-mode of bc-ghost contributes to the 4-points ghost function on a torus worldsheet? $$<c(z_1)b(z_2)\tilde{c}(\bar{z}_3)\tilde{b}(\bar{z}_4)>_{T^2} ...
3
votes
1answer
231 views

Ghost Number Conservation

I've been reading about gauge theory quantization, and understand it mostly. The only thing I don't get is why people talk about "ghost number conservation". As far as I can tell, the ghost number is ...
5
votes
1answer
365 views

Conservation of BRST current in QED

I am trying to understand the conservation of the BRST current in QED but am having some trouble. This is what I have so far, QED lagrangian density in Lorenz gauge is, $$L = ...
4
votes
1answer
208 views

A question about BRST current in bosonic string theory

I have a question about Eq. (4.3.3) in Polchinski's string theory book volume I, p. 131. It is said Replacing the $X^{\mu}$ with a general matter CFT, the BRST transformation of the matter fields ...
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1answer
100 views

A question of BRST symmetry of bosonic string theory

This question relates to this post I tried to verify Eq. (4.2.7) in Polchinski's string theory book vol I p. 127 but I miserably miss a sign $$ \delta_B (b_A F^A) = i \epsilon (S_2 + S_3) ...
2
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1answer
136 views

How do I show the existence of a conserved ghost number with BRST in bosonic string theory?

I have three questions about the BRST symmetry in Polchinski's string theory vol I p. 126-127, which happen together Given a path integral $$ \int [ d\phi_i dB_A db_A d c^{\alpha}] ...
2
votes
2answers
93 views

A question about surface term of ghost fields

(skip disclaimer) Hi, I have a question in Polchinski's string theory vol I p 90, after introducing the ghost fields $b_{ab}$ and $c^a$, it is claimed The equations of motion then provide a ...
6
votes
1answer
625 views

How to get the $i\epsilon$ prescription for a Faddeev-Popov ghost propagator?

In path integral formalism, for a physical field there will be an $i\epsilon$ term in the action, which comes from identifying the in and out vacuum, and in turn this $i\epsilon$ will naturally appear ...
6
votes
1answer
526 views

Energy-momentum tensor of Bosonic Ghost Action in String Theory

When quantizing bosonic string theory by means of the path integral, one inverts the Faddeev-Popov determinant by going to Grassmann variables, yielding: $$ S_{\mathrm{ghosts}} = ...
3
votes
2answers
864 views

Path integral quantization of bosonic string theory

I was reading through my notes on the path integral quantization of bosonic string theory when a general question about path integral quantization arised to me. The widely used intuitive explanation ...
5
votes
0answers
179 views

What is the fundamental difference between ghost and auxiliary fields?

I am somehow confused by the notion of auxiliary fields, such as for example the fields $F$ and $D$ which appear in supersymmetry, and the notion of ghost fields which appear for example in the BRST ...
6
votes
1answer
812 views

Faddeev-Popov ghost propagator in canonical quantization

Obtaining the propagator for the Faddeev-Popov (FP) ghosts from the path integral language is straightforward. It is simply $$\langle T(c(x) \bar c(y))\rangle~=~\int\frac{d^4 p}{(2\pi)^4}\frac{i ...
3
votes
1answer
205 views

Origin of Higgs ghosts

In M. Veltman's Diagrammatica, appendix E, one can find the full Standard Model lagrangian. Some sectors (e.g fermion-Higgs and weak sectors) contain so-called Higgs ghosts $\phi^+,\phi^-$ and ...
8
votes
1answer
623 views

Clarification on “central charge equals number of degrees of freedom”

It's often stated that the central charge c of a CFT counts the degrees of freedom: it adds up when stacking different fields, decreases as you integrate out UV dof from one fixed point to another, ...
4
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1answer
440 views

Hidden particles in higher derivative field theories

Given a higher derivative classical/quantum field theory with say one scalar field, particularly the Lee-Wick standard model. It has been shown that such a field theory encompasses two kinds of ...
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3answers
196 views

Is BRST ghost number conserved in quantum gravity?

Quantum gravity needs Faddeev-Popov ghosts. Feynman showed that. Take a black hole. Hawking pair production of ghost-antighost pair. One ghost falls into the hole and hits the singularity. The ghost ...
3
votes
2answers
574 views

What is the ontological status of Faddeev Popov ghosts?

We all know Faddeev-Popov ghosts are needed in manifestly Lorentz covariant nonabelian quantum gauge theories. We also all know they decouple from the rest of matter asymptotically, although they ...
8
votes
1answer
306 views

Who added $\frac{3}{2} \partial^2 c$ to the virasoro BRST current (and why)?

I've been looking at the literature on quantizing the bosonic string, and I noticed that there was a change made in the definition of the BRST current around 1992. However, I haven't found any ...
9
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2answers
421 views

Is ghost-number a physical reality/observable?

One perspective is to say that one introduced the ghost fields into the Lagrangian to be able to write the gauge transformation determinant as a path-integral. Hence I was tempted to think of them as ...
3
votes
3answers
775 views

Question on Conformal Field Theory

Since every question has to be asked in a seperate topic, I'm asking a question refering to the following topic: Beginners questions concerning Conformal Field Theory In particular I'm referring to ...
9
votes
2answers
714 views

Why do Faddeev-Popov ghosts decouple in BRST?

Why do Faddeev-Popov ghosts decouple in BRST? What is the physical reason behind it? Not just the mathematical reason. If BRST quantization is specifically engineered to make the ghosts decouple, how ...