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1answer
103 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
32 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 ...
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2answers
402 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
55 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
45 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
32 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} ...
2
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1answer
147 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
73 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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1answer
66 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
138 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 ...
4
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1answer
136 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
75 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) ...
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1answer
113 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
84 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 ...
5
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1answer
352 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
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1answer
294 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}} = ...
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0answers
124 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
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1answer
567 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 ...
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1answer
145 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
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1answer
405 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, ...
2
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1answer
341 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 ...
3
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3answers
167 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
474 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 ...
7
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1answer
221 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
274 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 ...
8
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2answers
492 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 ...