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Questions tagged [ghosts]

Ghosts are unphysical states that arise when quantizing gauge theories. Do not use this tag for 'ghosts' in the paranormal sense.

Ghosts are unphysical states that arise when quantizing gauge theories. Do not use this tag for 'ghosts' in the paranormal sense.

151 questions
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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, etc... But now I am puzzled by the fact that…
Just_a_wannabe
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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 illuminating discussion about why the change was…
Scott Carnahan
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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 just some auxiliary variables introduced into the…
Student
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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 does this engineering work?
user1845
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Clarifications needed on Gauge Fixing and Ghosts

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 $\Pi_0=0$ which is incompatible with the canonical…
jak
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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 invariance is thus obvious: by breaking the gauge…
lewton
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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 either anti-commuting or bosonic variables and the…
AngusTheMan
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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 $A_\mu\,^a$, because physically only the orbits…
PPR
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$bc$ CFT Energy-momentum tensor from Noether's theorem

Following Polchinski's book (String Theory 1), we have the $bc$ action: $$S = \frac{1}{2 \pi}\int~d^2z ~b\bar \partial c,\tag{2.5.4}$$ where $b$ and $c$ have holomorphic weights $\lambda$ and $1- \lambda$. From this action, it is said, that applying…
Trimok
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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 $$\langle T(c(x) \bar c(y))\rangle~=~\int\frac{d^4 p}{(2\pi)^4}\frac{i e^{-ip.(x-y)}}{p^2-\xi m^2+i\epsilon}.$$ But I am…
QuantumDot
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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}} =…
Funzies
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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 in loop diagrams, not as external legs). I've…
tparker
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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 problems in the topology of low-dimensional…
user113166
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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 in the denominator of the corresponding…
Jia Yiyang
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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 of a path integral is that you sum over all paths…
Funzies
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