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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Ghosts in QCD Lagrangian
The QCD Lagrangian is
$$
\mathcal{L}_{\text{QCD}} = -\dfrac{1}{2} \text{Tr}\, G_{\mu\nu}G^{\mu\nu} + \sum_i^{N_f} \bar{q_i} \left(i \gamma^\mu \mathcal{D}_\mu - m_i\right)\,q_i, \tag{1}
$$
where $\...
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Resources for Faddeev-Popov method. (Specifically for diffeomorphism gauge fixing.)
I am struggling to get the same result as this paper (eq. 3.10) for my ghost field when gauge-fixing diffeomorphisms in linearized gravity. I would appreciate it if someone could point me in the ...
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Mass dimension of ghost Lagrangian in BRST quantization
It seems from the BRST transformation rules that the ghost fields should be dimensionless:
For eg. in the Abelian case in 4D:
$$A_{\mu} \to A_{\mu} + d_{\mu}c.$$
Then the ghost Lagrangian density $\...
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Introduce Ghost Field to eliminate unphysical degrees of freedom in case of Photon Field
In wikipedia's article about ghost fields is stated the following which requires a bit more clarification:
An example of the need of ghost fields is the photon, which is usually described by a four ...
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Why does my microwave turn on other battery powered electronics?
Situation: I have a 8-10 yr old LG microwave in a small alcove built into the cabinetry of our kitchen counter. I have a pretty cheap Bomata battery powered coffee scale that I store on the countertop ...
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What is the physical meaning of ghost field and dilaton field in general relativity?
In this paper (24)，I found a action of gravity coupling to a free scalar field. According to the literature, the scalar field is ghost or dilaton depending on the sign of kinetic terms. But in this ...
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An explicit form for the co-BRST operator?
Take a theory with 1st class constraints $M_{\alpha}$. We gave ghosts $c^\alpha$ and their conjugates $b_\alpha$ for every constraint. The BRST operator $\Omega$ has ghost number $+1$ and has an ...
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Square of BRST operator
The BRST operator $\Omega$ can be expanded in powers of the ghost fields $c^{\alpha}$ and their conjugates $b_{\alpha}$ (which satisfy $\{c^\alpha,b_\beta\}=\delta^{\alpha}_{\beta}$):
$$
\Omega=c^{\...
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Calculating a Gaussian-like path integrals with Grassmann variables and real variables
I want to compute the following path integral
$$Z[w] = \frac{1}{(2\pi)^{n/2}}\int d^n x \: \prod_{i=1}^{n}d\overline{\theta}_id\theta \: \exp{\left(-\overline{\theta}_i \partial_j w_i(x)\theta_j -\...
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Ghost detection at the level of equations of motion
My question is about how to detect ghostly degrees of freedom at the level of equations of motion. It is not clear for me how does this work. Let me explain with an example:
Consider the following ...
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Faddeev-Popov ghost in the Standard-Model
When we quantize $SU(N)$ gauge theories using the path integral formalism, we must introduce Faddeev-Popov ghosts and will appears as scalar fermions coupled to our gauge bosons in the Lagrangian of ...
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Notation of ghost fields $b$, $\tilde{b}$, $c$, and $\tilde{c}$ in Polchinski
I am terrifically confused by the notation in Polchinski's string theory book from chapter 3 to chapter 4. The ghost action of the bosonic string in conformal gauge is (3.3.24)
$$S = \frac{1}{2 \pi} \...
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Constraint in BRST quantization of point particle
On page 130 of Joe Polchinski's String Theory volume 1 book, the Constraint or the missing equation of motion for point particle after gauge fixing is $H = 0$, and the BRST operator is the ghost $c$ ...
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Typo of P&S' QFT eq.(16.40)
First, begin with P&S's QFT eq.(16.39):
$$ \frac{1}{2}\left[\left(i \mathcal{M}^{\mu \nu} \epsilon_\mu^{-*} \epsilon_\nu^{+*}\right)\left(i \mathcal{M}^{\prime \rho \sigma} \epsilon_\rho^{+} \...
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Noether current for ``local" conformal transformation?
If the fields $b$ and $c$ have conformal weight $\lambda$ and $1-\lambda$ and action is:
$$S = \frac{1}{2\pi} \int d^2z \, b \bar \partial c,$$
under conformal transformations $z \rightarrow z+\...
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