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3
votes
3answers
771 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 ...
11
votes
1answer
333 views

Relation between cohomology and the BRST operator

Given a manifold $M$, we may define the $p$th de Rham cohomology group $H^p(M)$ as the quotient, $$C^p(M) \, / \, Z^p(M)$$ where $C^p$ and $Z^p$ are the groups of closed and exact $p$-forms ...
9
votes
2answers
698 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 ...
3
votes
1answer
340 views

Noether Current when the Lagrangian depends on second derivative of the fields

Let a Lagrangian density for a field theory of $N$ fields $\left\{\phi_i\right\}_{i=1}^N$ be given. Assume that the Lagrangian density depends on the fields, their spacetime derivatives, and their ...
10
votes
0answers
433 views

Noether currents for the BRST tranformation of Yang-Mills fields

The Lagrangian of the Yang-Mills fields is given by $$ \mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu} D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+ ...
8
votes
1answer
305 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 ...
2
votes
3answers
209 views

Quantizing first-class constraints for open algebras: can Hermiticity and noncommutativity coexist?

An open algebra for a collection of first-class constraints, $G_a$, $a=1,\cdots, r$, is given by the Poisson bracket $\{ G_a, G_b \} = {f_{ab}}^c[\phi] G_c$ classically, where the structure constants ...
4
votes
1answer
135 views

Negative open string norms after BRST cohomology?

The question Disappearance of moduli for condensate of open strings made me think. Suppose we have a Dp-brane completely wrapped over a $T^d$ compactification with $p\leqslant d$. Look at an open ...
2
votes
1answer
319 views

Lagrangian depends on second derivative of field

In case of the gauge-fixed Faddeev-Popov Lagrangian: $$ \mathcal{L}=-\frac{1}{4}F_{\mu\nu}\,^{a}F^{\mu\nu ...
2
votes
1answer
135 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}] ...
5
votes
1answer
352 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 = ...
3
votes
1answer
113 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 ...
9
votes
2answers
416 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 ...