Questions tagged [brst]
162 questions
21
votes
1 answer
Noether currents for the BRST tranformation of Yang-Mills fields
The Lagrangian of the Yang-Mills fields is given by
$$
\mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu}
D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+
\bar{c}^a(\partial\cdot D^{ab})c^b
$$
where the metric is…
soliton
- 1,721
18
votes
1 answer
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 respectively. Now consider symmetry operators $K_i$ which…
JamalS
- 19,600
17
votes
1 answer
What is the full algebra of BRST-invariant observables for general relativity?
The Hamiltonian formulation of general relativity - either in the ADM formalism or in Ashtekar variables - is straightforwardly a gauge theory. While the BRST formalism has primarily been developed to quantize such theories, it can be applied to…
ACuriousMind
- 132,081
15
votes
2 answers
Geometric Interpretation of BRST Symmetry
BRST quantization (and BRST symmetry in general), at least in this point in my understanding of them, seem rather arbitrary and slightly miraculous. However, the cohomological nature of the BRST charge $Q$ and the fact that a BRST transformation…
Bob Knighton
- 8,762
13
votes
1 answer
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
- 461
13
votes
1 answer
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
- 3,259
13
votes
2 answers
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
- 4,611
12
votes
2 answers
For the $U(1)$ problem, is the Kugo and Ojima Goldstone quartet wrong?
On page 96 in "Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem", Prog. Theor. Phys. Suppl. 66 (1979) 1, KO state the following:
Finally we should comment on the current belief that the $U(1)$ problem
…
user31927
- 161
12
votes
2 answers
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
12
votes
1 answer
BRST cohomology and Gupta-Bleuler$.$
Let $Q$ be the BRST operator. Define physical state as those in $\mathrm{ker}\,Q$ (modulo its image):
$$
Q|\psi_\mathrm{physical}\rangle\equiv 0\tag1
$$
It is often claimed1 that this condition becomes the Gupta-Bleuler condition if the gauge group…
AccidentalFourierTransform
- 56,647
12
votes
2 answers
Virasoro constraints in quantization of the Polyakov action
The generators of the Virasoro algebra (actually two copies thereof) appear as constraints in the classical theory of the Polyakov action (after gauge fixing). However, when quantizing only "half" of the constraints are imposed.
I understand it's…
Squark
11
votes
2 answers
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
- 2,581
- 1
- 19
- 33
10
votes
1 answer
Does the LSZ reduction method prove gauge-independence in massless gauge theories?
I've been working my way through L. Baulieu's excellent paper [Perturbative gauge theories,
Physics Reports, Volume 129, Issue 1, December 1985, Pages 1-74]. Towards the end, he goes on to prove that renormalized Yang-Mills theories that are BRST…
user45213
- 101
9
votes
1 answer
Constraints Generating Gauge Transformations and BRST
Given a gauge-invariant point particle action with first class primary constraints $\phi_a$ of the form ([1], eq. (2.36))
$$S = \int d \tau[p_I \dot{q}^I - u^a \phi_a]\tag{1}$$
we know immediately, since first class 'primary' constraints always…
bolbteppa
- 4,168
9
votes
1 answer
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
- 91