All Questions
19
questions
2
votes
0
answers
63
views
Hilbert Space in Categorical Gauged TQFT
I am trying to understand how gauge theory interacts with the categorical formulation of TQFT. I will formulate my doubts in two different questions.
I have understood gauging a TQFT in different ...
- 53
2
votes
1
answer
90
views
Peskin and Schroeder's discussion of the BRST operator
On page 519 of Peskin and Schroeder, the authors have the following discussion on the nilpotent BRST operator $Q$ that commutes with the Hamiltonian $H$.
Many eigenstates of $H$ must be annihilated ...
- 789
0
votes
0
answers
67
views
Unitarity gauge
Weinberg in Chapter 21, section 21.1, QFT 2, says that, in unitarity gauge $\tilde{\phi}_n(x) = \gamma^{-1}_{nm}(x)\phi_m(x)$,
we do not have degrees of freedom with negative probability, like time-...
- 433
4
votes
1
answer
365
views
Intuition for Hilbert space of a quantized gauge theory
In the standard explanation, the physical Hilbert space of a quantized gauge theory (such as QCD) is given by the cohomology of the BRST charge acting on some larger, unphysical Hilbert space.
More ...
- 1,455
4
votes
1
answer
207
views
Is unphysical states still unphysical in an interaction theory?
Maggiore A modern introduction to quantum field theory Section 4
: In free quantum electromagnetic field theory... since only the two degree of freedom transverse wave, the energy, and the momentum, ...
- 3,256
5
votes
0
answers
106
views
How do you write a resolution of unity (the identity) in gauge theories?
In, say, a quantum field theory of a single scalar field $\phi$, it is common to write the identity as ${\bf 1}=\int{\cal D}\phi\, |\phi\rangle\langle \phi|$, a useful thing to do in various path ...
- 3,492
5
votes
4
answers
504
views
Gauge ghosts & unphysical states in gauge theory
I have a general question about a statement from Wikipedia about ghost states as occuring in gauge theory:
"In the terminology of quantum field theory, a ghost, ghost field, or gauge ghost is an ...
- 1,395
4
votes
1
answer
310
views
BRST symmetry, gauge invariance and longitudinal gauge bosons
While quantizing a non-Abelian gauge theory covariantly, we first demand that the BRST charge acting on the physical states of the Hilbert space must be zero. However such physical states still have ...
- 870
3
votes
1
answer
390
views
Negative norm for bosons and fermions
How comes negative norm is such a big thing for fermions that Dirac equation was chosen over KG, while the same kind of problem for photons is just ok? In fact, many books in QED do not even mention ...
- 1,184
3
votes
1
answer
129
views
Question on BRST closed vectors which are also co-closed
I'm studying the BRST quantization formalism from this reference.
I have a question though, about page 44.
The author introduces a co-BRST operator on the extended Hilbert space (which also include ...
- 701
6
votes
0
answers
260
views
Is the vacuum degenerate in the Abelian Higgs model?
Consider the theory with Lagrangian
$$ \mathcal{L} = -\frac{1}{4}F_{\mu \nu} F^{\mu \nu} + (D_\mu \phi)^* (D^\mu \phi) - U(\phi) \,, $$
where $U(\phi)$ breaks the $U(1)$ symmetry of the system. If we ...
- 6,425
2
votes
1
answer
150
views
How is the state $|a_0 a_i\rangle$ physical?
For a state $|\psi\rangle$ to be physical we require that:
$$\langle\psi|a_0^\dagger a_0|\psi\rangle = \langle\psi|a_i^\dagger a_i|\psi\rangle$$
It is always said that physical state must contain ...
- 1,323
0
votes
1
answer
687
views
Negative norm states
If we have negative norm states such that $[a,a^\dagger]=-1$ how do we treat the normalization of two particle states ?
Suppose: $|aa\rangle = N a^\dagger a^\dagger |0\rangle$, after some work we ...
- 1,323
2
votes
0
answers
201
views
Weaker Gupta-Bleuler conditon $<\psi|(\partial_\mu A^\mu)^2|\psi> = 0$
Some context
In the Gupta Bleuler quantization procedure for gauge fields we introduce the gauge fixing term:
$$S_{GB} = \int dV-\frac{1}{2}(\partial_\mu A^\mu)^2$$
to the Lagrangian.
After ...
- 1,323
3
votes
1
answer
524
views
$U(1)$ Faddeev-Popov formalism
What is the correct series expansion for the $U(1)$ Faddeev-Popov ghosts?
I know that the $U(1)$ ghosts are only a phase such that they can be neglected in most cases but it turns out that this is ...
- 1,323