All Questions
Tagged with constrained-dynamicsgauge-theory
56 questions
4votes
1answer
315views
On gauge theories and redundant degrees of freedom
Given an action or Lagrangian with the additional information that it is a gauge system, how do we know this field has how many physical or redundant degrees of freedom? Is there any systematic method ...
- 49
3votes
0answers
47views
Faddeev-Jackiw canonical quantization
In the context of quantization singular systems, the Faddeev-Jackiw symplectic formalism transforms a pre-symplectic space into a regular symplectic space (phase space) by resolving constraints ...
0votes
0answers
62views
Why can we choose the Lagrange multiplier in Electrodynamics? [duplicate]
Consider a classical theory described by a Lagrangian $\mathscr{L}$ under the constraint $C=0$. We may make use of the Lagrange multipliers method and write the following, $$\mathscr{L}\mapsto\mathscr{...
- 51
1vote
0answers
77views
Find the Hamiltonian of a relativistic particle with the temporal gauge
Recently I have been taking some classes in string theory, but I am a mathematician and generally I lack a lot of background. So in the study guide that was given to us by the seminarist there is the ...
1vote
1answer
91views
Question about Poisson brackets and classical Virasoro generators in bosonic string
I am reading "String Theory and M theory" by Becker, Becker & Schwartz. I am confused about the following. They state that: "Classically the vanishing of the energy–momentum tensor ...
- 2,664
1vote
0answers
62views
Overview of quantization of gauge theories
I've searched for this topic and I want to know whether following statements are correct: Peierls bracket, presymplectic formalism and Dirac bracket gives equivalent presymplectic form on phase space....
- 93
3votes
2answers
154views
Effect of gauge-fixing via Lagrange multipliers on Euler-Lagrange equations
Preamble Consider the Lagrangian density for electrodynamics: $$L=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}-A_\mu J^\mu\tag{1}$$ With the usual definition of $F_{\mu\nu}=\partial_\mu A_\nu - \partial_\nu A_\mu$...
- 511
1vote
1answer
135views
Hamiltonian formalism (with symplectic form) for time-dependent Lagrangian
I have been working on some results that work for time-independent Lagrangians $L\Big(q,\dot{q}\Big)$ and return a Hamiltonian function $$ H(q,\dot{q})=\dot{q}^i \frac{\partial L}{\partial \dot{q}^i}-...
- 4,838
1vote
0answers
57views
Counting degrees of freedom in theories with two-forms [duplicate]
I am reading Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics. I am thinking that I can apply the same arguments to the case of a two form, whose components are ...
- 4,253
0votes
0answers
66views
Discrepancy in Maxwell's extended Hamiltonian
In the 4D Maxwell's extended Hamiltonian action, I obtain the same expression of Fuentealba, Henneaux and Troessaert (see the picture), up to the term "$\partial^i\pi^0 A_i$", although my ...
- 379
17votes
1answer
445views
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 ...
- 131k
9votes
1answer
744views
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, ...
- 4,150
5votes
1answer
232views
Understanding a supersymmetric quantum mechanical gauge theory model
I'm studying this paper on supersymmetric ground state wavefunctions. In section 5 "quantum mechanical gauge theories", it says: "We begin with the ${\cal N} = 2$ gauge theory which ...
- 223
1vote
1answer
73views
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 ...
- 790
2votes
2answers
80views
Does the following limit exist in the BRST formalism?
Consider the BRST operator $\Omega$ (which has ghost number $+1$) and the gauge fermion operator $\rho$ which has ghost number $-1$. Given an exact state $|\Phi\rangle$ (i.e. $|\Phi\rangle=\Omega|\Psi\...
- 790
