All Questions
Tagged with gauge-theory hamiltonian-formalism
50
questions
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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
$$
H(q,\dot{q})=\dot{q}^i \frac{\partial L}{\partial \dot{q}^i}-...
- 4,827
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0
answers
49
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Discrepancy in Maxwell's extended Hamiltonian
In the 4D Maxwell's extended Hamiltonian action, I obtain the same expression of Fuentealba, Henneaux and Troessaert (see the picture), up to the term "$\partial^i\pi^0 A_i$", although my ...
- 175
15
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What is the full algebra of BRST-invariant observables for general relativity?
The Hamiltonian formulation of general relativity - either in the ADM formalism or in Ashtekar variables - is straightforwardly a gauge theory. While the BRST formalism has primarily been developed to ...
- 126k
9
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Constraints Generating Gauge Transformations and BRST
Given a gauge-invariant point particle action with first class primary constraints $\phi_a$ of the form ([1], eq. (2.36))
$$S = \int d \tau[p_I \dot{q}^I - u^a \phi_a]\tag{1}$$
we know immediately, ...
- 4,101
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Problem evaluating an anticommutator in supersymmetric quantum mechanical gauge theory
I am trying to reproduce the results of a certain paper here. In particular, I'm trying to verify their eqn 5.31.
The setup is N = 4 gauge quantum mechanics, obtained by the dimensional reduction of N ...
- 213
5
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1
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209
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Understanding a supersymmetric quantum mechanical gauge theory model
I'm studying this paper on supersymmetric ground state wavefunctions. In section 5 "quantum mechanical gauge theories", it says:
"We begin with the ${\cal N} = 2$ gauge theory which ...
- 213
0
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0
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85
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Secondary constraint imposed gauge fields
I am asking about aspects of quantizing electromagnetic field followed in Weinberg's Quantum theory of fields Volume I, in section 8.2 . I am able to understand the primary constraint that arises from ...
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0
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77
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Gauge symmetry and the volume in phase space
Recently, I am reading a paper about the soft theorem and large gauge symmetry which is non-zero in the boundary.
In section 6, the author introduces the covariant phase space method to illuminate why ...
- 347
2
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1
answer
331
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Nilpotency of the BRST operator
I'm styding chapter 16 of Peskin and Schroeder, in section 16.4 on the BRST symmetry, Peskin and Schroeder first checks (on page 518) that if $Q$ is the BRST symmetry operator, then $$Q^2\phi=0\tag{16....
- 789
4
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71
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Hamiltonian and Lagrangian for a particle on a ring [duplicate]
In the book Condensed Matter Field Theory (A. Altland & B. Simons)(page 498, 2nd edition) they suggest the following Hamiltonian and Lagrangian for a particle on a ring in the presence of a ...
- 51
2
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Hamiltonian density of Abelian-Higgs Lagrangian
Given the Lagrangian density
$$\mathcal{L}=-(\nabla^{\mu}\phi)^\dagger(\nabla_\mu \phi)-\frac{\lambda}{4}\left(\phi^{\dagger}\phi-v^2\right)^2-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}\,,\quad \nabla_\mu\phi=\...
- 175
1
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1
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144
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How to derive infinitesimal gauge transformations from constraints?
I am reading some papers about quantizing the gravitational fields, for example, here, here, and here. Since the classical actions for gravitational fields are singular, they contain some constraints. ...
- 105
4
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1
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168
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Can I write the Hamiltonian $H$ in the standard way $p\dot{q}-L$ for a general QFT?
I have read some questions (and the Wikipedia article) about the hamiltonian formulation of a QFT, but the only example that seems to be brought up is the scalar case, saying that $$\mathcal{H}_S=\Pi\...
- 5,931
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1
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324
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What is the difference between gauge transformation and canonical transformation？
Recently I have been studying theoretical mechanics, then I have this question, Is the gauge transformation the same as the canonical transformation？
4
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136
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Dirac-Bergmann Algorithm Not Terminating in (1+1)-Dimensional $U(1)$ Charged Scalar QED
I am trying to compute the full set of second class constraints that specify (1+1)-dimensional $U(1)$ scalar QED after complete gauge fixing. (Specifically, I would like to use the Coulomb $\partial_1 ...
- 73