All Questions
Tagged with lagrangian-formalism gauge-theory
310 questions
1
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130
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Generic form of the matter Lagrangian in QFT
It seems to me like any sensible matter Lagrangian must obey the following constraints:
It must be invariant with respect to local $SU(N)$ transformations, diffeomorphisms of the space-time manifold, ...
- 1
3
votes
2
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132
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In particle physics, what is the *motivation* to have invariance of a defined Lagrangian under a transformation of phase $e^{i\alpha}$ of the fields?
In particle physics, one checks the invariance of the Lagrangian under global transformations of the fields $\psi\rightarrow e^{i\alpha}\psi$ and local transformations $\psi\rightarrow e^{i\alpha(x)}\...
4
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1
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315
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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
-2
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0
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136
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Electric gravity
Consider a model of gravity where I try to create curvature using electromagnetic fields. For that I will work with the following action
$$S[g, A] = \int d^4x \sqrt{g} g^{\mu\nu}g^{\alpha\beta}F_{\mu\...
- 1,604
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51
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Solving Equations of Motion Gives New Inconsistent Equations of Motion, Abelian Higgs
I am working with a particular effective Lagrangian related to the abelian Higgs model.
$$\mathcal{L}=-\frac{1}{4}{F}_{\mu\nu}{F}^{\mu\nu}+\frac{1}{2}[\partial_\mu \rho \partial^\mu \rho+B_\mu B^\mu \...
- 49
2
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1
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244
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Why is the theta term in the classical Yang Mills a total derivative?
I am currently reading and studying Yang-Mills theory from David Tong's lecture notes. The convection he uses for the curvature is the following, as seen in equation (2.4) in his notes:
$F_{\mu \nu} =...
- 231
2
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127
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Spectrum of the compact $U(1)$ gauge theory in (2+1)D
The $U(1)$ gauge theory in (2+1)D is described by the action
\begin{equation}
S = \int dt d^2x \mathcal{L}_{U(1)}, \quad \mathcal{L}_{U(1)}=\frac{1}{2g^2}\left(\boldsymbol{e}^2-b^2\right),
\end{...
1
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1
answer
112
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Why is the vector potential-dependent interaction term often neglected when taking the nonrelativistic limit of the scalar QED Lagrangian?
The scalar QED Lagrangian describing the interaction between the electron, proton and photon has the form
$$
\begin{eqnarray}
\mathcal{L}&=&-\frac{1}{4}F_{\mu\nu}^2-\phi_e^{\star}(\square+m_e^...
- 13
1
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36
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What is the physical meaning of BFV action in BFV formalism?
BFV formalism is the Hamiltonian counterpart of the Batalin-Vilkovisky (BV) formalism. Suppose we have a BV field theory
$$
(F, \omega, Q, S)
$$
which satisfies the variational formula with boundary:
$...
- 174
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77
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Find the Hamiltonian of a relativistic particle with the temporal gauge
Recently I have been taking some classes in string theory, but I am a mathematician and generally I lack a lot of background. So in the study guide that was given to us by the seminarist there is the ...
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3
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1
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81
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"Deriving" the covariant derivative
Suppose we are working in scalar QED with Lagrangian
$$\mathscr{L} = (D_\mu \phi)(D^\mu \phi)^* - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}.$$
I now want to find the form of the covariant derivative $D_\mu$ ...
- 619
1
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1
answer
75
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What's the form of EL equation for KG field with gauge covariant derivative?
In the situation when we have KG Lagrangian with normal derivative replaced by the covariant one (I'm using metric $\operatorname{diag}\{ +,-,-,- \}$ so $D_\mu = \partial_\mu + iq A_\mu,\ D^\mu = \...
- 333
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0
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83
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Understanding why a derivative in a nonabelian gauge theory jumps over a field in Peskin and Schroeder, eq. (16.32) [closed]
I'm learning about ghosts in gauge theories in chapter 16 of Peskin and Schroeder. I'm pretty good with everything going on in chapter 16.2, except for eq. (16.32) and the discussion below.
Eq. (16.32)...
- 619
1
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62
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Light-cone gauge
I'm trying to understand the existence of the light-cone gauge for the closed bosonic string in a more mathematical precise language.
Namely, when looking for critical points of Polyakov action, we ...
- 538
0
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1
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56
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Gauge transformations of non-abelian Chern-Simons theory
In non-abelian Chern-Simons theory, the gauge field transform as $ A_i \rightarrow g^{-1}A_i g +ig^{-1}\partial_i g$, where $g$ is the element of gauge group, while the action itself transform as
$$
...
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