# Tagged Questions

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### Electromagnetism theory and complex scalar field

I've got the following problem for classical field theory lecture: Find equations of motion (equations of field?), canonical and symmetrical tensor of energy-momentum in electromagnetic field ...
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### Lorentz invariance & Noether theorem of classical ED

I want to check invariance of the action under Lorentz boosts for classical electrodynamics. The action is $$S = \int \mbox{d}^4x F_{\alpha \beta} F^{\alpha \beta}$$ I assumed that the fields ...
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### Why don't people use Hamilton's equations for a relativistic free charged particle?

A charged relativistic free particle has the Hamiltonian in general: $$\mathcal{H} = \sqrt{p^2c^2+m^2c^4}.$$ I read somewhere that says, it is possible to go further and say that the EoM are ...
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### effect of a simultaneous local and a global $U(1)$ symmetry breaking

EDIT : I am trying to figure out the effect of symmetry breaking in a $U(1)_Y\times U(1)_Z$ invariant lagrangian where $U(1)_Y$ is local symmetry of the Lagrangian and $U(1)_Z$ is a global symmetry of ...
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### What are the equations of motion for the scalar field in the tetrad formalism?

The action of a massless scalar field in curved spacetime is given by: $$S(\phi)=\int d^{4}x \sqrt{-g}\left(g^{\mu\nu}\phi_{,\mu}\phi_{,\nu}\right)$$ Now the action can ...
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### Linear Classical Field Theories: a Mathematical Classification

Central to a mathematical understanding of the Bogolyubov transformation is the study and classification of linear lattice field theories. What follows might be familiar to many people, but I just ...
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In David Tong's lectures, he gives two Lagrangians as examples to derive the equations of motion: $$\mathcal{L} = \dfrac{1}{2}\eta^{\mu\nu}\,\partial_\mu\phi\,\partial_\nu \phi-\dfrac{1}{2}m^2\phi^2, ... 0answers 100 views ### Axion Model Field Theory Problem This is a homework problem for a field theory class dealing with an axion model. Originally, we are given that$$S[a]=\int_Md^4x \frac{1}{2}(\partial_{\mu}a(x))^2$$has a continuous global ... 2answers 432 views ### The variation of the Lagrangian density under an infinitesimal Lorentz transformation I'm trying to introduce myself to QFT following these lectures by David Tong. I've started with lecture 1 (Classical Field Theory) and I'm trying to prove that under an infinitesimal Lorentz ... 0answers 79 views ### Possible Error in deriving conformal generator My professor gave me the following derivation for the full generator of the Lorentz transformations. The starting point is to consider a subgroup of the conformal group that leaves the origin fixed ... 0answers 77 views ### Conserved charge from conserved current associated with translational invariance (c.f Di Francesco, 'Conformal Field Theory' P.45) Di Francesco calls the conserved charge arising from the conserved current associated with a translation invariant theory the 'four momentum'. While ... 0answers 63 views ### Spin-dependence of the directionality of dipole radiation I am interested in understanding how and whether the transformation properties of a (classical or quantum) field under rotations or boosts relate in a simple way to the directional dependence of the ... 1answer 69 views ### Can a classical (or quantum) field, particularly the EMF, have a frame of reference? I understand that a massless particle (such as a photon) cannot have a frame of reference. But the electromagnetic field does have mass; does it have a frame of reference? If so, I have a second ... 0answers 110 views ### Similarities between laminar-turbulence transition and others like BCS-BEC crossover, quark-hadron transition etc From my limited readings on fluid dynamics, my understanding is that as the system changes from near-laminar flows to full turbulence, the dimensionless Reynolds number changes from  R << 1 to ... 4answers 1k views ### Which exact solutions of the classical Yang-Mills equations are known? I'm interested in the pure gauge (no matter fields) case on Minkowski spacetime with simple gauge groups. It would be nice if someone can find a review article discussing all such solutions EDIT: I ... 2answers 406 views ### Hamilton formalism for Dirac spinors Let's have the Dirac free lagrangian:$$ L = \bar {\Psi} (i\gamma^{\mu}\partial_{\mu} - m) \Psi . $$I can rewrite it as$$ L = i\Psi^{\dagger}\partial_{0}\Psi - H_{d}, \quad H_{d} = ...
I'm reading these notes - page 8 and 9 - and I'm a bit confused. If we consider a field $\phi$ (which can be either bosonic or fermionic) transforming as: \phi(x) \rightarrow \phi(x) ...