# Questions tagged [classical-field-theory]

For questions where the dynamical variables are classical fields, that is, functions of several variables (typically, one time coordinate and several space coordinates). If the question comprises both classical and quantum fields, use the tag [field-theory] instead.

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49 views

### Is spin associated with rotations or boosts?

EDIT: It seems that I made an error and it was $S^{ij}$ that was used after all. I will not delete the question though because even though it is erroneous, the answer given below is rather insightful. ...
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### How to Derive the Poisson Brackets for Continuous Systems

Part of my research involves studying the classical mechanics of Electromagnetic fields. I have followed the procedure for determining the Lagrangian and Hamiltonian formulations for continuous ...
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### Understanding the Functional Poisson Bracket

In classical field theory (for a single field $\psi$) the dynamical variables are defined to be functions of the fields $\psi$, $\pi$, $\partial_{x_{i}}\psi$ and maybe $\mathbf{r}$, where $\pi$ is the ...
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### Why does the subclassification of fields under parity require the quantum theory?

The fields of relativistic field theory (scalars, vectors, tensors, and spinors) are all defined via their transformation properties under the restricted Lorentz group (which excludes discrete ...
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### Lagrange formalism in field theory

I recently had a discussion with a friend of mine who is like me studying physics. And we might got used to a misconception about the Lagrange-Formalism in field theory. In common field theory books ...
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### When is Schwartz's method for “integrating out” a field valid?

In Schwartz's QFT book, heavy fields are often "integrated out" by simply solving their equations of motion formally (i.e. allowing things like $\Box^{-1}$) and plugging them back into the Lagrangian. ...
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### Why a symmetry, in Lagrangian field theory, should allow a boundary term?

Following the discussion in this paper (discussion around Eq. (3) in Page 4) and these lecture notes (discussion in Section 1.2.1 in page 10) given a field theory in some spacetime $(M,g)$ described ...
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### What causes the evasion of the Goldstone theorem here?

For simplicity, I'll consider perhaps the simplest possible example of a gauge theory. Consider a spontaneously broken ${\rm U(1)}$ gauge theory of a charged scalar field coupled to the ...
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### Pertubational approach of a scalar field EOM

I am trying to understand a calculation in a QFT textbook. Given the equation of motion of a scalar field $h$ \begin{align} \Box h - \lambda h^2 - J = 0 \end{align} I now want to solve this equation ...
### Variational principle with $\delta I \neq 0$
In Covariant Phase Space with Boundaries D. Harlow allows boundary terms in the variation of the action. If we have some action $I[\Phi]$ on some spacetime $M$ with boundary \$\partial M = \Gamma \cup \...