# 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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### Can convergent perturbation series be incorrect for an action linear in the perturbation?

Non-perturbative effects are common in mathematics. For example, consider the function $$f(g) = e^{-1/g}+ g + \frac{1}{10} g^2$$ and suppose this function is the answer to some math problem. ...
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### Consistency of substitution of a canonical variable from EoM back into (momentum-less) action

I was reading this answer, where the issue of substituting equations of motion (eoms) into the action is addressed. I am fine with the basic idea that the action principle is destroyed when the eoms ...
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### For free fields, is there a one-to-one correspondence between probability distribution of classical field configurations, and states?

If I'm given the field operator of free fields (for example $\phi(x)$) as a function of space time, and a state (for example $\langle 0 |$, I can calculate the expectation value for every point in ...
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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: $$\mathcal{H} = \sqrt{{\bf p}^2c^2+m^2c^4}.$$ I read somewhere that says, it is possible to go further and say that the EoM are ...
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### Can someone explain the steps? [duplicate]

Can anybody expand the equation .What is ω and is i power of ω in equation 2.2. And how $f_λ(r_1,r_2,...,r_n,t)=0$;λ=1,2,...,Λ gives the last equation and what $∇_k$ means?
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### What are Connections in physics?

This question arises from a personal misunderstanding about a conversation with a friend of mine. He asked me a question about the "truly nature" of spinors, i.e., he asked a question to me about what ...
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### Simplest model in field theory which leads to a pseudo-Goldstone boson

What can be a simple (if not simplest) continuum field theory model that gives rise to a pseudo Goldstone boson (doesn't matter if it is a toy model)? For example, I would be very happy if one can ...
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### Carroll: Energy-momentum tensor for a scalar field theory

In Carroll's Introduction to General Relativity: Spacetime and Geometry, there is a section titled Classical Field Theory in chapter 1. There, he mentions that: "The action leads via a direct ...
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### Problems in deriving the Belinfante-Rosenfeld Energy momemtum tensor through variation

I am currently following Michael Stone's lecture notes (http://people.physics.illinois.edu/stone/torsion_review.pdf) on deriving the Belinfante-Rosenfeld Energy Momentum tensor in a variational ...
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### Landau Vol. 2: On four-vectors

In Chapter 1, section 6 of The Classical Theory of Fields by Landau and Liftshitz, I didn't understand the following: "Under purely spatial rotations (i.e. transformations not affecting the time ...
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### Does a traceless energy-momentum tensor really imply a massless field?

I read a paper where there was written that "a Traceless Energy-momentum Tensor implies a massless field", so I did a bit of calculations but I seems not really true, is it true? So now I'm ...
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### $T^{00} ≠$ Hamiltonian Density?

Check page 48-49 of http://walterpfeifer.ch/qft/QFT5.pdf?. It is apparent that the Hamiltonian density of the Maxwell Field is not positive definite when expressed in terms of the Four-vector ...
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### Criteria to Define a (Classical) Topological Field Lagrangian? + Conjecture

I have a question concerning topological field theories. I'd rather keep the discussion at the classical level, so as to concentrate on the feature of topological evolution, which is what interests me ...
Let $\pi: P \to M$ be a principal bundle and $\omega$ a connection on it. Given a section $\sigma: M \to P$ we define Yang-Mills fields by $$A=\sigma^*\omega$$ Now since under Lorentz transformation ...
Lagrangian density for a single-spin 0-real-bosonic field ($\phi$) is given by, $$\mathcal{L}=-\frac{1}{2}\partial_\mu \phi \partial^\mu \phi-\frac{m^2}{2}\phi^2$$ Now if we formulate the Euler ...