# Questions tagged [field-theory]

For questions where the dynamical variables are fields, that is, functions of several variables (typically, one time coordinate and several space coordinates). Comprises both classical field theory and quantum field theory. Use this tag when the question applies to both classical and quantum phenomena. Otherwise, use the specific tag instead.

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### What are non-propagating fields?

I have read at different places that in 3 spacetime dimensions, there are NO propagating gravitational degrees of freedom. This seems to imply that we have only "non-propagating" degrees of ...
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### Fourier Transformation if we only have relative coordinates

Let’s say we want to do a Fourier Transformation (FT) of a function $f(t-t‘,r-r‘)$ i.e. the function to be Fourier transformed only depends on relative coordinates. This is for example the case if we ...
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### Calculations with co- and contravariant formalism in QFT

i have another question regarding calculations with the co- and contravariant formalism in QFT. It is not that i don't understand all of this, but most of the time i'm missing some "middle" ...
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### Integration by parts on generic tensors

I try to rephrase here a my question (https://math.stackexchange.com/q/4661784/), explaining more specifically the case. Given a lagrangian $L=L(\theta_{\mu\nu},\phi)$ , the conserved Noether current ...
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### What is field? A form of matter or just a function of position? [duplicate]

I am new to electromagnetism. A few days ago, I decided to learn about electromagnetism through different books and i came across 2 different definitions about fields: A “field” is any physical ...
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### Three dimensional classical continuum limit, wave equation

Many textbooks of classical mechanics or classical field theory mention that a three dimensional "string" (the continuum limit of a lattice) leads to/can be described by the 3 dimensional ...
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### Do EM equations indicate that charged bodies are the source of the EM field?

As the title indicates, I'm not sure if Maxwell's equations or Gauss' law indicate that charged bodies are the source of the EM fields. This is question comes from the reading of this paper. As Mario ...
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### Question on the indexes of the lagrangians describing gauge theories

For a gauge group $SU(3)_{C}$ we can construct its principal and associated bundles; we can introduce spinor fields via spin structures and spinor bundles and so on, arriving in a lagrangian theory ...
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### How is the $SU(2)_L$ conjugation applied?

I'm reading a paper where they introduce the lepton doublets $L$ and "their $SU(2)_L$ conjugations" $\tilde{L}$, which I'm guessing means $$\tilde{L} = i\sigma_2L^*.$$ After $\textit{vev}$,...
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### Description of a Classical Klein-Gordon Field with Momentum Distribution

So if I want to solve the free KG equation, the solution is of the form $$\phi(x) = \int_{p\in \mathbb{R}^4}\frac{1}{2\omega_\vec{p}} \left( a(\vec{p})e^{-ipx} +b(\vec{p})e^{ipx} \right),$$ where the ...
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### Is the lattice spacing $a$ a dangerously irrelevant parameter?

Near a renormalization group fixed point, we can perform a scale transformation of length $L' = b^{-1} L$. In this case the relative lattice spacing should transform as $a' = b^{-1} a$. After $n$ ...
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### Representation of the Majorana Fermion

In Schwartz's QFT, in the Weyl basis, Majorana fermions are written on the same footing as Dirac fermions, as matrix $$\psi_{Majorana}=(\psi_L \quad i\sigma_2\psi_L^*)^T$$ I don't understand the ...
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### Why the classical Euler-Lagrange equation is assumed when deriving the Noether's conserved current?

As known, in QFT, the conserved currents, such as the energy-momentum tensor, can be derived from the Noether's theorem and expressed as the product of the field operators. These conserved currents ...
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