# 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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### How can I simplify the amplitude of the following Feynman diagram as to obtain equation (v)?

I am trying to find the amplitude for the following pair production $$\gamma(p_1) + \gamma (p_2) \to e^- (p_3) + e^+ (p_4)\tag{1}$$ In an old exercise I am given the possible answers but I am not ...
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### How would you define effective values? [closed]

How would you define effective values? For example, effective mass, effective potential, effective Lagrangian, etc...
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### How will we know whether the interacting $\phi^4$ theory eigenstates are bosonic states/symmetric?

For the free scalar field $\phi$, the commutation relation $[\phi(x),\pi(y)]=i\delta(\vec{x}-\vec{y})$ leads to the bosonic commutation relation $[a_p,a_q^\dagger]=\delta(\vec{p}-\vec{q})$. From there,...
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### Confusions on symmetry breaking and classical field theory

I am just reading some material about symmetry breaking and so-called effective action/potential Consider a lagrangian \begin{equation*} \mathcal{L}=\frac{1}{2}(\partial \phi)^2-\frac{1}{2}m^2\phi^2-...
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### Correlation length for ising-Kitaev chain: Coincidence or are they same?

The correlation length for the two-dimensional classical ising model goes as $$\xi_{ising}(T)\sim |T-T_c|^{-\nu};\qquad \nu=1$$ We can map the classical ising model to its quantum cousin, one-...
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### Are all vector-bosons gauge-bosons?

All QFTs that I come across have vector fields appearing as gauge-bosons. Is there any problem with vector fields that are not gauge-bosons? I am not so concerned about the theory producing results ...
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### In physics, are all functions fields?

I really confused if there is a function (mostly in physics, functions represents physical quantities) which is not a field? I feel all functions in physics are fields. Is there any functions which ...
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### First order expansion of Euler-Lagrange equations

I know that in field theory Euler Lagrange equations are $p_i-d_\mu p^\mu_i=0$. (Classical notations, $p_i=\frac{\partial L}{\partial y^i}, p_i^\mu=\frac{\partial L}{\partial y^i_\mu}$). Being a ...
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### Why fields are solutions of waves equations?

This could be extremely trivial but I am having problems figuring it out. I think I understand properly the difference between waves and fields. A field is a function valued on space or spacetime ...
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### How is the higgs field excited to give a Higgs boson?

I understand that the excitation of the Higgs field itself is the Higgs boson, and not the Higgs field itself, which does fit somewhat into the little String theory I've read (The excitations of the ...
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### Rescaling of effective hamiltonian coupling constants in the Wilsonain renormalization group

I am confused about an aspect of coupling constant rescaling in the Wilsonian renormalization group procedure. (I'm following Kardar's "Statistical Physics of Fields, Ch5). I think I understand the ...
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### How to deal with integral operators in the action, in the path integral of a field theory?

One could imagine adding to the free action of a scalar field theory some non-local operators given as integrals over the base manifold (or over the boundary) of some smooth function of the scalar ...
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### Perturbative expansion of the S-matrix in QFT

Beginner to QFT - While Taylor expanding the exponential term of the S-matrix, why is the 2nd order term (quadratic time integration term) written with two different dummy variables for time? (...
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### Is it true that in abelian Chern-Simons theory diffeomorphisms differ from ordinary gauge transformations trivially?

In Henneaux's Lectures on the Antifield BRST Formalism for Gauge Theories, it is claimed in Exercise 1 that diffeomorphisms $\delta_\xi A_\mu=\xi^\rho\partial_\rho A_\mu+\partial_\mu\xi^\rho A_\rho$ ...
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### Book as supplement to Fradkin's “Field Theories of Condensed Matter Physics”

I am trying to read Fradkin's book "Field Theories of Condensed Matter Physics" but I am finding it to be a bit hard to follow at some places. In particular, I find that Fradkin sometimes throws some ...
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