# 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 is the meaning of gauge theory and Yang-Mills theory? [duplicate]

I would appreciate it if you guys would help me to understand the idea behind these two concepts: Gauge field and Yang-Mills theory. What I think I understand is: Suppose we have a Lagrangian that ...
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### Can Chiral symmetry violating term in lagrangian violate charge conversation?

The regular Lagrangian is $\mathcal{L}=\bar{\psi}(i\gamma^\mu\partial_\mu-m)\psi$ If we add a chiral violating term $\mathcal{L}=\bar{\psi}(i\gamma^\mu\partial_\mu-me^{i\theta\gamma^5})\psi$ For the ...
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### How is the Feynman propagator (Green's function) connected with the field?

Let's take a look at the Feynman propagator for a massive scalar field: $$D_F(x-y)=\int\frac{dp^3}{(2\pi)^3}\int\frac{dp^0}{2\pi}\frac{ie^{-ip \cdot (x-y)}}{p^2-m^2}$$ We can use this as the Green's ...
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### Classical Mechanics Lagrangian from Underlying Quantum Field Theory

Does the K - T classical mechanics Lagrangian emerge from some structure of the Lagrangian of the underlying QFT?
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### Doubt on: $G = SU(2)_{L} \times U(1)_{Y}$ representations, the Chiral Spinor bundle and the "split" of covariant derivative for $G$

Firstly, I've made two other questions $[1]$,$[2]$ concerning the same situation, but I think that this one will clarify better what I'm trying to understand. I'm following the text book $[3]$ and I ...
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### Conjugate momentum for constant scalar field

I am reading Witten's Why Does Quantum Field Theory in Curved Spacetime Make Sense?, and I am caught up on what appears to be a straightforward computation. The discussion (on page six) centers around ...
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### Deriving Euler-Lagrange equation for vector field in curved spacetime

I'm trying to derive covariant Euler-Lagrange equations for a vector field. The variation of the action should be \begin{gather*} \delta S = \int \text{d}^n{x} \sqrt{|g|} \left( \delta\phi^\mu \frac{\...
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### What are the beta functions for electroweak and strong constants of interactions?

As the title says I want to find beta function for electroweak and strong constants ($g$ for W-boson, $g'$ for B-boson and $g_s$ for gluons) Beta function is the function that describes change in ...
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### Help with an integral in Peskin & Schroeder - QFT

In chapter 2, page 27, eq. 2.51, P&S solves the following integral - $$\frac{4\pi}{8\pi^3} \int _0 ^\infty dp \ \frac{p^2 \ \ \ e ^{-it\sqrt{p^2 + m^2}}}{2\sqrt{p^2 + m^2}}.\tag{2.51}$$ My ...
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### Why does the Lagrangian have $O(4)$ symmetry after Wick rotating (previously Lorentz symmetry)?

Pertaining to the answer within link. Why is it the case, that for Lorentz invariant Lagrangian $\mathcal{L}$, after Wick rotation, the $O(4)$ invariance is established, thus manifesting itself as ...
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### Canonically quantizing the charged scalar field with massive gauge boson

I have a specific confusion in canonically quantizing the theory of a complex scalar field $\Phi$ and a real vector field $V^\mu$, with a Lagrangian density: \begin{align*} \mathcal{L} = -(D_\mu \...
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### What is the problem with classical fermionic field?

Consider classical fermionic field. We have it's action, equations of motion and so we can get it's solutions, right? For example, we can consider gravitational solutions with fermions (in particular, ...
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### Doubt on transformation laws of tensors and spinors using standard tensor calculus and group theory

1) Introduction From standard tensor calculus, here restricted to Minkowski spacetime, we learned that: A scalar field is a object that transforms as: $$\phi'(x^{\mu'}) = \phi(x^{\mu})\tag{1}$$ A ...
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### Weinberg's Normal Ordering

I have the exact same question about Weinberg's volume 1 that was posted in physicsforums.com 10 years ago but it was never answered. I would greatly appreciate it if someone knows whether there is an ...
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### Proca equation gauge conditions

In massive case without any gauge conditions proca equation can be written as $\partial_\nu(\partial^\nu A^\mu- \partial^\mu A^\nu)+\left(\frac{mc}{\hbar}\right)^2 A^\mu=0$ Since $A_\mu$ is a $n$-...
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