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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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Free fermion Lagrangian invariance under chiral symmetry

I want to apply this transformation to a free-fermion lagrangian: $$ L=\bar{\psi}(\gamma^\mu{\partial_\mu \,- m)\,\psi}$$ $$ \psi ' =\psi\; e^{i \alpha \gamma_5} $$ $$ \bar{\psi}'=\bar{\psi} \;e^{-i \...
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0answers
30 views

Gravitons and self-interaction

In the book quantum field theory and standard model by Schwartz, there is a problem 9.4 that says by considering lorentz invariency of compton scattering, you can prove that for spin 1 field there ...
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1answer
26 views

Transformation of electromagnetic potential under local U(1) transformation

Let $\mathcal{L}=-(\partial _{\mu} \Phi^*)(\partial ^{\mu} \Phi)$ With $\Phi , \Phi^*$ being complex fields. When looking at local U(1) transformations in class, we saw that $\mathcal{L}$ is not ...
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1answer
90 views

Energy stored in system or field?

I am having difficulty in understanding whether fields store momentum and energy or particles store them or both fields and particles store them? System of potential energy In the above source it ...
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1answer
57 views

QFT Klein-Gordon Equation “trick”

Both in the Wald and Parker/Toms texts on QFT in curved space time, when introducing QFT in flat space time first, they solve the Klein Gordon equation over the whole real line by placing the “field ...
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0answers
57 views

How can we evaluate the following integral using the tricks of delta functions? [migrated]

I am trying to teach myself the statistical field theory formulation of statistical mechanics. Not part of a class, just self study in my free time. I appreciate any help here. I am starting with ...
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0answers
28 views

longitudinal and transverse components in higher dimensions

I am familiar with the Helmholz decomposition of a vector field in three dimensions: $$\vec{V}=\vec{\nabla}\wedge\vec{A}+\vec{\nabla}\phi$$ But I am interested to show that something similar can be ...
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3answers
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Which particle mediates the Aharonov-Bohm effect?

BACKGROUND The Aharonov-Bohm (AB) effect induces phase shifts between the two paths that an electron could take around an enclosed magnetic field. In radial coordinates, assume that the magnetic ...
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Field operators and “the source” term

So, in a book on QFT there is in the begining some talk about Klein-Gordon field and equation. This is solved by using simple harmonic oscilator formalism and a spectrum for a free H is found. But ...
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27 views

Why is field action not a pseduo-scalar in 4D?

If the Lagrangian density is a scalar and the 4-volume is a pseudo-scalar (w.r. to proper orthochronous LT), how is then action not a pseudo-scalar? If it is a pseudo-scalar (i.e. the above reasoning ...
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1answer
47 views

Is there a theory on the creation and genesis of fields?

I do not intend to ask theological questions on PSE, so, you can interpret, if you want, this question on a purely physical basis. Almost everywhere, in classical and non-classical physical theories, ...
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2answers
37 views

Radiation of a charged particle [on hold]

Take a uncharged particle. It hits a resting charged particle. Will the charged particle radiate then?
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29 views

Meaning of mass-deformation in string theory and quantum field theories

I was reading some papers in the ABJM theory. I keep reading the term mass deformation but am not sure what it really means. I think the papers assume the reader is familiar with the term. Example ...
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41 views

$SU(3)$ and flavor symmetry technical question

In the HW of a particle physics class I was asked about a global $SU(3)_G$ symmetry of $N$ complex scalar fields that transform as $\phi_i(3)$ with $i=1\dots N$, $i$ is the flavor index. The ...
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Gauge Fields from Compactified Gravity

I encountered compactifying a 5D black string along an extra dimension in Natsuume's AdS/CFT text. Upon compactification, the thermodynamics of a 4D black hole may be identified with the 5D black ...
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0answers
18 views

Hodograph transformation

What is hodograph transformation? Can you explain it in a readily understandable manner?
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1answer
43 views

Masslessness of Goldstone modes

Suppose we have a $G$-invariant action $S$ of a field $\phi$, where $G$ is a Lie group; let then exist a non-zero value $v$ of $\langle\phi\rangle$ such that the $G$-symmetry of the action is broken, ...
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1answer
100 views

Higgs Mechanism in Landau-Ginzburg approach

I'm experiencing some troubles with one of the exercises in Kardars book on Statical physics of fields (problem 5 Ch3) or see https://ocw.mit.edu/courses/physics/8-334-statistical-mechanics-ii-...
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1answer
41 views

Doubts in an introduction to classical field theory

I started to study classical field theory using the book "Field Quantization" of Greiner and Reinhardt, and I have some doubts. First, the book write the Lagrangian $L(t)$ as a functional of a field $\...
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35 views

Second quantisation for dynamical systems

The paper "Perturbative approach to an $A + B \rightarrow C$ reaction-diffusion system", (Z. Phys. B 96, 137-144 (1994)), by Conrad and Trimper, applies the Fock Space formalism for the master ...
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1answer
64 views

Why is important for the energy density to be positive definite in field theories?

Why is important that the energy density be positive definite in field theories?
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0answers
20 views

Fields and gauge transformations vanishing at infinity

I find that, in field theory, it is very often assumed that the fields (classical) vanish at infinity. The same assumption is also applied to gauge transformations, for example, when saying that the ...
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1answer
23 views

Ginzburg Criterion (Ising model)

In my statistical field theory class, we were told that we want the magnetization fluctuations in the Ising model to be smaller than their background. Specifically this was written as $$\langle\phi^2\...
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0answers
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Why is the Coulomb Gauge enough to fix extra degrees of freedom?

In classical electrodynamics, we have after the Coulomb gauge is applied: $$ \Delta U = -\frac{\rho}{\epsilon_0} $$ $$ \Box \vec{A} = \mu_0 \vec{j}-\frac{1}{c^2} \vec{\nabla} \frac{\partial U}{\...
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1answer
51 views

How to calculate the conserved energy $E$ from the Lagrangian?

I am reading a PhD thesis that considers the Lagrangian $$\mathcal{L}=\partial_\mu\phi\partial^\mu\phi^\star-U(|\phi^2|)$$ where $\phi$ is a complex scalar field and $U(|\phi|^2)$ is an arbitrary ...
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0answers
41 views

Constraints vs Boundary Conditions

I have a very broad question about how the mathematical framework that classical theories of physics utilize to solve problems. The question is: What are the intrinsic differences between the ...
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2answers
143 views

$SU(2)$ symmetry of $\mathcal{L}=\partial_{\mu}\Phi^{\dagger}\partial^{\mu}\Phi - \Phi^{\dagger}M\Phi$

I'm considering a Lagrangian of two complex scalar field: $$\mathcal{L}=\partial_{\mu}\phi_1^{*}\partial^{\mu}\phi_1-m_1^2\phi_1^{*}\phi_1+\partial_{\mu}\phi_2^{*}\partial^{\mu}\phi_2-m_2^2\phi_2^{*}\...
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4answers
124 views

Inconsistency between $d_A = d + A \wedge$ and $d_A = d(..) + [A,..]$?

I am confused by something basic stated in this https://physics.stackexchange.com/a/429947/42982 by @ACuriousMind and some fact I knew of. Here $d_A$ is covariant derivative. $d_A A=F$ --- @...
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0answers
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Particles and associated fields

When a particle is associated with a field. 1) It is said that the excitation of the field produces the particle, 2) it is also said that when the field is quantized, the quanta of the field is ...
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0answers
33 views

Gribov's phenomenon

In the well known textbook by Itzykson-Zuber "Quantum Field Theory" there is a discussion of the Gribov phenomenon in non-abelian gauge theories (see Section 12-2-1). To my taste, the discussion ...
4
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1answer
73 views

Quantum field theory with only 3-point vertexes

Given an arbitrary quantum field theory, can I always write it in terms of another (different) quantum field theory containing only operators with 3 fields? (i.e. vertexes with 3 legs) I guess that ...
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2answers
82 views

Is the derivative with respect to a fermion field Grassmann-odd?

Fermion fields anticommute because they are Grassmann numbers, that is, \begin{equation} \psi \chi = - \chi \psi. \end{equation} I was wondering whether derivatives with respect to Grassmann numbers ...
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Field Theory: Converting $\int_0^{x_0} d^dx$ to $\int_0^{x_0} dr$, where $r=^{\textrm{def}}\|x\|$

For my Statistical Field Theory class (http://www.damtp.cam.ac.uk/user/tong/sft/sft.pdf), the prof converts integrals over each element of a vector $x$ into a single integral over the magnitude of the ...
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1answer
127 views

Squaring the E&M (Maxwell) field strength tensor

In Section 3.4 of Schwartz's "Quantum Field Theory and the Standard Model", the square $F_{\mu\nu}^2$ of the field strength tensor $F_{\mu\nu} = \partial_{\mu} A_{\nu} - \partial_{\nu}A_{\mu}$ is ...
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0answers
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Adding a total derivative to the Lagrangian does not preserve $\int\mathrm{d}^3\mathbf{x}~ T^{00}$

In problem 3.3 of Schwartz's QFT, the first two questions ask us to prove that if we add a total derivative to the Lagrangian: $$ \mathcal{L}\mapsto\mathcal{L}+\partial_\mu X^\mu\tag{1} $$ then $$ \...
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0answers
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Simplify Yang-Mills Equation of Motion in the 1-form gauge field $A$

We know the Yang-Mills theory Equation of Motion (eom) without source $$ * D * F = * (d (* F ) + [A, (* F )])= 0. $$ My question is that what are the most simple form we can boil down this ...
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Interpretation of vanishing Noether charge

I was told that Gauge symmetries are redundancies because the Noether charge of a gauge symmetry vanishes, i.e. that there exist no observable quantities that would allow you to distinguish two ...
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1answer
46 views

Mistake or Rewriting of Yang-Mills in Nakahara

I am familiar with Yang-Mills equation of motion E.O.M. (without matter or source fields) in differential form. $$ D * F =0 $$ and Bianchi identity $$ D F=0 $$ where $F= dA + A \wedge A$ and $D=d + [...
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1answer
51 views

Why do terms in a field theory Lagrangian that are polynomial in the fields collectively called the “potential”?

Field theory Lagrangians are often of the form of a kinetic term plus a source term minus a potential term. How do we know that the potential term is a polynomial in the fields? On a related note why ...
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1answer
79 views

Connection between gauge invariance and Lorentz invariance

This question is presented in the context of Weinberg's QFT book treatment, in particular considering the electromagnetism chapter. It begins in chapter 5 where Weinberg argues that in order to have ...
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1answer
33 views

Magnetic field due to a circular ring

In the EMFT notes of MIT Course-ware, the derivation of the magnetic field due to a circular ring at its axis, using Biot-Savart's Law and the cylindrical coordinate system is done as follows, I am ...
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0answers
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Why is it that the equation of a massless scalar field *must* be conformal invariant?

I'm reading a paper [1], p.111 where it is said that: However, the equation of scalar field with zero mass must be conformal invariant while equation $\square\varphi=0$ does not satisfy this ...
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0answers
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Interpreting the conserved charge in scalar QED

In scalar QED, applying Noether's theorem for internal global symmetries results in a Noether current that is dependent on the gauge because of the presence of the covariant derivative. $$j_\mu=-i(\...
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3answers
41 views

Why is it that magnetic fields(or any field)not move in space? [closed]

When I imagine a magnetic field produced by a magnet, or the electric field produced by a charge, I've learned that the fields are stationary, however, their value(across space) changes. If I placed ...
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0answers
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Lagrangian of Phonon-photon

A quite interesting but also hard problem are Polaritons. As far as I have understand the concept it's about phonons coupling to light. The Lagrangian function should therefore have a term for the ...
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1answer
218 views

Relating the Yang-Mills field-strength to the Maxwell tensor in $SU(2)$ gauge theory

I'm studying topological monopoles in a $SU(2)$ Yang-Mills theory with spontaneous symmetry breaking, through the book "Topological Solitons", by Manton and Sutcliffe. In section 8.2, the authors ...
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1answer
59 views

Confused about scalar fields

A scalar field is one which is unchanged under rotation. But how do we decide whether a given field (e.g., the temperature in a room) is unchanged under rotation or not? We need to measure the ...
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2answers
54 views

Electromagnetic linear response theory in function integral language [closed]

I'm being confused with the discussion in Altland&Simons' textbook, page P391-392. How is eq(7.46) derived? Specificly, Here we have the action: $$S[\bar{\psi},\psi,A]=\int dx \bar{\psi_\sigma}\...
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2answers
76 views

How to unify the rotation matrix of $SU(2)$ operator and $(z_1, z_2)$ representation?

I am following the Xiao-Gang Wen's book: Quantum Field Theory of Many-body Systems. In Ch. 5.6 about non-linear $\sigma$ model, it use a rotation operator $U$ to change the spin quantization from $z$ ...
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0answers
40 views

Motivation for Weinberg angle in electroweak gauge interaction?

Suppose I have the following lagrangian If we only focus on the neutral current in the lagrangian: Where $L$ is defined as: And $Y_L$,$Y_{R}^{\nu}$,$Y_{R}^{e}$, are the hypercharge values of the ...