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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57 views

Second quantisation for fermions

I am trying to build a model for reactions on a lattice in the Doi-Peliti formalism. Suppose there exists a lattice of $N$ sites indexed by $i$. Each site can be either occupied or unoccupied. ...
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23 views

Some questions on a certain Lagrangian related to $n$ dyons

I am trying to understand Gibbons and Manton's article. I am trying to understand the Lagrangian that they wrote down, from a physical point of view. Let me paraphrase from that article. "Consider $...
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1answer
62 views

The relation between Chern-Simons Theory and Yang-Mills Theory

So from this page, I know that there is a relation between Chern-Simons Theory and Yang-Mills Theory, but I have difficulty proving the identities in the document. I was going to prove $$\partial_\...
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48 views

Regarding notation used for infintesimal parameters of the Lorentz algebra and generators of the Lorentz group

I have a confusion regarding the notation that is used for infintesimal Lorentz transformations and the parameters that define the Lorentz transformation (used in various books such as Srednicki's and ...
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2answers
158 views

Gaussian path integral is equivalent to saddle-point?

If we have a path integral involving many fields, $$Z = \int \mathcal D \phi_1 \cdots \mathcal D \phi_n \exp(-S[\phi_1,\ldots, \phi_n]),$$ and $\phi_n$ occurs only quadratically-- i.e. the $\...
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55 views

Question on the $1/N$ expansion

My question is from Coleman's Aspect of Symmetry, on the large $N$ approximation. We will consider the $O(N)$ version of the $\phi^4$ theory. Its Lagrangian density is given by: $$ \mathcal{L}=\...
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2answers
117 views

Why is effective mass a tensor?

So I came across the effective mass concept for solids the other day. It was mentioned that the effective mass is a tensor and may have different values in different directions. However, this is stark ...
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1answer
34 views

Heuristic for large $x$ behavior from small $q$ behavior of Fourier Transform

If I have a function $h(\mathbf x)$ which may be written $$h(\mathbf x)= \int \frac{\text{d}^d\mathbf q}{(2\pi)^d} \, h(\mathbf q) e^{-i \mathbf q \cdot \mathbf x}$$ and assume spherical ...
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42 views

Is Brandt-Neri-Coleman stability analysis valid?

My question is related to the problem of stability of magnetic monopoles in Yang-Mills-Higgs theories. I have read "The Magnetic Monopole 50 years later" from Coleman and, in section 3.5, he discusses ...
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51 views

Independents fields and the Lagrange Density of Schrodinger equation [duplicate]

I have a doubt about the lagrangian of the Schrodinger equation. If we consider the wave function $\psi(\textbf{x},t)$ that satisfy the Schrodinger equation as a field, one way of construct the ...
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20 views

Validity of Random Phase Approximation in 2D/3D semimetals

In, for instance, this paper and this one the authors look at many-body effects in two- and three-dimensional semimetals, which have a low-energy quasiparticle dispersion relation of the form $\...
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1answer
48 views

What if the two Higgs doublet model is proved right? [closed]

Two higgs doublet model predicts five higgs bosons. If five higgs will be found then how it will impact the known physics?
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1answer
44 views

How a discrete z2 symmetry removes flavour changing neutral current from Two Higgs Doublet Model?

By applying a discrete Z2 symmetry to the theory of Two Higgs Doublet Model it is ensured that fermions of one type couples to only one doublet. But how FCNC is removed by doing so? Because if all ...
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113 views

Finite conformal transformations of fields from infinitesimal

I know that in conformal field theories conformal group acts not by pushforwards but (e.g. for scalar field $\phi$ with conformal dimension $\Delta$) $$ \phi(x) \mapsto \phi'(x') = \left| \frac{\...
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61 views

Proving Poisson bracket relations $\{\phi, P^r\}=\Pi^r$ in Ticciati's “QFT for Mathematicians”

Let $\phi$ be a scalar field, and $\Pi$ be the conjugate momentum of $\phi$. Let $\cal L=\cal L(\phi, \partial_\mu \phi)$ be the Lagrangian density. Define the stress-energy tensor as $$ T^{\mu\nu}=\...
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1answer
67 views

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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1answer
221 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 invariance of Compton scattering, you can prove that for spin 1 massless field ...
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1answer
35 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
125 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
65 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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53 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
77 views

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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30 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
53 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
40 views

Radiation of a charged particle [closed]

Take a uncharged particle. It hits a resting charged particle. Will the charged particle radiate then?
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1answer
49 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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47 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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22 views

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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1answer
46 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
109 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
48 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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37 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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85 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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27 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
31 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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38 views

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
59 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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70 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 ...
2
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2answers
181 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
151 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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1answer
139 views

Is there a sharp distinction between particles and fields?

The quantisation of the electromagnetic field, proposed originally by Planck, blurs the distinction between particles and fields. 'Point' particles become fuzzy and subject to a wave equation. Also, ...
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34 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 ...
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1answer
79 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
102 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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41 views

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
326 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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54 views

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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36 views

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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27 views

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
61 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 + [...