The Stack Overflow podcast is back! Listen to an interview with our new CEO.

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.

Filter by
Sorted by
Tagged with
5
votes
0answers
148 views
+50

Magnetic field “lines” in $D \ne 4$ spacetimes

The electromagnetic field is represented by an antisymetric tensor $F_{ab} = -\, F_{ba}$ (the faraday). In $D = 4$ spacetimes, it has 6 independent componenents: 3 describing the electric field: $F_{...
3
votes
0answers
59 views

What significance do field-operators have, if they don't correspond to observables because of non-hermicity?

Since field-operators are not always hermitian (for example in case of a complex scalar field, or the dirac-field), they don't (in the quantum-mechanical sense) correspond to observables. Does that ...
0
votes
0answers
24 views

Can there be quantum spin liquids in 1D?

It seems like everyone studies quantum spin liquids in either 2D or 3D. Can not there be quantum spin liquids in 1D?
1
vote
2answers
37 views

What happens to the symmetry after gauge fixing?

Given a theory with gauge symmetry. After gauge fixing where does the symmetry go? Does the gauge symmetry turn into a global symmetry? For example there is a way to quantize fields theory with BRST ...
1
vote
1answer
75 views

Conserved current from the three $SU(2)$ transformations

We are asked to show that the following Lagrangian is invariant under the three $SU(2)$ transformations $\Phi \rightarrow \exp{({\frac{i}{2}{\alpha_j\sigma^j}}) \Phi}$, where $\Phi$ is a doublet ...
0
votes
0answers
31 views

Variation of the Ricci tensor “squared” and antisymmetrization of the derivatives

I'm dealing with some extension of GR, with action: $S=\int d^4x\Big[\sqrt{-g} f(R,R_{\mu\nu}R^{\mu\nu})$ Varying this action gives: $\delta S=\int d^4x\Big[\delta\sqrt{-g} f(R,R_{\mu\nu}R^{\mu\nu})...
2
votes
1answer
57 views

How to take derivative with respect to Lagrangian of complex field?

Basics: The Lagrangian in field theory was written as $$\frac{\partial \mathfrak{L}}{\partial \varphi}=\partial_\mu(\frac{\partial\mathfrak{L}}{\partial(\partial_\mu\varphi)})$$. Question 1: Is $\...
0
votes
0answers
39 views

Conservation of angular momentum from Noether's theorem and Lorentz invariance

Noether's theorem has been stated in the form that if the assignment $\phi \mapsto \phi + \delta \phi$, $x^{\mu} \mapsto x^{\mu} + \delta x^{\mu} $ leaves the action invariant, then the quantity $$ f^{...
2
votes
2answers
87 views

Is this a gauge symmetry?

Imagine a hypothetical action: $$S=\int \left(\frac{\partial}{\partial t}\phi(x,t)\right)^2 d^3x dt$$ Now we have a symmetry of the action: $$\phi(x,t)\rightarrow \phi(x,t)+\chi(x).$$ At time $t$, $\...
1
vote
1answer
103 views

Does the potential $V(φ)$ of a scalar field decrease with the expansion of space?

If a scalar field (eg. inflaton field) starts with a high potential. Does the potential $V(φ)$ of the scalar field decrease with the expansion of space? If it doesn’t decrease, would it mean that ...
1
vote
0answers
35 views

If the lagrangian density changes by a total derivative of the lagrangian density

When we derive energy momentum tensor current by actively transforming field. We see that lagrangian ( density) changes by a total derivative of the lagrangian. If a total derivative of the function ...
1
vote
2answers
346 views

The meaning of covariant but not manifestly covariant

What is the most general meaning of the expression covariant, but not manifestly covariant? Suppose I have a general (local) change of coordinates, $x^{\prime} = f(x)$, on an $(n+1)$-dimensional ...
0
votes
0answers
31 views

Action of 1-form symmetry in Maxwell theory

I am reading Lectures on Gauge Theory by David Tong 1. In 3.6.2 first example that the author talk about pure $U(1)$ gauge theory in 4D. In this example, he talk about two 1-form symmetries: electric $...
1
vote
1answer
41 views

Derivation of the Klein-Gordon solution via Fourier Transforms

I recently graduate with a bachelor's in physics, and I've been trying to take the next steps toward learning QFT. To this end, I have been working through Peskin and Schroeder's textbook step-by-step....
0
votes
1answer
39 views

Why can't a Weyl Fermion have mass?

My understanding was that a particle may have mass if there is a quadratic term in the fields without derivatives. For a single left-handed Weyl fermion, the following expression is lorentz invariant, ...
0
votes
1answer
44 views

Klein-Gordon equation with position-dependent mass [closed]

Does there exist a general solution for a differential equation like: $$\ddot{\phi}(x,t) - \partial^2_x\phi(x,t) + \phi(x,t)m^2(x) = 0,$$ where $m(x)$ is a known function.
1
vote
0answers
18 views

Doubt about 3D generalization of the Elastic Field Equations

My only source is $[1]$. In $[1]$ Finn introduces an example (in a totally undergraduate level discussion) that the problem on waves propagating in a solid cylindrical bar, firstly induces you to ...
0
votes
1answer
50 views

Would the Michelson-Morley Experiment have Discovered our Atmosphere?

We all know the earth is surrounded by an atmosphere, and we know that it is the medium through which sound travels. If the Michelson and Morley experiment was modified to find sound’s medium would ...
1
vote
1answer
30 views

Scale invariance in (2+1)D nonrelativistic field theory

Context: I am reading a paper named 'Nonrelativistic field-theoretic scale anomaly' on scale invariance in nonrelativistic field theory. The Lagrangian density for the scalar field is given by, $$\...
0
votes
0answers
30 views

What's the meaning of a “temporal polarization”?

For a massive vector four-field there are only three physical linearly-independent polarizations. For a field excitation at rest, these can be described by \begin{align} \epsilon^1_\mu \equiv \begin{...
1
vote
0answers
23 views

6D (2,0) superconformal field theory

I'm looking for a good reference book or textbook to study on 6D (2,0) superconformal field theory as a part of string theory.
1
vote
0answers
51 views

What if the Lagrangian $\mathscr{L}$, a Lorentz scalar, is replaced by a Lorentz vector?

As an answer to this post, I made an impression that if $\mathscr{L}$ were not a Lorentz scalar in Eq.$(1)$ (see below), then Eq.$(1)$ would not be covariant. But now I think that is wrong! I state ...
0
votes
0answers
10 views

Potential functions for separation and isochronic gauges

Most potentials in physics are expressed as a radius or another geometric norm/gauge. I am looking to understand the significance of the choice of potential functions for force/pressure separation in ...
2
votes
2answers
222 views

Water flow in salt solutions contemporary exposed to an electrical and constant magnetic field

When a permanent magnet is held motionless close to a salt solution which already has been exposed to an electrical field a flow in the water will be induced and can be detected by applying some ...
1
vote
2answers
147 views

Different definitions of Functional Derivative

In studying QFT and General Relativity, I came across two different definitions of Functional Derivative, and I'd like to know if they are equivalent. Firstly, in Wald's book General Relativity, as ...
1
vote
2answers
223 views

Fields: Fundamental and Physical, yet Unobservable?

I'm currently working through Robert Klauber's Student Friendly Quantum Field Theory, which by the way is much more accessible than other texts like, say, Peskin and Schroeder, for others also coming ...
1
vote
1answer
50 views

Expanding about background field

I refer to this set of lecture notes by Hugh Osborn, equation 4.184 on p.70. We expand an action $S[\phi]$ around a background field $\varphi(x) = \phi(x) -f(x)$ If we expand the action $S[\phi]$ ...
1
vote
2answers
52 views

Units of the Scalar field theory Lagrangian density [closed]

The Lagrangian (with units $J$) connects to the Lagrangian density (with units $J/m^3$) as: $$ L=\iiint_V \mathcal{L}d^3x $$ Let $\mathcal{L}$ be the classical Lagrangian density of the scalar free ...
5
votes
3answers
200 views

Maxwell's equations from continuum limit

In appendix A.6 of Schroeder's Thermal Physics, he mentions (in regards to classical fields): The usual approach is to first pretend that the continuous object is really a bunch of point particles ...
2
votes
2answers
664 views

A traceless stress energy tensor?

I'm trying to solve this exercise: Suppose an arbitrary theory (Flat space-time?) with a single field (Is a scalar field?) invariant under dilations, i.e. $x\mapsto b x$ and $\phi \mapsto \phi$. ...
1
vote
3answers
175 views

Do the equations of motion simply tell us which degrees of freedom are superfluous?

A massless spin $1$ particle in 4D has 2 degrees of freedom. However, we usually describe it using four-vectors, which have four components. Hence, somehow we must get rid of the superfluous degrees ...
0
votes
1answer
126 views

Harmonic oscillator hamiltonian (QTF)

I have a little doubt about the harmonic oscillator hamiltonian written at the beginning of Peskin&Schroeder's "An introduction to quantum field theory"; I enclose the picture of the page. It ...
3
votes
1answer
51 views

Is there a general behavior of energy gap under renormalization?

Perform real space renormalization on a discrete lattice model with a finite energy gap. Is it always true that under the flow of coarse-graining, the energy gap will only increase? I think the ...
0
votes
2answers
74 views

How does gauge-fixing really work?

Leaving technical issues like Gribov copies and residual gauge freedom aside, how do gauge fixing conditions like the Coulomb condition \begin{equation} \partial_i A_i =0 \end{equation} or the axial ...
2
votes
4answers
113 views

Why does Lorenz gauge condition $\partial_\mu A^\mu =0$ pick exactly one configuration from each gauge equivalence class?

For a vector field $A_\mu$, there are infinitely many configurations that describe the same physical situation. This is a result of our gauge freedom $$ A_\mu (x_\mu) \to A'_\mu \equiv A_\mu (x_\mu) + ...
2
votes
1answer
47 views

Why does Coulomb gauge condition $\partial_i A_i =0$ pick exactly one configuration from each gauge equivalence class?

There are infinitely many configurations of a vector field $A_\mu$ that describe the same physical situation. This is a result of our gauge freedom $$ A_\mu (x_\mu) \to A'_\mu \equiv A_\mu (x_\mu) + \...
7
votes
2answers
1k views

Showing that Coulomb and Lorenz Gauges are indeed valid Gauge Transformations?

I'm working my way through Griffith's Introduction to Electrodynamics. In Ch. 10, gauge transformations are introduced. The author shows that, given any magnetic potential $\textbf{A}_0$ and electric ...
4
votes
1answer
127 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 ...
1
vote
2answers
131 views

The simple harmonic oscillator model relating particles and fields in QFT

In all of the introductory Quantum Field Theory texts I gave read so far, (such as Zee, Srednicki, Luke), there is an introduction to the concept of fields as operators, following the simple harmonic ...
0
votes
0answers
26 views

How build a topological charge from of the mapping between physical and inner space?

How build a topological charge from the mapping between physical and inner space? When we make a mapping between two coordinates system, we normally relate both systems by coordinate transformation as,...
0
votes
1answer
67 views

Angular momentum in the Maxwell field theory/Chern-Simons theory?

I'm trying to calculate the angular momentum in the chern simons theory. But equivalently, I was trying a calculation of angular momentum in the Maxwell field theory, which will hopefully be ...
0
votes
0answers
44 views

Count degrees of freedom of gauge tensors

For degrees of freedom (dof) it is said that spin-1 massless boson like photon has 2 dof in 4d, like U(1) gauge theory. it is said that spin-2 massless boson like photon has 2 dof in 4d, like ...
3
votes
1answer
278 views

Does a gauge group $G$ determine the Principal $G$-bundle?

I'm trying to understand the mathematical underpinnings of gauge theories in the language of principal $G$-bundles and associated vector bundles. Not long ago, I had assumed that the physical choice ...
0
votes
0answers
31 views

Conjugate momenta in field theory

In classical mechanics for particles, the Euler-Lagrange equations are given by: $\frac{d}{dt} \frac{\partial L}{\partial \dot q} = \frac{\partial L}{\partial q}$ and the momentum conjugate to q is ...
3
votes
1answer
70 views

How does the $U(1)$ global symmetry break in the gauged $XY$ model?

I'm studying the particle vortex duality, and I'm confused how we're able to say that in the Coulomb phase, the "hidden" $U(1)$ global magnetic symmetry spontaneously breaks. gauged XY model: $\...
0
votes
1answer
55 views

Is there a superfluous statement in Schwartz's QFT book in deriving Euler-Lagrange equations?

Please help me with the following confusion. Yesterday I was looking at the derivation of Euler-Lagrange equation in several QFT textbooks using stationarity of the action. At the last step one needs ...
0
votes
0answers
46 views

Classical action is zero in Klein-Gordon theory for a particle wavepacket

I'm interested in rewriting actions in the form $$ S = -\int H dt + \int p_i dx^i, $$ (where $H$ is the Hamiltonian and the $p_i$ are conjugate momenta) and then evaluating them along a classical ...
3
votes
0answers
56 views

Kosterlitz-Thouless transition and renormalisation group theory [closed]

I'm trying to understand the Kosterlitz-Thouless transition in 2d systems. There is a section in Altland and Simons' Condensed Matter Field Theory that discusses the phenomenon, but I don't really ...
-1
votes
1answer
53 views

Field equation of motion for this Lagrangian

In my first QFT exam I was supposed to derive the equations of motion for all fields for this Lagrangian: $$\mathcal{L} = \bar{\Psi}(i\gamma^\mu\partial_\mu-M)\Psi+g\bar{\Psi}\gamma^\mu\Psi\bar{\Psi}\...
4
votes
1answer
69 views

Geodesic equation in Einstein-Cartan manifold

In GR we use the Riemannian manifold without any torsion to describe the theory. Hence, the geodesic equation can be interpreted as "a trajectory of a free falling particle" or "equation of motion". ...