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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 ...

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17 views

Magnetic moment of a radially symmetric current

In my latest assignment I'm tasked with finding a magnetic moment $\mu$ of a hydrogen atom, whose current distribution $\mathbf{j}(\mathbf{r})$ looks like $$\mathbf{j}(\mathbf{r})=\frac{e\hbar}{3^8 \...
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15 views

Why are there outward forces on the ends of a flat plate capacitor?

I'm working my way through some formulas for electrical forces on the dielectric in a flat plate capacitor. In particular, I have formulas for forces that operate on the interface between the ...
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4answers
322 views

Where does Field Theory come from?

About my background: I'm currently a 4th year undergrad, and planning to do a PhD in theoretical physics. I think I have a decent understanding of basic physics, and I know how to do calculations in ...
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1answer
40 views

Constraints on correlation functions of Quasi Primary Fields

I have problems understanding constraints on correlation functions of quasi primary fields (QPF) following DiFrancesco's Conformal field theory book. In chapter 4, section 4.2.1, a QFP is defined as a ...
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26 views

Equivalence between Dirac and Majorana action in CFT

In Mussardo's Statistical field theory Chapter 12, section 12.3 about the conformal field theory of a free fermion field he talks about the complex fermion field (Dirac field) $$ \Psi(z,\bar{z}) = \...
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1answer
42 views

Supersymmetry: spin of the superpartners

I'm currently working on my master thesis, and I need to know a bit of supersymmetry. I have been looking the theory and I have a basic knowledge about it. I have a problem with understanding the ...
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1answer
26 views

Derivation of EL equations for real scalar field

I am looking to derive Eq. (1.11) from these notes on QFT from Tong’s notes: http://www.damtp.cam.ac.uk/user/tong/qft/one.pdf But Im the second equation, is there not suppose to be a factor of 1/2 ...
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1answer
41 views

$U(1)_V$ invariance

I'm working with an interaction Lagrangian of the form: $${\cal L}_{int} = \bar{\psi}\Theta\chi \tag1$$ Where $\Theta$ contains other operators, coupling constants, etc. I'm trying to unveil if ...
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3answers
54 views

What is the difference between electric field and electric field intensity?

I have read in my text book that electric field is the space or region around a charge in which an electric test charge would experience an electric force, while intensity is the force per unit charge....
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2answers
45 views

Effect of Co-ordinate Change on Euler-Lagrange Equations for Scalar Fields

Consider a single scalar field $\phi$ on a manifold $\mathcal{M}$. Suppose in $\{x^\mu\}$ co-ordinates, the Lagrangian density is $\mathcal{L}(\phi, \frac{\partial \phi}{\partial x^\mu})$. This means ...
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0answers
17 views

does anyone know the moment tensor with 2 time components?

I have the moment tensor with the following on paper: $I_{xx},I_{yy},I_{zz}$ But i can't find this one: $I_{00}$ as in: $h_{xx}=(2G/r)I^{''}(t_r)$ where $h_{xx}$ is the affect on a metric ...
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Released energy through bubble nucleation

I am reading the paper by Coleman "Fate of the false vacuum: Semiclassical theory" which explains how bubble nucleation occurs in first-order phase transition in field theories. I will summarise the ...
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2answers
486 views

Does the Heisenberg equation for fields and canonical momentums hold as well for the hamiltonian density operator instead of the Hamiltonian operator?

In quantum field theory, with the field $\phi$ and the momentum $\pi$ being operators, their time evolution is governed (in the Heisenberg-picture) by the Heisenberg equation: \begin{align} \dot{\phi}...
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1answer
33 views

Majorana fermions

If you write the Majorana spinors as $$\chi = \begin{pmatrix}\psi_L\\ i\sigma_2\psi_L^* \end{pmatrix} \tag1$$ It satisfies the Dirac equation that leads you to the Majorana equation $$i\bar{\sigma}^\...
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1answer
46 views

Chemical Potential and interactions

I'm interested in an model with interactions between different kind's of particles. Each particle species has it's own chemical potential. I want to treat the system in the Matsubara formalism. Here, ...
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1answer
20 views

Magnetic Force on a current carrying conductor

Why does a current carrying conductor parallel to the magnetic field not experience a force?
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0answers
26 views

What does it mean if the Lagrangian density has explicit spatial dependence?

First off, I have seen this post here which asks seems to ask my question, but it is not properly answered. If the Lagrangian has explicit time dependence, then the total energy, and Hamiltonian, is ...
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2answers
34 views

Conservation of improved energy momentum tensor of a real massless scalar field

So I'm supposed to find that the improved energy momentum tensor of the scalar field $\phi$ satisfying the evolution equation $\Box \phi = 0$ is conserved. The improved energy momentum tensor is: $T^{...
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1answer
40 views

Derivation of the adjoint of Dirac equation

My goal is to deduce the adjoint of Dirac equation: $$ \overline \psi (i\gamma^\mu \partial_\mu+m)=0 \tag{1} $$ My process: I started with Dirac equation $(i\gamma^\mu \partial_\mu-m)\psi=0$. ...
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36 views

Noether charges of spacetime translation in KG field

When applying a spacetime translation $x^\mu\rightarrow x^\mu+a^\mu$ the KG lagrangian density changes by - $$\mathcal{L} \rightarrow \mathcal{L} + a^\nu \partial_\mu \delta^\mu_{\;\nu} \mathcal{L}$$...
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28 views

Obtaining Spinor Lagrangian from Copying 4-Vector Lagrangian

I am reading Schwartz's book on QFT and I am currently on writing a lagrangian for spinors. We note that $\psi^\dagger_R\psi_R$ and $\psi^\dagger_R\vec{\sigma}\psi_R$ can be written as a 4-vector (as ...
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4answers
171 views

What causes $A^{\mu\nu}_{\pm}=F^{\mu\nu}\pm i \tilde{F}^{\mu\nu}$ to have three independent components rather than six?

Both the elctromagnetic field strength tensor $F^{\mu\nu}$ and its dual $\tilde{F}^{\mu\nu}$ defined as $\tilde{F}^{\mu\nu}=\frac{1}{2}\epsilon^{\mu\nu\lambda\rho}F_{\lambda\rho}$ are examples of ...
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2answers
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Lagrangian of EM field: Why the $B$-field term has a minus sign in front of it in the Lagrangian?

I know that $L = T - U$ and that, in the non-relativistic case $$L= \frac{1}2mv^2 - q\phi(r,t) + q\vec{v}\cdot\vec{A}(r,t).\tag{1} $$ My lecturer used the following form of the Lagrangian density ...
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2answers
100 views

Why isn't the electromagnetic field considered as the medium for electromagnetic waves by scientists in general?

According to a google search, the definition of a medium in physics is the substance that carries a wave. The definition of a substance in physics is matter with specific composition and properties. ...
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93 views

Meaning of the simplest potential of quintessence models. Fields in denominator?

I am reading Sec. 1.12 of the Cosmology book by Weinberg. In this section he explains the very simple model of quintessence which attempts to provide a dynamical explanation of the smallness of the ...
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2answers
84 views

Quantum Mechanics Defining a field

I am currently in a basic class where I am being taught some concepts of QM.. We were taught today some field theory but we were not given the definition of field in QM. I looked around but my book ...
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1answer
61 views

What is the overlap $\langle \phi | 0 \rangle$ for a scalar field?

Consider a massive free real scalar field $\hat{\Phi}$ (with $\mathcal{L}[\Phi] = \partial_{\mu}\Phi\partial^\mu \Phi - \tfrac{1}{2} m^2 \Phi^2$). I was wondering what is the overlap for the ...
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24 views

Point approximated scalar field with diffusion

I need help with finding an approximate model for a scalar field using randomly spaced points and only by knowing the distance between them. I have some points on the 2d plane and each Point has a ...
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3answers
66 views

Confusion over use of contravariant notation in Noether's theorem and Lagrangian filed theory

The variational principle clearly gives $$\frac{\partial \rho}{\partial t} + \overrightarrow{\nabla}\cdot \mathbf{J} = 0.$$ So the sign is positive. However in my lecture notes it is claimed that ...
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1answer
64 views

Conserved current in scalar QED

Consider a theory of a free massless complex scalar $\phi$ which undergoes global $U(1)$ transformations. The conserved current associated to this symmetry is the usual scalar current $$ J^\mu = i\...
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59 views

Lagrangian density for a complex scalar field

I am taking a course on classical field theory, and am not entirely sure as to what motivates the for of the Lagrangian density for a complex scalar field. In my lecture notes, this is first ...
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1answer
86 views

Why is $4=3\oplus 1$? What are propagating modes? Etc

In Schwartz's QFT book, he said that the vector representation of the Lorentz group, $V_\mu$ that is four-dimensional, is the direct sum of two irreducible representations of $SO(3)$: a spin-0 ...
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72 views

Proof of treating $\psi^*$ as a field independent from $\psi$?

Given $L=\partial_\mu\psi^*\partial^\mu\psi -m^2\psi^* \psi$. The field equation is obtained by applying Euler–Lagrange equation on $L$ by treating $\psi^*$ independent of $\psi$. I am trying to ...
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1answer
77 views

What sort of particles corresponds to the $(1,1/2)$ representation of the Lorentz group?

Every irreducible massive unitary representation of the Poincaré group is specified by a mass and a non-negative half integer spin. Every massless irreducible unitary representation of the Poincaré ...
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1answer
20 views

Interaction term in free energy for Gaussian Fixed Point

In general in statistical field theory, the free energy $F_0$ as a function of our order parameter $\phi$ can be written as $$F_0[\phi]=F_0[\phi^-]+F_0[\phi^+]+F_I[\phi^-,\phi^+]$$ where the last ...
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2answers
102 views

Must a classical Lagrangian or a Hamiltonian be a real function?

$\bullet$ Is it fair to assume that the classical Hamiltonian or Lagrangian of a system (a particle or a field) is always a real-valued function? $\bullet$ If not, can you provide counter-examples? ...
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1answer
37 views

What happens to the gauge covariant derivative if the theory contains multiple fields in different representations?

I'm studying a graduate level course in QFT, and I have a potentially very stupid question that I can't find adressed anywhere (which I guess implies that I'm missing something fundamental). I'm ...
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1answer
67 views

What exactly are the sections in gauge theories?

In trying to understand precisely how fiber bundle theory maps to physical models, I came across this quotation: We can think of the elements of the principal bundle as generalized frames for the ...
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0answers
32 views

How to calculate Noether current in quantum field theory?

I'm studying particle physics with an experimental approach. I have still few theory lectures including QFT. However, I'm lost about calculating Noether current. I saw this formula for example in my ...
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1answer
60 views

Why do we consider solitons as a composite object?

Can someone explain why do we consider solitons as a composite object? I know that there are dual theories which the role of fundamental and solitonic objects can be mapped to each other, but I can't ...
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0answers
32 views

Dependence of the second time derivative of a field with its source

In Hans Ohanian's book «Gravitation and Spacetime» (page 96), the following is stated to find the equations of motion of an arbitrary classical field, with the case of the electromagnetic field as an ...
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1answer
53 views

Is it enough to assume $F_{\mu\nu}\to 0$ at infinity but not $A_\mu$ to derive the equation of motion?

Suppose the the Lagrangian $\mathscr{L}$ of the free electromagnetic field is augmented with the term $$F_{\mu\nu}\tilde{F}^{\mu\nu}=\partial_{\mu}(\epsilon^{\nu\nu\lambda\rho}A_\nu F_{\lambda\rho}).$$...
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1answer
73 views

Why are two different gauge transformations of $A_\mu=0$ in $U(1)$ gauge thoery equivalent?

Two inequivalent gauge transformations of $\mathbb{A}_\mu=0$, described by $U$ and $\tilde{U}$ of a pure $SU(N)$ Yang-Mills theory as $$\mathbb{A}_\mu=\frac{i}{g} U\partial_\mu U^\dagger~\text{and}~\...
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1answer
156 views

Eigenstates in QFT and amplitude of a field operator

I've seen in different posts (such as here) that given a field $\hat{\phi}(x)$, its eigenstates $|\phi\rangle$ are of the form: $$|\phi\rangle\ = e^{\int dx\phi(x)\hat{\phi}(x)}|0\rangle\tag1$$ I ...
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2answers
168 views

Varying the Einstein-Hilbert action without reference to a chart

In most treatments of General Relativity, when the the Einstein-Hilbert action over some manifold $\mathcal{M}$ (plus Gibbons-Hawking-York term if $\mathcal{M}$ has a boundary), given by $$S=\frac{1}{...
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0answers
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Is there a multiscale analysis for field theories?

Consider a (zero dimensional) Gaussian field theory described by the dynamical action $$S = \int_t \tilde{\phi}(t) \left[\partial_t \phi(t) + M(t) \phi(t)\right] - \gamma \tilde{\phi}(t)^2\, .$$ $\...
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3answers
1k views

How do fields co-exist physically? [closed]

How do we actually visualize the effect of two fields interacting in the same region of space? If fields are just mathematical formulations to explain things that have no physical meaning, how are ...
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1answer
100 views

Doesn't the “Mexican hat” potential give a misleading impression that the barrier height between two vacua is finite?

For $\mathbb{Z}_2$ symmetry breaking in a Classical Field Theory described by a potential $$V(\phi)=\lambda(\phi^2-v^2)^2,\tag{1}$$ there is a finite energy barrier of height $\epsilon=\lambda v^4$ ...
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0answers
20 views

What does it mean for something to interact with a mean field?

I think I just don't understand what a mean field is very well except that it's sometimes used as an approximative technique.
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43 views

What should I learn to understand 6d (2,0) theory? [closed]

I'm a first-year graduate student, I heard that 6d (2,0) theories can provide various dualities between lower dimension field theories, and can give many beautiful results in mathematics. So I ...