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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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1answer
56 views

Show that a theory is scale invariant

I'm a bit new to this invariant transformations for fields so I've been having trouble manipulating them and I would appreciate any guidance. I saw in this wikipedia article that, for example, a $\...
3
votes
1answer
79 views

Redefinition of spacetime coordinates for Noether's Theorem

In the derivation of Noether's theorem some authors consider not only redefinitions of the fields \begin{equation} \phi(x) \rightarrow \phi'(x) = \phi(x) +\delta\phi(x) \end{equation} but also ...
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0answers
34 views

Fermionic scattering in Yukawa Theory

The scattering process I'd like to describe is the following fermion-fermion scattering in Yukawa Theory $\psi_{p1} + \psi_{p2} \rightarrow \psi_{p1'} + \psi_{p2'}$ The interaction Hamiltonian for ...
28
votes
3answers
2k views

Can the center of charge and center of mass of an electron differ in quantum mechanics?

Traditionally for a free electron, we presume the expectation of its location (place of the center of mass) and the center of charge at the same place. Although this seemed to be reasonable for a ...
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0answers
31 views

General Relativity Lagrangian Part 2

This is a continuation of this. I am asked to calculate the second order correction to h in T. So I wrote $h=h_0+h_1+h_2+...$ where $h_0$ is the first order, $h_1$ is the second and so on. Plugging in ...
1
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2answers
28 views

Coupling of a massless vector to a conserved current

In order to describe one-particle states of spin-1 in a Lagrangian description, we need to use a field $A_\mu$. This is a 4-vector up to gauge transformations, which means that under Lorentz ...
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0answers
31 views

Field Interaction [closed]

Can someone please explain (if possible) the fundamentals of the (for lack of a better word) physical interaction that governs the behavior between fields?
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0answers
68 views
+50

At what stage is it necessary to introduce a field theory in the regeon-pomeron-odderon model of hadron interactions?

I've been reading some papers from G.F. Chew and S. C. Frautschi and they do not even bother to introduce the concept of "Field" when they describe hadron interactions. My impression is that they do ...
-1
votes
2answers
108 views

Relativistic EM Lagrangian and the derivation of equations of motion

As mentioned in my other post, I am attempting to learn from Gross'"Relativistic quantum mechanics and field theory", and I have a question concerning the manipulation of the antisymmetric 4x4 tensors ...
3
votes
1answer
64 views

Klein-Gordon-Equation contains no Spin

I have a question about an argument used in Schwabl's "Advanced Quantum Mechanics" concerning the properties of the Klein-Gordan-Equation (see page 120): Since the eigenenergies of free solutions are ...
0
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0answers
51 views

Klein-Gordon-Equation provides a Scalar Theory that doesn't contain Spin [duplicate]

I'm reading actually Schwabl's "Advanced Quantum Mechanics" and encounter an understanding problem while considering the Klein-Gordan-equation. Here the excerpt: Obviously, since the eigen energies ...
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1answer
32 views

Energy-momentum tensor non-minimal scalar field

If we consider a non-minimal coupling term between gravity and scalar field for inflation, we can have some modifications for density and pressure of scalar field. I have some problems to obtain the ...
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0answers
44 views

In scalar-tensor theory, what the scalar field means?

I mean, in general relativity we can have an action with an scalar field, for example: $$S=\int d^4x\sqrt{-g} [\frac{R}{2\kappa}+L_{m}-\frac{1}{2}\zeta R\phi^2-\frac{1}{2}\partial_\mu\phi\partial^\mu\...
1
vote
1answer
38 views

Maximum velocity of interactions

In chapter 1, Section 1, para 7, of Landau & Lifshitz, Classical Theory of Fields, they argue that if a body moves faster than maximum velocity $V_m$ of interactions, that implies we can have an ...
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0answers
44 views

Green's function: relation to DOS and analyticity

It is not uncommon to see the (retarded) Green's function being defined in terms of the DOS: $$ G^R(\omega) := \int \frac{\rho(\varepsilon)}{\varepsilon-(\omega+i0^+)} \mathrm d \varepsilon. $$ I ...
1
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1answer
31 views

Wess-Zumino model: simplified vs non-simplified?

According to Ryder Quantum Field Theory page 440 the "simplified Wess-Zumino model" has the lagrangian $$ \mathscr{L} = \frac{1}{2}(\partial_\mu A)^2 + \frac{1}{2}(\partial_\mu B)^2 + \frac{1}{4} \...
0
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1answer
38 views

How to calculate the mass-matrix for a Lagrangian with $SO(3)$ and $SU(2)$ symmetry?

Consider a Lagrangian: $$\mathcal{L}=\frac{1}{2}\partial_\mu\phi_i\partial^\mu\phi_i - V(\phi);\\V(\phi)=-\frac{1}{2}\mu^2\phi_i\phi_i+\frac{1}{4}\lambda\phi_i\phi_i\phi_j\phi_j.$$ I understand that ...
0
votes
1answer
54 views

Is the inverse of the Klein-Gordon equation ever used in physics?

The Klein-Gordon equation (scaling constants) is $$\square u = -m^2 u.$$ I am wondering if the equation $$\square u = m^2 u.$$ for real $m$ ever shows up in the physical literature?
2
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0answers
40 views

Symmetry group of a Lagrangian [closed]

I apologise in advance for my English. I would like to ask you about this exercise that was assigned by the professor during class. Consider the Lagrangian density: $$\mathcal{L}=-\partial_{\...
1
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0answers
89 views

Do quantum fields with energy stored in it usually exert pressure?

There are types of quantum fields in the universe like spinor, vector, tensor, scalar fields. Do these fields with energy stored in it (as energy density) usually exert pressure, or be pressureless? ...
-1
votes
1answer
51 views

Field theory if no fundamental space-time [closed]

If there is no fundamental space-time, is the field concept also doomed? If so, how can we derive unified field theory in a background space-time if there is no background space-time or worst, no ...
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0answers
19 views

Commutation relation, field and conserved charges

One more question on basic commutation relation for fields. Let $\phi(x)$ be a scalar field and $$ P^\alpha = \int d^3x T^{0\alpha}, $$ where $T^{\alpha\beta}$ is the energy momentum tensor. Now, ...
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0answers
35 views

Index Notation Difficulty (Mixed index, i.e Torsion 3-form)

My question regards an index "notation" difficulty I've faced regarding the Torsion 3-form tensor (regarding properties of the Kalb-Ramond 2-form) and its Kronecker. I start with the co-variant: $$H_{\...
2
votes
2answers
69 views

Transformation of coordinates in Noether's Theorem

I am confused, in the proof of Noether's theorem, by the change of boundary in the action integral during the transformation of coordinates. I have seen on Wikipedia that along with the change of ...
10
votes
2answers
915 views

Are all fields in the universe we know of quantum fields?

Are all fields in the universe we know of quantum fields? Do all fields that exist must be inherently quantum in nature? How about fields that are yet to be discovered (ie. a new field like Higgs ...
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0answers
41 views

Looking for guidance on Symmetries and Spacetime Coordinate Transformations

I am looking for resources that would in depth explain spacetime coordinate transformations and symmetries. For instance, it would explicitly carry out the transformation, say, scale transformation (...
0
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0answers
43 views

Noether Current in $O(N)$ and $U(N)$ Model and Fixed Points

Does anyone know (or know how to derive) the Noether current in the $O(N)$ model $\mathcal{L} = - \frac{(\partial_\mu\phi^i)^2}{2} + \frac{\lambda}{4!}[(\phi^i)^2]^2 \ $ ? It would also be nice to ...
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0answers
17 views

$USp$ global symmetry in $d=3$, ${\cal N}=4$ supersymmetric QFT

Define a 3-dimensional QFT with $N=4$ supersymmetry (4 supercharges), and the field content is $g$ $N=4$ hyper-multiplets (that are in a representation $R$ of some group $G$). Each hyper-multiplet is ...
1
vote
2answers
125 views

In what sense is the stress-energy tensor the derivative with respect to the metric?

In Di Francesco et al (the big yellow book), section 2.5.2, it is suggested that the (symmetrized) stress energy tensor can be interpreted as the functional derivative of the action with respect to he ...
4
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2answers
86 views

Where did the concept of field come from?

What made scientists start to think about what was previously 'forces-exerted-by' (Newtonian view) to fields (e.g. electric fields and magnetic fields)?
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0answers
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Can we do a Wick rotation by an angle not being $\pi/2$?

If a state obeys an evolution equation, we can replace t by -t. we get another equation and it is interesting to study its solutions. it we replace t by it (wick rotation) we get again another ...
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0answers
24 views

How the the wavefunction in Klein Gordon equation intially obtained from schrodinger's equation changed to field in QFT? [duplicate]

Initially in quantum field theory we study about klein gordon equation but how do we change the wavefunction approach to field.
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2answers
56 views

General relativity - scalar gravitational field, variation principle

I have a basic question about the variation principal when applied to a scalar gravitational field in general relativity. Consider the action $$S_M = \int d^4 x\sqrt{|g|}g^{uv}\partial_u \phi\...
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0answers
42 views

Massive Real Vector Field Identity

Let's consider the classical Lagrangian density for a real vector field $V^{\mu}$ of mass $M$: $$L_{V} = -\frac{1}{4} V_{\mu\nu}V^{\mu\nu} + \frac{1}{2} M^{2} V_{\mu}V^{\mu} $$ The Eulero-Lagrange ...
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0answers
41 views

Effective classical action for QED

In the book by Ramond, effective action of $\phi^4$ theory is obtained by a saddle point approximation around a classical field configuration of $\phi$ field. Can such an effective action be derived ...
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0answers
63 views

Gluon field strength tensor example

can someone show an example of calculating the gluon field strength tensor as I can’t find one on the internet I have linked a photo here https://wikimedia.org/api/rest_v1/media/math/render/svg/...
3
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3answers
128 views

Particles vs fields

I've been reading the book "The Standard Model in a Nutshell" by Dave Goldberg and I'm confused by the notion of a particle. Case 1: Suppose that $\phi$ solves the Klein-Gordon equation, i.e. $(\...
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0answers
15 views

Accelerated expansion without the need of scalar potential

This is realted nonminimal derivative coupling (NMDC), it is said that this model doesn't require any scalar potential for accelerated expansion model? Anyone can explain?
2
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1answer
84 views

can conserved currents be spacelike?

Given a conserved current $J_\mu$ in flat space, $\partial_\mu J^\mu=0$ on some set of equations of motions, can it be taken spacelike at least in some finite region of space, or there exist some ...
4
votes
1answer
64 views

What justifies compactifying space and spacetime, in the context of instantons?

When studying Yang-Mills instantons, there are two instances where one compactifies a space. When classifying vacuum states, one demands $A_\mu(\mathbf{x})$ to become a constant as $\mathbf{x} \to \...
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2answers
155 views

Is quantum field theory a field theory of quantum mechanics or a quantum theory of fields?

Quantum field theory can describe and extend phenomena of classical fields, such as electromagnetism. I had assumed for a long time that it was itself a "field theory", by which I mean it is a set of ...
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0answers
28 views

Speed of sound in non-conformal strongly coupled plasma?

For a conformal system in (d+1)-dimensions, the speed of sound is given by $ v_{s} = 1/\sqrt{d}$ (for ex : $\mathcal{N}=4$ SYM in four dimensions). Is it possible to have a non-conformal strongly ...
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0answers
31 views

Acceleration from scalar-matter coupling in classical field theory

I have came across a text where an interaction term in a classical Lagrangian is presented that couples a matter density $\rho$ and a scalar field $\phi$ as \begin{equation} \mathcal{L}_{\text{int}} =...
3
votes
3answers
77 views

A confusing point of the Hamiltonian for a particle interacting with electromagnetic fields

In non-relativistic quantum theory the Hamiltonian for a particle interacting with electromagnetic fields is $$H=\frac{(\mathbf{p}-\mathbf{A}*e/c)^2}{2m}+e\phi+\int\,d^3x \frac{\mathbf{E^2}+\mathbf{B^...
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0answers
46 views

Fields in Lagrangian

This Lagrangian was mentioned in Schwartz book of quantum field theory: Consider the Lagrangian $$L = -\frac{1}{4}(F_{μν})^2− |φ|^2 − ieA_μ(φ^*∂_μφ − φ∂_μφ^*) \tag{3.67} $$ where $φ$ represents ...
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1answer
94 views

How a symmetry transformation acts on quantum fields

I study particle physics and am finally tired of pushing through QFT with annoying doubts which seem to be both very simple and fundamentally important, and to which several professors of mine couldn'...
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0answers
27 views

Lagrangian density of the electromagetic field [duplicate]

Why the Lagrangian density of the electromagetic field like $$\mathcal{L}(A_\mu,\partial_\nu A_\mu)=c_1F_{\mu\nu}F^{\mu\nu}+c_2A_\mu j^\mu$$ defines the only possible structure consistent with gauge ...
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0answers
18 views

Helicity conservation and proof $\phi_L^*\phi_R-\phi^*_R\phi_L=0$

Helicity was defined as below: $E\xi=\pm\sigma\cdot p \xi$ where $p$ was the momentum operator and $E$ was the energy operator, $\sigma$ was the Pauli matrix. $\displaystyle H=\frac{\sigma\cdot p}{|p|...
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0answers
42 views

Distinction between actions of fields vs. waves

When a magnet attracts a nail, it is an action of a field. However, wehen electrons move in a radio antenna, it is an action of a wave. At the quantum level, we often hear that an electromagnetic wave ...
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1answer
44 views

Calculating conserved currents associated with Lorentz invariance

I was trying to solve Problem 3.2 ( problem 3 in chapter 2) in Quantum Field Theory and the standard model for Matthew D. Schwartz. The problem says : Calculate the conserved currents Kμνα associated ...