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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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1answer
67 views

How groups act on fields in QFT?

I read a lot a posts on how to verify what are the symmetries of a given Lagrangian but I really can't find what I need and can't even get it by myself, this because I don't actually understand how ...
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0answers
17 views

Terms in Lagrangian and it's connection with Poincare group

For electromagnetic theory, there are different lagrangians, in QFT. My question is can I study the properties of Poincare group by knowing all the terms in the Lagrangian. For example, the Chern-...
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0answers
35 views

Feynman Rules from Lagrangian with charge conjugation matrix

I'm dealing with a doubly charged scalar singlet that interacts only with the right-handed muon as follows, $$\mathcal{L} = \lambda \psi_{R}C\psi_{R} \phi^{++},$$ where $\lambda$ is the coupling, $\...
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0answers
55 views

Mathematical representation of Symmetry Transformation

Consider a general Hamiltonian that is made up of three terms $\mathcal{H}$ = term I + term II + term III . Suppose the combination of charge conjugation and parity (CP) is a symmetry of this ...
0
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1answer
25 views

General formulation of time reversal symmetry action on fermions

I'm wondering about a general way to define the action of time reversal on a fermion field $\psi$. From a few sources I've read (e.g. appendix A of Witten's paper on fermion path integrals), it seems ...
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0answers
26 views

Energy-momentum tensor of the Dirac field

I'm trying to compute the energy momentum tensor for the dirac field $$\mathcal{L}=\bar\psi(i\gamma_\mu\partial^\mu-m)\psi $$$$T^{\mu\nu}=\frac{\partial\mathcal{L}}{\partial(\partial_\mu\psi)}\partial^...
2
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1answer
82 views

Gauge-invariance of Lagrangians

I am rereading David Bleecker's Gauge Theory and Variational Principles, and I have realized I don't understand something. The offending part is in 3.3 (page 50-52), however I am reproducing the ...
2
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1answer
30 views

Does two Higgs doublet model predicts two Higgs bosons?

Does 2HDM predict two higgs boson? Why two doublets are needed? I need a simplified answer as i am new to BSM
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2answers
55 views

Is there a name for the un-integrated Lagrangian?

The "action" is a functional of fields and their derivatives integrated over a space-time volume. A Lagrangian is just integrated over the space dimensions. But what is the name of the thing to be ...
0
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2answers
56 views

Hodge dual and QED

I was studying the paper Topological massive gauge theories in three dimensions by Deser, Jackiw and Templeton. In the paper, they use Hodge dual for some reason which I don't understand at all. So I ...
5
votes
2answers
295 views

Poincare transformations and “three kinds of infinitesimal variations”

I'm currently reading these$^1$ lec. notes as an introduction to relativistic QFT. In chapter two (pp.57-61) he introduces the concept of field variations along with some formulas for the different ...
0
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2answers
88 views

Finding the expression for probability density (the Klein Gordon equation)

Source: Quantum Field Theory for the Gifted Amateur by Tom Lancaster, Stephen J. Blundell. I am struggling to understand the logical step from the outline of the 'proof' in the footnote, to the fact ...
3
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0answers
36 views

What does triviality and non-triviality mean in field theory?

I am studying polymer physics and their basic field theoretical models which has connections to $\Phi ^{4}$ field theory. I frequently come in touch with statements about triviality and non-triviality ...
0
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2answers
87 views

How is solving Proca equation equivalent to scalar field equation?

My prof. told me that using differential forms proca equation reduces to solving for scalar field equation. How is that? I can’t see how does one relate to Scalar equation using differential forms. ...
1
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1answer
75 views

Phase separation in physics

I would look to familiarize myself with the current literature of phase separation. If one can direct me to statistical/thermodynamics theories of phase separation. Has phase separation been ...
2
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2answers
61 views

Duality transformations, such as between a massless scalar field and the Kalb-Ramond field

There is a kind of duality transformations between antisymmetric tensor fields which I learnt from a series of lectures by Gia Dvali on quantum field theory. I have not been able to locate a source ...
1
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1answer
33 views

Differentiating between the characteristics of a positive and a negative charge

I am keen in knowing the physical difference between the fields produced by positive and negative charges. Thus far, I can only give myself an unsatisfactory answer: that in a field produced by a ...
3
votes
1answer
84 views

Symmetry group of two complex scalar fields with different masses

Which is the symmetry group of the following Lagrangian: $$ \mathcal{L} = (\partial^\mu \phi_1^\dagger)(\partial_\mu \phi_1) + (\partial^\mu \phi_2^\dagger)(\partial_\mu \phi_2) - m_1^2\phi_1^\dagger\...
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0answers
38 views

How to perform parity tranformation in a Lagrangian?

In this forum https://www.physicsforums.com/threads/how-to-check-if-lagrangian-is-parity-invariant.333562/ appears a discussion about the performing of the parity transformation in the Dirac ...
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2answers
70 views

What does $U^{-1}(\Lambda)\phi(\Lambda y) U(\Lambda) = \phi(y)$ physically mean?

In QFT, let $U(\Lambda)$ denote a unitary representation of the Lorentz group. Let $\phi(x^{\mu})$ be scalar field operators in the Hilbert space; in other words: $$U^{-1}(\Lambda)\phi(x^{\mu}) U(\...
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3answers
73 views

What is the difference between electromagnetic field and electromagnetic radiation?

What is the difference between electromagnetic field and electromagnetic radiation?
1
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1answer
32 views

Electric Flux of A Point Charge Derivation

I am trying to understand the derivation of Gauss's Law and came across this line describing the electric flux through a small area of a sphere from a point charge: Source $$ E\cdot\Delta A_i = E_n\...
5
votes
1answer
106 views

How many degrees of freedom in a massless $2$-form field?

Consider the Kalb-Ramond field $B_{\mu\nu}$ which is basically a massless $2$-form field with the Lagrangian $$ \mathcal L = \frac{1}{2}P_{\alpha\mu\nu}P^{\alpha\mu\nu}\,, $$ where $P_{\alpha\mu\nu} \...
3
votes
1answer
64 views

$(1,0)$ representation of $\text{SL}(2,\mathbb{C})$ and selfdual antisymmetric tensors

The $(1,0)$ representation of $\text{SL}(2,\mathbb{C})$ is realized on two indexed symmetric spinors $\psi^{ab}$ transforming like $$D^{(1,0)}(A)\psi^{ab}=\sum_{c,d=1}^2A^a_cA^b_d\psi^{cd}$$ for all $...
0
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3answers
49 views

Does the electro-dynamical lagrangian contain a (Dirac) wave-function?

Consider a lagrangian for quantum electro-dynamics. It contains the two fields: the vector $A$-potential inside $F_{\mu\nu}$ and the matter field $\psi$ (Dirac's spinor). A series of questions arise ...
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vote
1answer
67 views

Index position when varying an action with respect to the metric

I'm confused about where we should put tensor indices when we vary an action wrt the metric. For example, if I have in the Lagrangian a term such as $$ A_{\mu\nu}B^{\mu\nu}, $$ do I necessarily have ...
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0answers
36 views

Decoupling of degrees of freedom in Klein-Gordon equation

In David Tong's notes in QFT he states that the degrees of freedom decouple in momentum space for the Klein-Gordon eq. He writes that this can be seen by using the Fourier transform (see picture below)...
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2answers
81 views

Doesn't dark matter imply a new force?

Given that every particle that we have experimental confirmation of is an oscillation of its field (from what we know), and given dark matter is thought to be a particle yet undiscovered according to ...
0
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2answers
34 views

Variation of a integration involving derivatives

I'm having problem with calculating the functional derivative of $F$ with respect to $\phi(x)$ while $$F = \int d^{4}x \phi^2 \partial_{\mu}\phi\partial^{\mu}\phi.$$ I want to obtain $\frac{\delta F}...
5
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5answers
154 views

$m$ in Klein-Gordon Equation

The Klein-Gordon equation is given by $$ (\square + m^2) \phi(x) = 0 $$ where $\square$ is the d'Alembertian operator, $m \in \mathbb{R}$ and $\phi$ is a scalar field. Question: What is $m$ in the ...
10
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2answers
139 views

What is the intuition behind the statement that non-equilibrium systems with static disorder are self-averaging?

In this paper(1) by C. De Dominics, he makes the argument that in a dynamical statistical mechanics system, one doesn't need to apply the replica trick and can directly disorder average the generating ...
2
votes
3answers
68 views

Lorentz transformation of vector field

Under a Lorentz transformation, a vector field transforms as: $A'_{\mu}(x')=\Lambda^{\nu}_{\mu}A_{\nu}(x)$ My question is, why is the Lorentz transformed vector field evaluated at $x'=\Lambda x$, ...
0
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2answers
75 views

These terms are so foreign to me that they feel like unnecessary jargon; what do these terms mean, and are they relatively common?

No pun intended in the title. ;) I am having trouble understanding this sentence on Wikipedia's page for Unified Field Theory: Governed by a global event $\lambda$ under the universal topology, ...
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0answers
25 views

Is it possible to use laser-like technology to create effective force field?

By laser-like lechnology I mean a coherent ray of particals or waves with the same amplitude/energy. This ray would be emited on limited distance (lets say 2meters) where it will be absorbed by ...
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0answers
49 views

Massless $\phi^4$ theory

Most of the standard textbooks on QFT discuss in some detail the massive $\phi^4$ theory in 4d space-time. I would be interested to see a discussion of massless $\phi^4$ theory (in fact other non-...
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0answers
35 views

When and how was the need for symmetry in the stress-energy tensor first realized

This question is somewhat historic. Let $\Theta_{\mu\nu}$ denote the canonical stress-energy tensor of some matter field $\psi$ in special relativity. It is often stated that the reason why we want ...
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0answers
41 views

Retrieving the non-relativistic formulas for electric and magnetic fields from relativistic formulas

I was checking the formulas for the electric and magnetic fields components E and B given in this link from Wikipedia: https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity#...
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2answers
58 views

Momentum density of the EM field - Classical field theory

The Lagrangian density of the EM field is given by $$ \mathcal{L} = \frac{1}{8\pi}\left(E^2-B^2\right) $$ Let $\vec{A}$,$\phi$ be such that $$ \vec{E} = -\frac{1}{c}\frac{\partial\vec{A}}{\partial t} -...
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1answer
37 views

Question about Mode expansion of free compact boson

$(1+1)$-Dim free compact boson, Lagrangian is $$\mathcal{L}= \frac{1}{2}(\partial_\mu\phi(\sigma,t))^2$$ with $\phi(x,t)\sim\phi(x,t)+2\pi r$ and periodic boundary condition along $x$, i.e. $\phi(\...
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vote
2answers
57 views

Varying a scalar field Lagrangian density

I was varying a scalar field density and I look at this term $${\cal L}~=~-\frac{1}{2}\partial _\mu\phi\partial^\mu\phi.$$ The result that I need to come is $$-\frac{1}{2}\delta(\partial _\mu\phi\...
0
votes
1answer
41 views

Physical explanation of Dirac-Born-Infeld (DBI) inflation

I am studying the Dirac-Born-Infeld (DBI) inflation model and came across this question in a past exam paper from Cambridge that considered the following Lagrangian: $$\mathcal{L}=\sqrt{-g}A(X,\phi)$$...
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0answers
35 views

A Scalar Function Tranformation — Question on Notation in 't Hooft Document

I started reading a document by Gerard 't Hooft which can be found here. Right at the start I am puzzled by a simple expression. It is equation 2.2 showing how a scalar function transforms. I ...
4
votes
1answer
81 views

Bound on Quantum Chaos

I am currently reading the paper A Bound on Chaos. In this paper, they evaluate the quantity C(t), which is an out-of-time-order correlator (OTOC), and use very clever arguments to show that there ...
1
vote
1answer
84 views

$\partial^{\nu} \partial_{\nu}$ vs. $\partial_{\nu} \partial^{\nu}$

I was doing a problem regarding field theory. I am given the following lagrangian density: $$\mathcal{L}=\frac{1}{2}\partial_\mu\phi_i\partial^\mu\phi_i-\frac{m^2}{2}\phi_i\phi_i$$ for three scalar ...
0
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1answer
35 views

Magnetic field around solenoid and toroid

Solenoid is proving a little bit confusing While getting through solenoid I found that the field outside it is extremely small and is negligible. Also the field at ends is half of that of center. ...
0
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1answer
51 views

Scalar particles are described by a real scalar field or by a complex one?

Well, in the title is already stated my main question. I know you can use a complex scalar field to describe two real scalar fields, by using just one that involves both of them. But, in the modern ...
3
votes
1answer
66 views

Why do we impose de Donder gauge?

In the field language, a massless particle corresponds to irreducible representations of the Lorentz group. In particular, given a spin-2 massless particle, we can embed the creation and annihilation ...
4
votes
3answers
108 views

Vector calculus in classical fields

The action is defined as: $$S = \int d^2\textbf{x}\,dt \left[\left(\frac{\partial h}{\partial t}\right)^2 + (\nu \,\nabla^2h)^2\right]$$ The equation of motion is asked for, so use Euler-Lagrange: $$\...
0
votes
0answers
32 views

Variation of vector field under Lorentz transformation and gauge transformation

In a paper I am reading, it is stated that under a Lorentz transformation, the coordinates transform as $x^{\mu} \to \Lambda^{\mu}_{\nu}x^{\nu}$, and so the change in the (vector) field at the same ...
1
vote
1answer
56 views

Obtaining Brans Dicke theory scalar (wave) equation

I have trouble with obtaining d'Alambert equation for scalar field in Brans-Dicke gravity (http://www.scholarpedia.org/article/Jordan-Brans-Dicke_Theory). B-D gravity langrangian density is given by: ...