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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How particles interact with the electromagnetic potential $A^\mu$?

It is well known that one reason quantum mechanics started to being developed, was because scientist wanted a model to explain electron orbits in atoms. Borh interpreted that the for orbits to exist ...
Álvaro Rodrigo's user avatar
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33 views

Ward identity in scalar QED; gauge transformations & plane wave solutions for polarization

I am prepping for my QFT2 exam tomorrow, and in one of the mock exams I found the following question (and I'm not quite sure how to go about this). Given the following Lagrangian: $$ L = -\frac{1}{4}...
Sophie Schot's user avatar
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0 answers
29 views

Can you tell me, given these 2 vertices in scalar QED, where these terms come from?

I have a question regarding two vertices in scalar QED. The first question concerns the 3-vertex (phi, phi and a photon). The Feynman rule associated here is $-ie(p1+p2)_{\mu}$. My question regarding ...
Sophie Schot's user avatar
-1 votes
1 answer
36 views

What is the point of arranging (1/2,0) spinor into Majorana spinor?

Using Srednicki's notation: For a massive left-handed spinor $\psi$: $\mathcal{L}=i\psi^{\dagger}\bar{\sigma}^{\mu}\partial_{\mu}\psi-{1\over 2}m\psi\psi-{1\over 2} m\psi^{\dagger}\psi^{\dagger}$ It ...
Bababeluma's user avatar
1 vote
0 answers
48 views

Counting degrees of freedom in theories with two-forms [duplicate]

I am reading Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics. I am thinking that I can apply the same arguments to the case of a two form, whose components are ...
schris38's user avatar
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103 views

Are eigenvalues of slashed covariant derivative real?

I am trying to demonstrate that the slashed covariant derivative $$ \gamma^\mu D_\mu = \gamma^\mu(\partial_\mu -iA_\mu) $$ has real eigenvalues: $$ \gamma^\mu D_\mu \varphi_m(x)=\lambda_m \varphi_m(x)...
Gorga's user avatar
  • 75
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1 answer
38 views

Covariant derivative property

I am trying to demonstrate this propertie $$ \not{D}^2= \mathcal{D}^\mu \mathcal{D}_\mu-\frac{i}{4}\left[\gamma^\mu, \gamma^\nu\right] F_{\mu \nu} $$ where $\not{}~$ is the Feynmann slash, and $D_\mu ...
Gorga's user avatar
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1 answer
61 views

Infinitesimal transformation of the Yang-Mills field

I am trying to obtain the infinitesimal transformation for the Yang-Mills field $A_{\mu}$. I want to show that $$ A^{\prime a}_\mu=A_\mu^a-\partial_\mu \theta^a-g_s f^{a b c} \theta^b A_\mu^c $$ For ...
David Lazaro's user avatar
0 votes
1 answer
89 views

Why is the derivative necessary to connect left and right-hand spinors?

I am studying Weyl and Dirac spinors. Suppose we have two Weyl fermions $\eta, \chi$ transforming under $(1/2,0)$ representation of the Lorentz group. I learned that to construct Lorentz invariant ...
IGY's user avatar
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131 views

Finite dimensional irreducible projective representations of $SO^+(1,3)$

Conventions: Take the Minkowski metric tensor to have signature $(+, -, -, -)$. Use Hermitian (instead of skew-symmetric) generators of rotations $J_i$ and anti-Hermitian (instead of symmetric) ...
Silly Goose's user avatar
  • 1,963
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0 answers
66 views

How to take the second-order gauge covariant derivative in quantum field theory?

I am studying quantum field theory and gauge theory, and I am confused about how to take the second-order gauge covariant derivative of a field. (1) The first way is to write the second order gauge ...
Ruan's user avatar
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1 answer
60 views

How to calculate the time derivative of electromagnetic field? [closed]

How can I calculate the time derivative of an electric field from its space derivative? That is, I know $\frac{dV}{dx}$, and I need $\frac{dV}{dt}$. In general, $\frac{dV}{dt}$ = $\frac{dV}{dx} \times ...
katang's user avatar
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1 answer
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Does every field correspond to a particle?

I know that particles in QFT are just excitations of its corresponding field. But is it possible to have a field which cannot generate particles? If yes, what terms must be added to the Lagrangian so ...
Gabriel Ybarra Marcaida's user avatar
2 votes
0 answers
69 views

How do Maxwell's equations follow from the action of Lorentz generators on field strength?

Following Warren Siegel's book on Field theory (pg. 223), one might derive the action of Lorentz generators $S_{ab}$ on an antisymmetric 2-tensor field strength $F_{cd}$ which arises for example in ...
Sanjana's user avatar
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0 answers
64 views

What is the Lagrangian for the interaction of graviphoton with matter?

There are some models that postulate the existence of graviphoton. What is the Lagrangian for the interaction of graviphoton with matter?
physics_2015's user avatar
4 votes
0 answers
106 views

Interpreting $4D$ massive scalar momentum space action as a gauge-field action in 1D?

Consider the following action for massive scalar as follows $$S = \int d^4x \left(-\frac{1}{2}\partial^{\mu}\phi\partial_{\mu}\phi-\frac{1}{2}m^2\phi^2\right) \tag{1}$$ with Minkowski signature $(-,+,+...
Dr. user44690's user avatar
1 vote
1 answer
56 views

Planar spin in two-dimensional CFT

I have several questions regarding the definition of planar spin. I was reading the big yellow book (by Di Francesco et. al.) Section 5.1.5 looks a little mysterious. Look at 5.25, which is the two-...
hossein mohammadi's user avatar
2 votes
1 answer
51 views

Is it possible to solve numerically the classical Yang-Mills for a generic source?

The classical Yang-Mills equation in the presence of a source $J^\nu(x)$ can be written as $$ \partial_\mu F^{\mu \nu} - i g [A_\mu, F^{\mu \nu}] = J^\nu (x), $$ where $F^{\mu \nu} = \partial^\mu A^\...
aruera's user avatar
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1 vote
0 answers
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Complex gaussian integral with a complex action and different source terms [duplicate]

I am trying to use the following Gaussian path integral identity $$\int D[\phi_1,\phi_1^*,\cdots,\phi_n,\phi_n^*] \exp(i\int z^\dagger D z+i\int f^\dagger z+z^\dagger g) = \det{D}^{-1}\exp(-i\int f^\...
user1830663's user avatar
1 vote
1 answer
80 views

Hamiltonian density of EM fields

I'm learning about the field theory of electromagnetism. The Lagrangian density for an electromagnetic field can be taken to be $$ \mathcal{L} = -\frac{1}{4} F^{\mu\nu} F_{\mu\nu} + \mu_0 A^\mu J_\mu $...
Bio's user avatar
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1 answer
70 views

Is there an equivalent to the Klein-Gordon and Dirac Equations for Vector and other fields?

The Klein-Gordon equation describes a scalar field, and the Dirac Equation describes a spinor field. Is there an equivalent equation for a vector field? As well as spin 3/2 and spin 2 tensor fields? ...
zion does math weird's user avatar
0 votes
0 answers
82 views

Mathematical description of higher spin gauge theories

Ordinary Yang-Mills gauge theory giving spin 1 gauge bosons can be mathematically described by connection 1-forms and curvature of principal bundles. I wonder, what the proper mathematical description ...
Flo's user avatar
  • 39
2 votes
1 answer
80 views

Do matter fields in classical gauge theories have a physical meaning?

When you want to describe a Classical gauge theory, you need the following objects : A (pseudo)-Riemannian manifold $M$ (your spacetime) A Lie group $G$ describing the local internal symmetry of your ...
eomp's user avatar
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0 answers
45 views

On discretization in QFT and second quantization

Some time ago i saw in a QFT lecture series by the IFT UNESP that in QFT we need to discretize space by dividing it into tiny boxes of an arbitrary Volume $ \Delta V $ and then define canonical ...
Tomás's user avatar
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1 vote
0 answers
62 views

How are chiral bosons defined?

What is the definition of chiral bosons? Until now I only knew the derivation of the chiral fermions (used in the Dirac field equation).
Davide's user avatar
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0 votes
2 answers
514 views

Can we define time as a field? [closed]

The main objective is, can we relate time in terms of a field, I know time differs in many properties from an usual field. But I always imagine time as an forward moving field and we all know it is ...
Ash's user avatar
  • 47
0 votes
1 answer
61 views

Field transformation under conformal transformation

In 1 (see references below), I'm trying to derive how a spinless field transforms under a conformal transformation, specifically eq. (2.41). CFT references/lectures are the most confusing I've seen ...
mathemania's user avatar
2 votes
0 answers
124 views

Ambiguity of Lagrangian density in field theory [duplicate]

In classical mechanics, we know $L(q,\dot{q},t)$ and $L(q,\dot{q},t)+\frac{d}{dt}\Lambda(q,t)$ give the same Euler-Lagrange equation $\frac{d}{dt}\frac{\partial L(q,\dot{q},t)}{\partial \dot{q}_i}=\...
watahoo's user avatar
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1 vote
1 answer
93 views

Why does we quantize fields $\phi(t,x)$ and not $\phi$?

In classical mechanics, the action of a theory is determined by its Lagrangian: $$S(q) := \int L(q(t),\dot{q}(t),t)dt $$ In the following, let us assume that $L$ does not depend explicitly on time. ...
MathMath's user avatar
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0 answers
46 views

QFT by Schwartz Problem 3.1 Solution

I am having trouble while solving in the Problem 3.1 of the QFT book by Schwartz. Problem Find the generalization of the Euler-Lagrange equations for general higher-order Lagrangians of the form $\...
darkphysics's user avatar
0 votes
0 answers
35 views

Infinitesimal translation of the scalar field (QFT) [duplicate]

I'm following my professor's notes on QFT, and I cannot understand this passage. It's about an infinitesimal transformation for the coordinates of a scalar field $\phi$. The passage reads: Let us ...
Martin and Friends's user avatar
4 votes
1 answer
183 views

Field equations for Maxwell and Einstein tensors in a weak field limit

I am following this paper here (arXiv here). What I want to do is derive equations ($2.7$) and ($2.8$) given in section $2$. While the authors include the higher order Euler Lagrangian terms in their ...
ShKol's user avatar
  • 302
2 votes
1 answer
156 views

Srednicki 36.5 symmetry question

This is from the intro to a problem 36.5 in Srednicki and not part of the problem itself. I am having trouble proving that $$\mathcal{L}=i\psi_j^\dagger\sigma^\mu\partial_\mu\psi_j$$ Has $U(N)$ ...
JohnA.'s user avatar
  • 1,694
3 votes
0 answers
97 views

Klein-Gordon mode functions in curved spacetime

I'm currently tackling QFT in curved spacetimes for the first time, mainly using "Quantum fields in curved space" by Birrell and Preskill's notes on QFT in curved spaces, to get a general ...
Ric's user avatar
  • 113
3 votes
1 answer
61 views

Cauchy problem for the Klein-Gordon equation

Let $(M, g_{\mu\nu})$ be a globally hyperbolic spacetime and let $\Sigma$ be a spacelike Cauchy surface. The covariant Klein-Gordon equation has a well-posed initial value formulation, in the ...
Ric's user avatar
  • 113
1 vote
2 answers
100 views

Charge conjugated Dirac equation

I would very much like to understand the motivation behind the correlation between: $(i\partial\!\!/-eA\!\!/-m)\psi=0$ and $(i\partial\!\!/+eA\!\!/-m)\psi_c=0$ when dealing with the derivation of the ...
Xhorxho's user avatar
  • 133
0 votes
1 answer
55 views

CFT In Embedding Space

I am trying to figure out how a translation or a conformal transformation explicitly look like in embedded space. Given a CFT in Euclidian (or Minkowski) coordinates $x^\mu$ we can embedded them in $d+...
ssm's user avatar
  • 194
1 vote
1 answer
118 views

Choice of hypersurface in Klein-Gordon inner product

Let $M$ be a globally hyperbolic spacetime, with metric $g_{\mu\nu}$. Consider the covariant Klein-Gordon equation $$(g^{\mu\nu}\nabla_{\mu}\nabla_{\nu}+m^{2})\phi=0$$ Define the following indefinite ...
Ric's user avatar
  • 113
0 votes
0 answers
51 views

Can you assume the energy-momentum tensor is symmetric if you only impose Lorentz symmetry?

The proof showing that the energy-momentum tensor is symmetric uses the fact that $\partial_\nu T^{\mu\nu}=0$ due to translation symmetry, the definition of the conserved current and that $\partial_\...
Chris G's user avatar
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0 votes
0 answers
38 views

Help with calculating Lagrangian with scalar potential

I was reading Schwartz's QFT, I came across a lagrangian density, $$ \mathcal{L} = -\frac12 h \Box h + \frac13 \lambda h^3 + Jh ,\tag{3.69} $$ Calculating the Euler-Lagrange equation, $$ \partial_{\mu}...
Watanabe.N's user avatar
2 votes
1 answer
92 views

Can field itself have a speed?

I've seen many examples about a particle moving relative to field. But I never saw a field moving relative to observer (or a particle). So, can field have a speed? I thought about some possibilities: ...
Song's user avatar
  • 55
1 vote
1 answer
94 views

Deriving Klein-Gordon equation in curved spacetime [closed]

I try to drive The Klein-Gordon equation for a massless scalar field in case of FRW metric: $$ ds^2= a^2(t) [-dt^2 + dx^2] $$ So I start by: $$\left(\frac{1}{g^{1/2}}\partial_{\mu}(g^{1/2}g^{\mu\nu}\...
Dr. phy's user avatar
  • 333
1 vote
0 answers
103 views

Do all solutions to the Dirac equation transform as spinors?

Usually, the Dirac equation is introduced as the equation $D \psi = 0$, which is form invariant under Lorentz transformations ($\Lambda$), when $\psi$ transforms as a spinor $\psi' \to S(\Lambda) \psi$...
Sidd's user avatar
  • 1,230
4 votes
1 answer
234 views

Phase transition in Ising Model

Consider the NN Ising model as \begin{equation} H = -J \sum_{<ij>} \sigma_{i} \sigma_{j} - h \sum_{i} \sigma_{i} \end{equation} This model has a global $\mathbb{Z_{2}}$ symmetry in the absence ...
Santanu Singh's user avatar
0 votes
0 answers
45 views

Orthonormality of the mode functions of the Klein-Gordon field in a globally hyperbolic space

In chapter 3 of "Quantum fields in curved space" of Birrell and Davies, the authors make the following statements. Consider a real Klein-Gordon field $\phi$ in a globally hyperbolic ...
Ric's user avatar
  • 113
2 votes
1 answer
657 views

Massless limit of the Dirac theory

What is the physical reason why there is no mixing between left-handed and right-handed Weyl spinors in the massless case of the Dirac theory? Why does the chirality of a massive particle change ...
Michael's user avatar
  • 21
1 vote
1 answer
55 views

Action of a Scalar Field in Path Integral Formulation Peskin & Schroeder (Pag. 285)

I'm really confused on the discretization stuff on this chapter of P&S. My question is related to the computation of the Action in scalar field theory done in page 285. When they compute the ...
Leon's user avatar
  • 43
0 votes
0 answers
56 views

Symplectic basis for the real solution space of the covariant Klein-Gordon equation

In lecture 12 of his course on "Quantum field theory for cosmology", that can be found for free on the web, professor Kempf makes the following statements. Consider a real Klein-Gordon field ...
Ric's user avatar
  • 113
1 vote
0 answers
44 views

Q1.1(a) Sakurai Advanced Quantum Mechanics For energy-momentum tensor [closed]

I need to prove that the energy-momentum tensor density is defined as: \begin{equation} \mathcal{T}_{\mu\nu}=-\frac{\partial \phi}{\partial x_\nu}\frac{\partial\mathcal{L}}{\partial(\frac{\partial \...
Md Kaif Faiyaz's user avatar
3 votes
2 answers
130 views

Algebraic QFT from a Lagrangian

In physics, the fundamental description of physical theories frequently revolves around the concept of a Lagrangian. My expertise encompasses diverse algebraic formulations within the domain of ...
Gabriel Palau's user avatar

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