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
1 vote
0 answers
33 views

Why do we use pole mass in LSZ formula?

I am reading "Quantum Field theory and the Standard Model" by Schwartz. It derives LSZ formula in chapter 6, \begin{equation} \langle f|S|i\rangle =\left[i\int d^4x_1e^{-ip_1x_1}(\Box + m^2)\...
1 vote
0 answers
27 views

Specific Heat of SYK Model

For the SYK model, One can prove that for $N\to \infty$ the total energy can be written as the derivative of the imaginary time Green's function (see related question): $$\langle H \rangle=\frac{N}{4} ...
  • 1,197
0 votes
0 answers
21 views

Field Theory perspective needs tested [closed]

This question involves 'fields'. I compare gravitational fields to electromagnetic fields and also consider how to understand the related waves. The reason for this is that I know that nearfield to a ...
-1 votes
1 answer
32 views

Integration with the Dirac delta function

I have equation like $$I = \int \prod\limits_{i=1}^{N} dr_{i}e^{-\mathrm i\beta \int dr \sum\limits_{i}q_{i}\delta(r-r_{i})\phi(r)}.$$ First, I did integration in the exponent and got \begin{align} I &...
0 votes
0 answers
18 views

Can we discuss about setting partition function of 1:1 salt electrolyte?

I have 1:1 salt whose density is described by $\rho(r) = \sum\limits_{i=+,-}\sum\limits_{j=1}^{N_{i}}q_{i}\delta(r-r_{ij})$, where $i$ denotes ion species such as +, - and $j$ represents number of $j$ ...
0 votes
0 answers
57 views

Exercise 14.1 from Schwartz's Quantum Field Theory

I'm trying to understand the proof of Exercise 14.1 from Schwartz's Quantum Field Theory offered Here For the most part, the proof makes sense to me. However, I am not sure how the equality on the ...
2 votes
0 answers
105 views

Mathematically Rigorous Introductory Resources for Condensed Matter Physics

I am looking for textbooks, lecture notes, lecture videos on rigorous introductions to condensed matter physics. I'd prefer to not be referred to monographs for an introduction as they tend to be ...
0 votes
0 answers
10 views

Where I should start from to study statistical field theory of electrolyte? [closed]

I recently have interest in statistical field theory (SFT) of electrolytes, mostly studied by Henri Orland and David Andelman. I watched all his video lectures in the youtube. Now, I want to study the ...
0 votes
0 answers
16 views

Frequency-dependent interaction will be retarded in time

In condensed matter physics, I often heard that Frequency-dependent interaction will be retarded in time. I don't quite understand this statement. Can anyone give me some arguments or references? ...
  • 1,713
2 votes
1 answer
80 views

Peskin and Schroeder's QFT eq. (9.14): Gaussian momentum field integration of phase space path integral

On Peskin and Schroeder's QFT book page 282, the book considered functional quantization of scalar field. First, begin with $$\left\langle\phi_b(\mathbf{x})\left|e^{-i H T}\right| \phi_a(\mathbf{x})\...
  • 551
0 votes
1 answer
73 views

Relativistic invariants of a classical field in 4D fashion: why the relation between the components of the current density holds?

I'm trying to understand how is justified the following relation between the first component of the current density integrated over the volume and the scalar product of the 4-vector current density ...
0 votes
1 answer
35 views

Relativistic derivation of energy for a photon inquiry

In Susskind's Special Relativity & Classical Field Theory, he presents the following argument for the energy of massless particles: We know there is a relationship between the components of the ...
1 vote
1 answer
64 views

Doubt in classical field theory/electromagnetism

What is the basic difference between electromagnetic fields, electromagnetic waves and constant electromagnetic fields?
  • 335
1 vote
1 answer
84 views

Scale factor in conjugate scalar field inside conformally flat spacetime

Consider a lagrangian density of a scalar field $$ \mathscr{L} = \frac{1}{2} \partial_\alpha \phi \partial^\alpha \phi - \frac{1}{2} m^2 \phi^2 $$ inside a conformally flat spacetime with scale factor ...
  • 760
1 vote
0 answers
34 views

Conservation law for quantum field theory with boundary

Consider a scalar field theory defined on 1+1 D space time where the space is limited to [-L,L]. The Lagrangian density of the theory is \begin{equation} \dot\Phi^2-(\partial_x\Phi)^2-h\partial_x\Phi(...
3 votes
1 answer
312 views

Similarity transformations in QFT

I am trying to understand the gaps in my knowledge that prevents me from completely understanding quantum field theory. Sometimes I ask pretty basic questions, but please excuse me if I make a blunder....
3 votes
1 answer
218 views

What's the difference between the conjugate momenta in the classical mechanics and in field theory?

In the classical mechanics the conjugate momenta was typically a derivative of the Lagrangian, i.e. \begin{equation} p_i=\frac{\partial L}{\partial \dot q_i}.\tag{1} \end{equation} However, in the QFT ...
0 votes
1 answer
23 views

How do we know that field produced by contact forces is time invariant?

I don't get the fact that action reaction forces act at the same time(Newton's third law). If this is so then it shouldn't be true for time invariant field since they would reach from source to sink ...
0 votes
1 answer
23 views

Clarification for derivatives under a change of variables

In Special Relativity and Classical Field Theory by Susskind, he says that we can imagine a function of $(x+ct)$, then he says that we can consider its derivatives and easily see that $$\frac{\...
1 vote
2 answers
62 views

Meaning of Bogolyubov transformations

I'm reading "Introduction to Quantum Fields in Classical Backgrounds" - V. F. Muckhanov, S. Winitzki. I don't understand what kind of "freedom" makes Bogolyubov transformation ...
  • 760
1 vote
1 answer
77 views

Question on asymptotic flatness

What is the theoretical argument for the asymptotical flatness of the four-potential? Can one assume asymptotical flatness for the scalar dilaton field as well?
0 votes
0 answers
27 views

Question about dilaton monopole interaction derivation

I am trying to understand how one derives the dilaton monopole interaction. In "Black holes and membranes in higher-dimensional theories with dilaton fields", Gibbons and Maeda mentioned ...
2 votes
2 answers
33 views

In the context of field-theoretic constrained dynamics, do we have the freedom to choose the Lagrange multipliers to be time-independent?

Let us work in a box $(t,\overrightarrow{x}) \in [0,1] \times [0,1]^3$. For any function on this box, we impose some Dirichlet boundary condition on the temporal direction and periodic boundary ...
  • 1,169
0 votes
2 answers
63 views

Spacetime transformation in field theory

I'm trying to understand Noether's theorem in QFT. I stumbled across one small doubt, Please explain why is there a negative sign instead of plus sign in the following:
0 votes
1 answer
47 views

Intuitive interpretation of the scaling dimension of an operator?

I am reading Field Theories of Condensed Matter Physics by Fradkin and in equation (4.10) it shows that an operator transforms irreducibly under scalings as $$\phi_n(xb^{-1}) = b^{\Delta_n}\phi_x(x)$$ ...
1 vote
0 answers
25 views

Parity transformation of spinor helicity brackets

I'm trying to figure out why a parity transformation $P: (E, \textbf{p} ) \rightarrow (E, - \textbf{p})$ implies $\langle i \ j \rangle \rightarrow - [i \ j]$ and $[i \ j]\rightarrow - \langle i \ j \...
0 votes
0 answers
37 views

How to decompose Dirac spinor into plane wave solutions?

Suppose that we know Dirac spinor $\psi$ (as complex numbers) in every point in 3d space (4th dimension is time) How do we decompose it into plane wave solutions $u^s(p) e^{ipx}$ and $v^s(p) e^{ipx}$? ...
1 vote
0 answers
34 views

Non-local Euler-Lagrange equations and Noether theorems

Following up my Noether theorem issues: how can Euler-Lagrange and Noether theorems be formulated for non-local lagrangians? Two examples from the literature: Example 1. Let $L(\phi, F(\phi))=-\dfrac{...
  • 5,697
1 vote
1 answer
55 views

What are the differences between electroweak interactions before and after unification?

I am very confused by this point, although its mathematical description is not hard. I still cannot see how these two theories are "unified", which term in lagrangian indicates this ...
  • 935
1 vote
0 answers
68 views

What is the meaning of gauge theory and Yang-Mills theory? [duplicate]

I would appreciate it if you guys would help me to understand the idea behind these two concepts: Gauge field and Yang-Mills theory. What I think I understand is: Suppose we have a Lagrangian that ...
  • 590
1 vote
0 answers
35 views

How would we integrating high energy part of a relativistic quantum field theory to get a non-relativistic theory?

Relativistic quantum field theory (RQFT) is a after spring of quantum theory and special relativity. A novel thing in RQFT is the existence of anti-particle. That is, consider a relativistic field $\...
  • 21
0 votes
0 answers
26 views

Charge conjugation and Parity for QCD $\theta$ term

I am studying Charge Conjugation ($C$) symmetry and Parity symmetry ($P$) on QCD $\theta$ term: $\tilde{G}G= \frac{1}{2}\epsilon^{\mu \nu \lambda \rho}G^a_{\mu \nu}G^a_{\lambda \rho} \propto G^a_{0i}G^...
  • 935
0 votes
0 answers
43 views

Can Chiral symmetry violating term in lagrangian violate charge conversation?

The regular Lagrangian is $\mathcal{L}=\bar{\psi}(i\gamma^\mu\partial_\mu-m)\psi$ If we add a chiral violating term $\mathcal{L}=\bar{\psi}(i\gamma^\mu\partial_\mu-me^{i\theta\gamma^5})\psi$ For the ...
0 votes
0 answers
31 views

Dynamical critical exponent in stochastic vector model

For stochastic $O(N)$ model given by: $$S[\psi,\phi]=\int \frac{d\omega\, dk^D}{(2\pi)^{D+1}} \left( \vec{\psi}(-k,-\omega).\vec{\phi}(k,\omega) \left(-i\omega + \gamma k^2+r \right) -2T\vec{\psi}(-k,-...
  • 1,197
0 votes
1 answer
36 views

Deriving equation describing fermion-antifermion field

We know the Lagrangian of massless interacting Dirac field $\mathcal{L}=\bar{\psi}i\gamma^\mu(\partial_\mu-iA_\mu)\psi$ Now consider charge conjugation operator $C=i\gamma^2$ The Lagrangian for charge ...
1 vote
1 answer
106 views

Noether charge on complex scalar field

For complex scalar field, we write the Lagrangian as: $$ \mathcal{L}=\partial_{\mu}\phi^{*}\partial^{\mu}\phi-m^2 \phi^{*}\phi $$ with the $U(1)$ symmetry, and under infinitesimal transformation: $$ \...
  • 551
2 votes
2 answers
214 views

How is the Feynman propagator (Green's function) connected with the field?

Let's take a look at the Feynman propagator for a massive scalar field: $$D_F(x-y)=\int\frac{dp^3}{(2\pi)^3}\int\frac{dp^0}{2\pi}\frac{ie^{-ip \cdot (x-y)}}{p^2-m^2}$$ We can use this as the Green's ...
  • 1
0 votes
1 answer
68 views

Classical Mechanics Lagrangian from Underlying Quantum Field Theory

Does the K - T classical mechanics Lagrangian emerge from some structure of the Lagrangian of the underlying QFT?
0 votes
1 answer
40 views

Doubt on: $G = SU(2)_{L} \times U(1)_{Y}$ representations, the Chiral Spinor bundle and the "split" of covariant derivative for $G$

Firstly, I've made two other questions $[1]$,$[2]$ concerning the same situation, but I think that this one will clarify better what I'm trying to understand. I'm following the text book $[3]$ and I ...
  • 2,741
1 vote
2 answers
61 views

Conjugate momentum for constant scalar field

I am reading Witten's Why Does Quantum Field Theory in Curved Spacetime Make Sense?, and I am caught up on what appears to be a straightforward computation. The discussion (on page six) centers around ...
  • 194
1 vote
0 answers
38 views

Deriving Euler-Lagrange equation for vector field in curved spacetime

I'm trying to derive covariant Euler-Lagrange equations for a vector field. The variation of the action should be \begin{gather*} \delta S = \int \text{d}^n{x} \sqrt{|g|} \left( \delta\phi^\mu \frac{\...
  • 760
1 vote
0 answers
36 views

What are the beta functions for electroweak and strong constants of interactions?

As the title says I want to find beta function for electroweak and strong constants ($g$ for W-boson, $g'$ for B-boson and $g_s$ for gluons) Beta function is the function that describes change in ...
1 vote
0 answers
51 views

Non-minimally coupled inflation — expansion

In the Wikipedia article on "Inflaton" there appears the following formula: $$S=\int d^{4}x \sqrt{-g} \left[\frac{1}{2}m^2_{P}R-\frac{1}{2}\partial^\mu\Phi\partial_{ \mu }\Phi-V(\Phi)-\frac{ ...
  • 11
3 votes
1 answer
161 views

Pauli-Lubanski vector for Maxwell's equation

In the book quantum field theory by Itzykson and Zuber, page 53, the authors prove that Dirac's equation has spin 1/2 by showing that if $\psi$ is a solution to Dirac's equation, then compute that $\...
1 vote
1 answer
56 views

Field shift in free Klein-Gordon theory

I am reading Peskin & Schroeder Ch9 and am stuck on a calculation going from equation 9.36. The problem is essentially a change of variable of a Klein-Gordon field. Beginning, we have an integral ...
  • 165
0 votes
0 answers
35 views

Chern-Simons forms: interpretation and generalizations

Studying again differential geometry, anomalies and topology, I wondered if there is ANY physical interpretations (in terms of QFT or even classical field theory) of the Chern-Simons forms, via vacuum,...
  • 5,697
0 votes
3 answers
97 views

Why Electron Quantum Field Wants Little Energy But Photon Field Doesn't

In this Quora post: https://qr.ae/pv5tac, it states that the electron quantum field "wants" to reduce the energy it has, so when a particle and an anti-particle interact and the charges ...
1 vote
2 answers
93 views

What's the difference between these two lagrangian? [closed]

The lagrangian for scalar field is defined as, $$L=L(\phi,\partial_{\mu}\phi,\partial_{\mu}\partial_{\nu}\phi)\tag{1}$$ $but$ there is also another lagrangian which is defined as, $$L=L(\phi,\nabla_{\...
3 votes
2 answers
173 views

Help with an integral in Peskin & Schroeder - QFT

In chapter 2, page 27, eq. 2.51, P&S solves the following integral - $$ \frac{4\pi}{8\pi^3} \int _0 ^\infty dp \ \frac{p^2 \ \ \ e ^{-it\sqrt{p^2 + m^2}}}{2\sqrt{p^2 + m^2}}.\tag{2.51}$$ My ...
0 votes
1 answer
33 views

How to properly get low energy effective field theory of superfluid?

I am following chapter 3 of X. G. Wen's book "Quantum Field Theory of Many-Body Systems". The following action for a weakly interacting Bose gas is derived: $$S[\varphi,\varphi^*] = \int dt \...

1
2 3 4 5
51