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-3
votes
2answers
85 views

Why can't two real photon, gluon, graviton, and $W$ and $Z$ fields interact by means of their virtual counterparts (the mediators of the process)?

It is a fact that two real (massless) photons, gluons, or gravitons can't react by means of their virtual counterparts (for example, two external photons that interact via one of these massless ...
1
vote
1answer
80 views

Are force carrying particles always virtual particles?

Of course we have real (i.e. non-virtual) photons, but when photons play the role of "force carrier" are they virtual? Same thing for gluons. Real gluons have been detected, but when playing the role ...
4
votes
1answer
73 views

Quantum field theory with only 3-point vertexes

Given an arbitrary quantum field theory, can I always write it in terms of another (different) quantum field theory containing only operators with 3 fields? (i.e. vertexes with 3 legs) I guess that ...
1
vote
1answer
76 views

Why coupling constants with negative mass dimensions lead to non-renormalizable theories?

can somebody explain or point to the relating mathematics showing Why coupling constants with negative mass dimensions lead to non-renormalizable theories?
0
votes
0answers
23 views

Deriving effective interactions, e.g. phonon-mediated electron-electron interaction

Upshot of the question: how can I derive the effective electron-electron interaction brought about by the electron-phonon interaction? I've read derivations of the electron-phonon interaction and ...
0
votes
2answers
85 views

Variance of an interacting quantum field in its vacuum state

A non-interacting quantum field $\hat{\phi}(x)$ can be decomposed into $a_{\textbf{k}}$ and $a_{\textbf{k}}^\dagger$. This enables us to calculate the variance of a free field. For example, the ...
2
votes
1answer
77 views

Interacting conformal field theories in spacetime dimensions higher 6?

Are there any papers which directly tackle the question of whether or not there exists interacting CFTs in spacetime dimensions higher than 6? It has been proven that there do not exist any ...
1
vote
0answers
44 views

Non-minimal coupling between a neutral atom and the EM field

Let us say that I have neutral bosonic atoms interacting with an EM field. I can write down the Lagrangian as \begin{align} \mathcal{L}=\eta^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi^{\dagger}-m^2|...
3
votes
1answer
141 views

What is the definition of “force” in quantum field theory?

In quantum field theory, there are certain interactions that we seem to associate with the action of "forces." For example, the exchange of a gauge boson between two matter particles is associated ...
1
vote
1answer
42 views

How to know what type of diagram contributes to a two-to-two process?

There are 3 types of diagrams that can contribute to a two-to-two process; the $s$-channel, $u$-channel and $t$-channel. How do I know what diagrams can contribute to a process? I know that in QED, ...
0
votes
0answers
48 views

Propagators in interaction with derivatives

Given a Lagrangian density containing an interaction with derivates, it's easy how to guess the Feynman rules for vertexes. However i was wondering about propagators: in S-matrix expansion it's ...
6
votes
1answer
94 views

QFT Why do in and out states have a non-trivial overlap?

Im trying to follow chapter 4 about interacting fields in Peskin and Schröder. They define the S matrix by $_{out}<p_1 p_2 | k_a k_b>_{in} = <p_1 p_2 | S | k_a k_b>$, where $S = \lim_{T\...
0
votes
0answers
61 views

Calculation of a 4-point function by path integrals

In Srednicki's book in chapter 8 a four-point function is computed as a sum of products of propagators: $$<0|T\phi(x_1)\phi(x_2) \phi(x_3)\phi(x_4)|0> = \frac{1}{i^2}[\Delta(x_1 -x_2)\Delta(...
4
votes
1answer
288 views

Feynman rules out of the Lagrangian

Accordingly to chapter 10, section 10.6 Feynman Rules of 'Introduction to Elementary Particles' by David Griffiths, there is a way to extract the vertex and propagators just by inspection of the ...
3
votes
1answer
170 views

Can interacting quantum field theory describe more than just scattering?

From my understanding we do not yet know how to make much out of interacting QFT other than scattering amplitude at asymptotic infinity. (Correct me if I misunderstand.) But path integral, in ...
1
vote
0answers
102 views

Why isn't energy conserved in time-ordered diagrams?

I'm new to particle physics, and I'm reading chapter 5 of Prof. Mark A. Thompson's "Modern Particle Physics", which talks about Time-ordered perturbation theory vs QED. However, in page 119 he wrote: ...
1
vote
0answers
182 views

Kallen-Lehmann representation derivation

I'm trying to understand the derivation of the Kallen-Lehmann representation given in Peskin & Schroeder (pages 211-214). I would really appreciate if anyone on here could answer a few questions I ...
2
votes
1answer
67 views

Clarifications on the assumptions made for QFT interactions

I am reading about scattering and S-matrix in the context of quantum field theory and although I understand the math and the physical interpretation of the final results, I am confused about some ...
1
vote
0answers
16 views

Quantum Field interaction transferred via “exchanging fermions” [duplicate]

In Standard Model every fundamental interaction is described by means of exchanging gluons of particular kind. It is very natural as gluons has spin with values given by inteegers, and can share the ...
2
votes
0answers
83 views

Feynman rules for anomalous vertex [closed]

We can read Feynman rules directly from the lagrangian in the simplest cases, but for the following lagrangian I am a few stuck $\mathcal{L}=4g\phi\epsilon^{\mu\nu\rho\sigma}\partial_{\mu}A_{\nu}\...
0
votes
1answer
65 views

Decay and scattering terms in a field theory Lagrangian

Consider two genetic terms in a generic Poincare invariant quantum field theory: A trilinear term of the form $\phi_1\phi_2\phi_3$, and a quartic term of the form $\phi_1\phi_2\phi_3\phi_4$ where ...
4
votes
1answer
277 views

Feynman diagram of spin Hamiltonian

I am confused about the Feynman diagrams of spin Hamiltonian, for example, the Heisenberg model, the quartic terms like this $[1]$: \begin{align} V &= -\frac{z}{4}\frac{J}{N}\sum_{1,2,3,4}\delta_{...
7
votes
2answers
551 views

Propagator Correction in $\phi^4$ theory - why doesn't this secular growth break perturbation theory?

The free propagator for a massive $m\neq0$ real scalar field is the following: $$ G_{0}(x,y) \ = \ \int \frac{d^{4}p}{(2\pi)^4} \frac{e^{i p \cdot (x-y)}}{p^2 +m^2 - i \epsilon} $$ It is a well-...
2
votes
1answer
163 views

Is there a Quantum-Mechanics analog to QFT's quartic $\lambda \phi^{4}$ interaction?

In QFT; for the quartic-interacting real scalar field $\phi$ we have the Lagrangian density: $$ \mathcal{L} \ = \ \frac{1}{2} \left( \partial^{\mu} \phi \right)\left( \partial_{\mu} \phi \right) + \...
5
votes
2answers
687 views

Why are derivatives in interaction terms treated differently from derivatives in the kinetic term?

I know that derivative couplings in a Lagrangian interaction, such as $$\mathcal{L}_{int} = \lambda \phi (\partial_{\mu}\phi)(\partial^{\mu}\phi)$$ bring down two momentum factors into the matrix ...
1
vote
0answers
86 views

Visual simulation of elementary particles and interactions thererof?

Pardon me for a very stupid question, but knowing that SM predicts so much about sub-atomic particles, their interactions and whatnot, means that we have formalized these into some sorts of equations,...
4
votes
1answer
90 views

Are interacting and free field operators equal in the Schroedinger picture?

Taking for example a scalar hermitian field (which in the free case would obey to the Klein-Gordon equation), is it true that in the Schroedinger picture the following expression hold true both in a ...
4
votes
0answers
305 views

How can I see where this formula for a general vertex factor comes from?

I have been reading Srednicki from the beginning and doing all the exercises, and I hit a big roadblock at Q10.4, as I can't seem to figure out what Srednicki is doing in his solution. Luckily, I ...
2
votes
1answer
107 views

Force via “exchange particles” or “via field”

More or less I have come across two concepts to explain non contact forces: FIELD CONCEPT: modification of space by the source which in turn produces force on the other (That is in my classroom ...
2
votes
1answer
250 views

Status of particles in interacting QFT

From my readings in QFT and answers such as this, I've read that the concept of particles and particle-number in interacting systems becomes ill-defined in QFT. Of course, in the real world, a number ...
1
vote
0answers
89 views

Finite-Temperature $\phi^{4}$ theory - Why is the massless $T\neq 0$ contribution diverging?

I'm following Chapter 3 of Kapusta and Gale's Finite-Temperature Field Theory here. I'm considering the following integral (the unrenormalized self-energy evaluated at zero-four momentum): $$ \...
2
votes
1answer
253 views

Calculating vertex factor for scalar field theory

I am practising basic QFT and am having some trouble with calculating the vertex factor of an interacting theory involving two real scalar fields, $\phi_{1}$ and $\phi_{2}$. If I create a generic ...
4
votes
2answers
431 views

S-matrix derived directly in terms of the interaction picture

Consider a quantum mechanical system with Hamiltonian $$H=H_0+H_{\text{int}}.$$ Consider $H_0$ to be time-independent, so that its associated time-evolution operator is $U_0(t,t_0)=e^{-i(t-t_0)H_0}$....
3
votes
1answer
661 views

Computing a Gaussian Path Integral (with integral in exponent)

I have been studying the path integral approach to QFT and set myself the challenge of starting from a $\phi^3$ interaction Lagrangian and following the method through to completion. I started with: $$...
4
votes
1answer
239 views

Vacuum bubbles and LSZ reduction

Let me preface this by saying that I don't have an issue with this: $$ \langle\Omega|T\phi_H\cdots\phi_H|\Omega\rangle = \frac{\langle 0|T\phi_I\cdots\phi_IS|0\rangle}{\langle 0|S|0 \rangle}, $$ ...
17
votes
1answer
548 views

QFT and its non-rigorous assumptions

I have been trying to figure out all the non-rigorous assumptions of QFT (as performed in an operator theory) that allow it to function as it currently is. So far, the three big candidates I found are ...
31
votes
3answers
2k views

What is the issue with interactions in QFT?

I've started studying QFT this year and in trying to find a more rigorous approach to the subject I ended up find out lots of people saying that "there is no way known yet to make QFT rigorous when ...
1
vote
0answers
429 views

$\phi^{4}$ theory Feynman rules

One of the momentum space Feynman rules in $\phi^{4}$ theory (for correlation functions) is that for an external point with 4-momentum $p$ (with direction headed towards the external point), we need a ...
1
vote
1answer
373 views

Computing S-Matrix Elements from Feynman Diagrams

In Peskin and Schroeder (PS), the Feynman rules for calculating correlation functions are first presented. Only terms involving all field contractions need to be considered. In Section 4.6, this is ...
4
votes
3answers
587 views

$\phi^{4}$ theory

Consider a scalar field theory with a $\phi^{4}$ interaction term $$\mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)^{2}-\frac{1}{2}m^{2}\phi^{2}-\frac{\lambda}{4!}\phi^{4},$$ where $\lambda\ll 1$. I am ...
1
vote
1answer
115 views

Are all field interactions carried out through force-mediating particles?

To my knowledge, all field interactions are carried out through force-mediating particles. For example, electromagnetic interactions are carried out through exchanging photons. However, under the ...
0
votes
1answer
484 views

S-matrix and time-evolution operator

On page 108 of Peskin Shroeder. If the formula $$ |\mathbf{P_\cal{A}}\mathbf{P_\cal{B}} \rangle \propto \lim_{T\to \infty(1-i\epsilon)} e^{-iHT}\, | \mathbf{P_\cal{A}}\mathbf{P_\cal{B}} \rangle_0 \...
1
vote
0answers
46 views

Can the MSW effect be modified by non-standard neutrino-neutrino interactions?

The MSW effect describes how propagation of neutrinos through matter can resonantly enhance the neutrino mixing. The reason for this enhancement is that the presence of electrons in matter changes the ...
0
votes
1answer
68 views

Energy-momentum relation for dressed particles and how interactions change mass

When a free real scalar field $\phi(x)$ described by the Lagrangian \begin{equation}\mathscr{L}=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2\end{equation} is quantized, a quanta ...
9
votes
1answer
3k views

How can the Feynman rules be read off the Lagrangian?

I am reading Peskin. In his functional methods chapter he says that (i) "Once the quadratic terms in the Lagrangian are properly understood" and (ii) "The propagators of the theory are computed" ...
2
votes
1answer
115 views

Why is it that the interacting fields cannot be decomposed into Fourier modes like free fields?

In quantum field theory, a free scalar field can be decomposed into Fourier modes. But why is that, an interacting field cannot have Fourier decomposition? Can we not decompose any arbitrary ...
4
votes
1answer
1k views

What's the significance of a dimensionless coupling constant?

In the preface to Mark Srednicki's QFT book (an online draft version can be found here http://web.physics.ucsb.edu/~mark/qft.html), Mark mentions that the $\phi^3$ theory in 6 dimensions would be a ...
7
votes
1answer
211 views

$\phi^{n}$ quantum scalar field theories where $n$ is not an integer

Consider a quantum scalar field theory with interaction terms of the form $\phi^{n}$, where $n$ is not an integer. Where are some examples of widely-studied quantum field theories which involve such ...
5
votes
1answer
256 views

Feynman diagram representation of variational derivative of S-matrix

For quite some time I am struggling to understand section 6.4 in Weinberg volume 1. He observes there that if interaction hamiltonian density is extended by coupling to c-number fields $\epsilon$, $$ \...
2
votes
2answers
885 views

About the notion of the self-interaction of a field

In QFT it's very common to hear (read) about the self-interactions of a field. e.g. there's the self-interaction terms of the Higgs field, that come with $\lambda^3$ and $\lambda^4$, right? But I ...