3
votes
0answers
104 views

Feynman rule for deriative interaction: an example

Consider a theory for a finite number of real scalar fields $\phi _i$ with interaction terms of the form $$ -\lambda _{ijk}\phi _i\partial _\mu \phi _j\partial ^\mu \phi _k, $$ with the sum over ...
2
votes
2answers
170 views

Potential in Quantum field theory

I studied free particle field like Dirac field and Klein Gordon field. My question is about interaction. How can I put a potential term in the Lagrangian density? $\mathcal{L} ...
2
votes
0answers
69 views

In QFT, how can it be shown that the field out, ${\phi_{out}}$, is a free field if the field in, ${\phi_{in}}$, is a free field?

In the Dirac picture of QFT interacting fields, if the field in, ${\phi_{in}}$, is a free field, then I know that the field out, ${\phi_{out}}$ should also be a free field. How can this be shown? ...
3
votes
1answer
191 views

Deriving Feynman Rules (with the presence of a gluon field strength tensor)

If I have a Lagrangian of the form: $$ \mathcal{L} = k \bar{\psi} \varepsilon^{\mu \nu} \lambda^a \phi G^a_{\mu \nu} + h.c. $$ [where $\phi, \psi$ are fermions, $\lambda^a$ are Gellmann matrices, ...
3
votes
1answer
332 views

Gell-Mann Low Theorem and Vacuum Energy

I know that the sum of vacuum bubbles can be related to the Vacuum energy, but I'm trying to understand how this follows from the Gell-Mann Low theorem/equation. My question will use equations from ...
1
vote
0answers
101 views

Range of forces from mass of force carrier?

Why is $\frac{\hbar}{mc}$ a good estimate of the range of the four forces, where $m$ is the mass of the carrier particle of the force? Inputting the pion mass gives $1.4\ \mathrm{fm}$ for the hadronic ...
10
votes
1answer
727 views

Interpretation of derivative interaction term in QFT

I am trying to understand what a term like $$ \mathcal{L}_{int} = (\partial^{\mu}A )^2 B^2 $$ with $A$ and $B$ being scalar fields for instance means. I understand how to draw an interaction term in ...
4
votes
2answers
138 views

Interpretation of an “interaction” term

In QFT a polynomial (of degree >2) in the fields is said to be an interaction term, Ex.: $\lambda\phi^4$. Question Is it possible to give an interpretation to terms like $\frac{1}{\phi^n}$? (for ...
1
vote
1answer
253 views

How does the dressed Klein-Gordon propagator look in position space?

The free Klein-Gordon propagator in momentum space $\sim (p^2-m^2+i\epsilon)^{-1}$ has just a single pole at $p^2=m^2$. The passage to Fourier space is difficult but possible. The result is very ...
2
votes
2answers
460 views

Why $\lambda\phi^4$ theory, where $\lambda>0$, is not bounded from below?

Why the following interaction, in QFT, $$\displaystyle{\cal L}_{\rm int} ~=~\frac{\lambda}{4!}\phi^4$$ where $\lambda$ is positive, represents a theory that is unstable (or unbounded from below as it ...
6
votes
1answer
104 views

Expectation values of interacting fields

I was motivated to ask this question by the equality claimed in equation 10.3.3 of Weinberg's volume 1 of QFT books. My interpretation of that, If $O_s$ is a quantum field of spin $s$, $\psi_s$ is ...