All Questions
11
questions
1
vote
0
answers
75
views
Scalar particle Compton scattering using relativistic Lagrangian formulation of electromagnetism
We know that parallel to scalar QED, a common formalism that describes a massive particle coupled to electromagnetism is through a relativistic worldline formalism, which writes
$$\mathcal{S}=\int\ ds\...
- 76
0
votes
0
answers
60
views
How diagrams with loop and several propagators contribute to $S$-matrix element?
I studied Feynman rules with Schwartz textbook and what caught my eye was diagrams such as second and third on this picture (diagrams to the second order of $g$ for $\mathcal{L} = \frac{g}{3!}\phi^3$ ...
3
votes
0
answers
152
views
Finding the interaction vertices
Given a Lagrange density $$\mathcal{L} = \frac{1}{2}\partial_\mu \phi \partial^\mu \phi - \frac{m^2}{2}\phi^2 - \frac{\lambda_3}{3!}\phi^3 - \frac{\lambda_4}{4!}\phi^4$$ where $\phi$ is a scalar field,...
- 298
2
votes
1
answer
96
views
More general propagator of a real scalar field
I have some Lagrangian containing a real scalar field $\phi$ with mass $m$. Let $A \in \mathbb{R}$ be some constant. The Lagrangian takes the form:
\begin{equation}
\mathcal{L} = -\frac{A}{2} (\...
- 1,187
3
votes
2
answers
466
views
What is the equivalence theorem in quantum field theory?
Let $L(\phi)$ be a Lagrangian and $\phi$ a quantum field.
The equivalence theorem says that the $S$ matrix remains invariant under field redefinition.
Let us take for example the Lagrangian $$L=\...
- 445
0
votes
0
answers
180
views
Proof of Weinberg effective field theorem?
In the book Effective field theory at page 6 there is this Weinberg's theorem
To any given order in perturbation theory, and for a given set of asymptotic states, the most general possible ...
- 445
2
votes
0
answers
219
views
Classical action as $S$-matrix generating functional at the tree-level
I have seen repeated statements that the $S$-matrix generating functional at the tree-level is the same as the action calculated on the classical solutions of the equation of motion corresponding to ...
- 93
1
vote
0
answers
159
views
Connected part of $S$-matrix generating functional
I am currently studying an article by A.Jevicki et. al. (https://doi.org/10.1103/PhysRevD.37.1485) and I am a little confused. They say that the generating functional of the $S$-matrix is related to ...
- 93
2
votes
1
answer
360
views
S-matrix expansion for the $\phi^4$ theory and the interaction picture
My question is about the perturbative expansion of the S-matrix using Dyson's expansion.
Let the Lagrangian density of the $\phi^4$ theory be
\begin{equation}
\mathcal{L} = \frac{1}{2}\left[\partial_\...
- 107
10
votes
4
answers
615
views
Why can we shift the field $\phi$, so that $\langle \Omega | \phi(x) | \Omega \rangle = 0$?
Problem
Introduction
In different derivations of the LSZ reduction formula the author makes a shift of the field $\phi(x)$
$$
\phi'(x) = \phi(x) - \langle \Omega | \phi(x) | \Omega \rangle,
$$
and ...
- 199
3
votes
0
answers
723
views
S-matrix for $\phi^3$ theory
In the book Quantum Field Theory for the gifted amateur by Tom Lancaster & Stephen J Blunden, in the chapter about expanding the S matrix they give an example using the $\phi^4$ Langrangian, $$
\...
- 88