All Questions
18
questions
2
votes
3
answers
112
views
How do vacuum bubbles "dress" terms in the $S$-matrix numerator?
I am self-studying QFT using the book "A modern introduction to quantum field theory" by Maggiore. On page 124-125 he's doing the calculation in the interaction picture for a process with ...
- 613
0
votes
1
answer
124
views
The definition of the path integral
I still have big conceptual questions about the path integral.
According to (24.6) of the book "QFT for the gifted amateur" from Lancaster & Blundell the path integral is equal to
$$Z =\...
- 9,778
1
vote
0
answers
147
views
LSZ reduction formula relation
LSZ formula gives a relation between the scattering amplitudes and correlators as
$$\langle f |i \rangle = (-i)^{m+n}\int \Pi_{i=1}^m d^4x_, e^{ik_i'x_i (\Box_{x_i} -m^2)}\Pi_{j=1}^n d^4x_, e^{ik_j ...
- 3,464
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
1
answer
339
views
$S$-matrix elements in path integral approach
How to calculate $S$-matrix elements of quantum electrodynamics using path integral formalism?
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
2
answers
313
views
Which vacuum do I use for the path-integral?
In Weinberg, vol. 1, Section 9.2, Weinberg defines the in and out vacua as states with no particles (9.2.4):
$$a_{\rm in}|{\rm VAC,in}\rangle=0$$
$$a_{\rm out}|{\rm VAC,out}\rangle=0$$
He does this ...
- 1,647
3
votes
0
answers
292
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 ...
6
votes
1
answer
674
views
Why the vacuum-to-vacuum amplitude?
I am reading "QFT in a Nutshell" by Zee, and the beginning of the book progresses like this:
Section I.2: Show how $\langle q_F|e^{-iHt}|q_I\rangle=\int Dq\ e^{iS}$.
p. 12: Says that we ...
- 77
3
votes
1
answer
614
views
Clarification of Path Integral formulation
I am reading from Schwarz book on QFT the Path Integral chapter and I am confused about something. I attached a SS of that part. So we have $$\langle\Phi_{j+1}|e^{-i\delta H(t_j)}|\Phi_{j}\rangle=N \...
- 581
17
votes
2
answers
441
views
Quantum symmetries: $S$ or $Z$?
Let $I$ be the action of some QFT (gauge-fixed and including all the necessary counter-terms); $S$ the associated scattering-matrix; and $Z$ the partition function (in the form of, say, a path ...
8
votes
2
answers
488
views
In Feynman functional integrals why do we integrate the action over all time?
Say the definition of a propagator in quantum field theory is:
$$G_F(x,y)=\int \phi(x)\phi(y) e^{i S[\phi] } D\phi$$
where $S$ is the action. Why do we integrate the Lagrangian density from $t=-\...
user84158
2
votes
0
answers
877
views
Foundation of path Integral formulation of QFT, derivation and meaning of LSZ formulas
I'm currently studying path integral in quantum field theory. I am comfortable with path integrals, and also path integral formulation of QM, but I was asking if there is a self consistent coherent ...
13
votes
2
answers
3k
views
Physical meaning of partition function in QFT
When we have the generating functional $Z$ for a scalar field
\begin{equation}
Z(J,J^{\dagger}) = \int{D\phi^{\dagger}D\phi \; \exp\left[{\int L+\phi^{\dagger}J(x)+J^{\dagger}(x)}\phi\right]},
\end{...
- 1,336
4
votes
0
answers
992
views
Polology in Functional Integration
Completeness of Hilbert space (on-shell states) is a very powerful concept in canonical quantization, for example, to study the nonperturbative characteristics of the S-matrix, like polology (pole and ...
- 631