All Questions
26
questions
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
2
votes
1
answer
114
views
Schrodinger's picture and Heisenberg's picture in finding interaction ground state and two-point correlator
In section 4.2 of An Introduction to Quantum Field Theory by M.E.Peskin and others, it derives interaction ground state by observing the time evolution of ground state in free field theory (pg.86), ...
- 529
3
votes
1
answer
121
views
Explict Form of Ground State in Interacting Field Theory
In An Introduction to Quantum Field Theory by Peskin and Schroeder chapter 4, it has discussed about the ground state $|\Omega\rangle$ (where $|0\rangle$ is the ground state in free field theory) in ...
- 529
4
votes
2
answers
296
views
Derivation of Peskin & Schroeder eq. (4.29)
Background material:
These are the parts that I can follow.
Previously Peskin & Schroeder have derived already the expression of the interaction ground state $|\Omega\rangle$ in terms of the free ...
- 838
3
votes
2
answers
363
views
Proof that asymptotic particle states are free
In quantum field theory, It’s often said that the interacting annihilation operator (defined by the Klein Gordon inner product between the interacting field and a plane wave) behaves like the free ...
user310742
3
votes
1
answer
445
views
Asymptotic states in the Heisenberg and Schrödinger pictures
One can show that, in the interacting theory, the operators that create single-particle energy-momentum eigenstates from the vacuum are
\begin{align}
(a_p^{\pm\infty})^\dagger=\lim_{t\to\pm\infty}(...
- 1,060
3
votes
0
answers
201
views
Vacuum matrix elements
On page 87, section 7.2.3 titled Vacuum matrix elements of Quantum Field Theory and the Standard Model by Matthew Schwartz, the author writes that the vacuum state $|\Omega>$ is annihilated by the ...
- 904
4
votes
1
answer
419
views
Resolution of the Identity in Quantum Field Theory
In Peskin and Schroder's QFT book, on page 212, eq.7.2, they use the completeness relation in a derivation involving the two-point correlation function:
$$
\mathbf{1}=|\Omega\rangle\langle\Omega|+\...
- 1,421
2
votes
0
answers
148
views
Wave function of a real scalar field in interacting quantum field theory
In interacting real scalar field theory, if I intuitively define the "wave function" of a state as
$$\Psi(x)\equiv\langle\Omega|\hat{\phi}(x)|\Psi\rangle.$$
Does this wave function satisfy ...
- 21
4
votes
2
answers
407
views
Infinite time limit in two-point correlation function
I am reading the derivation of the two-point correlation function in Peskin and Schroeder (section 4.2). I don't understand the infinite time limit that is taken between eq. (4.26) and (4.27).
They ...
user255856
2
votes
0
answers
178
views
Interaction vacuum and free vacuum states [closed]
Why we prepare in and out states from interacting vacuum rather than free vacuum even if the total Hamiltonian is just free Hamiltonian at times far past and far future? What is really the difference ...
- 21
2
votes
1
answer
1k
views
$\phi^4$-theory, S-matrix Feynman diagram to first order from Peskin and Schroeder
This relates to page 111 in Peskin and Schroeder.
We have the $\phi^4$ S-matrix for a 2-particle to 2-particle scattering reaction:
$$-i\frac{\lambda}{4!}\int d^4x \langle p_1p_2|\mathcal T\left(\phi(...
- 6,963
2
votes
1
answer
385
views
Why does sending $T\rightarrow \infty(1-i\epsilon)$ in the slightly imaginary direction cause the $n=0$ term to decay slower?
This is in reference to equation 4.27 in Peskin and Schroeder. To derive a formula for the interacting vacuum in terms of the free vacuum we evolve the free vacuum in time with the full Hamiltonian ...
- 6,963
10
votes
4
answers
615
views
Why can we shift the field $\phi$, so that $\langle \Omega | \phi(x) | \Omega \rangle = 0$?
Problem
Introduction
In different derivations of the LSZ reduction formula the author makes a shift of the field $\phi(x)$
$$
\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