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Tagged with path-integralpropagator
116 questions
7votes
2answers
313views
Tree-level of two-point function
I am currently learning AQFT (advanced QFT) with the lecture notes of Osborn (I've had a course on QFT but this was not with the path integral formalism) and at some point he says the following $$\...
- 105
1vote
1answer
89views
Performing the shift in the Dirac generating functional to complete the square
I'm following Peskin & Schroeder p.302, and am trying to show that the generating functional for the Dirac field can be written as $$ Z\left[\bar{\eta}, \eta\right] = Z_0 \exp \left[-\int d^4 x d^...
- 33
1vote
1answer
262views
The path integral for $\phi^3$ theory solved explicitly in terms of Feynman diagrams
I'm currently working through Srednicki's book on QFT and I try to better understand the path integral and the Feynman diagrams. Equation 9.11 reads $$\begin{align}Z_1(J) \propto& \sum_V\frac{1}{V!...
1vote
0answers
62views
Time translation invariance of the two-point function
Please refer to this 2023 lecture note by Douglas Ross. In this note, they compute the generating functional for the correlators given by Eq (4.7) for a harmonic oscillator action. $$\begin{aligned} &...
- 1,552
2votes
1answer
103views
What is the physical meaning of the normalization of the propagator in quantum mechanics?
Suppose we have a quantum field theory (QFT) for a scalar field $\phi$ with vacuum state $|\Omega\rangle$. Then, in units where $\hbar = 1$, we postulate that the vacuum expectation value (VEV) of any ...
0votes
1answer
72views
Why isn't the free particle particle a function of the absolute value of the difference of the time?
The one-dimensional free particle Lagrangian is given by $$ \mathcal{L} = \frac{m}{2}\dot x^2. $$ Since the Lagrangian is translation-invariant, one usually argues that the propagator can only be a ...
2votes
2answers
219views
Time ordering for a time-dependent Hamiltonian in Path integral derivation
I am currently taking a class on Quantum Field Theory. The propagator was defined as: $$K(x,t;x',t') = \langle x|\hat{T}e^{{\frac{-i}{\hbar}\int_{t}^{t'}dtH(t)}}|x\rangle$$ where, $\hat{T}$ is the ...
- 123
2votes
1answer
130views
The definition on vacuum-vacuum amplitude with current in chapter of External Field Method of Weinberg's QFT
I'm reading Vol. 2 of Weinberg's QFT. As what I learnt from both P&S and Weinberg, the generating function is defined as $$ Z[J] = \int \mathcal{D}\phi \exp(iS_{\text{F}}[\phi] + i\int d^4x\phi(x) ...
1vote
1answer
59views
Fermionic propagator [closed]
Given the fermionic generating functional $$Z[\eta]=\ det^{\frac{1}{2}}(K_{ij})e^{-\frac{i}{2}\eta_{i}G^{ij}\eta_{j}},\tag{1}$$ where $$G^{ij}=K^{-1}_{ij}$$ is the Green function of our theory, then ...
- 81
1vote
0answers
160views
Derivation of massive photon propagator
I'm trying to derive the massive photon propagator using the path integral formalism for a theory with $$ \mathcal{L} = -\dfrac{1}{4} F_{\mu\nu} F^{\mu\nu} + \dfrac{1}{2} m^2 A_\mu A^\nu, \text{with } ...
1vote
1answer
90views
Time ordered correlator from path integral: equation of motion?
Consider a Lagrangian $L(\phi)$ for a field $\phi$ (assume it is a free real scalar for simplicity). Then the time ordered propagator can be expressed as a path integral $$ \langle\Omega|T\{ \phi(x) \...
- 3,794
2votes
1answer
413views
Physical interpretation of photon propagator
Physically, propagator represents the probability amplitude of a particle to travel from one point to another. But the photon propagator $$D_{\mu\nu}(x,y) = \langle 0 | \mathcal{T}[A_\mu(x) A_\nu(y)] ...
- 1,177
1vote
1answer
280views
Application of Cauchy residue theorem to Matsubara sums
For reference, this derivation is closely related to the discussion on pp. 169-173 of Altland and Simons. In quantum field theory (specifically when calculating free fermionic propagators via coherent ...
- 75
2votes
1answer
131views
Why must the propagator exponent be imaginary?
In response to asmaier's question, qmechanic showed why the propagator must be $\exp(cS)$. That made perfect sense. But can it also be shown that $c$ is imaginary? I believe it follows from ...
0votes
1answer
595views
How is the free particle propagator derived? [closed]
The free particle propagator is a well known function, for example, see Wikipedia. However, I cannot find a source that explains how to derive the free particle propagator. Please explain how the free ...
- 395
