The path-integral tag has no wiki summary.
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2answers
949 views
When can I use Wick's theorem?
Wick's theorem means that for fermions, a four point correlation function (for example) can be written in terms of two point correlation functions:
\begin{equation}
\langle b_l^\dagger b_l ...
13
votes
2answers
65 views
Calculating correlation functions of exponentials of fields
In their book Condensed Matter Field Theory, Altland and Simons often use the following formula for calculating thermal expectation values of exponentials of a real field $\theta$:
$$ \langle ...
13
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2answers
157 views
Applications of the Feynman-Vernon Influence Functional
I am looking for a reference where the Feynman-Vernon influence functional was defined and used in the context of relativistic quantum field theory. This functional is one method to describe ...
14
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1answer
62 views
Instantons and Non Perturbative Amplitudes in Gravity
In perturbative QFT in flat spacetime the perturbation expansion typically does not converge, and estimates of the large order behaviour of perturbative amplitudes reveals ambiguity of the ...
3
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2answers
335 views
When is many-body perturbation theory valid?
I'm calculating expectation values (thermal, time-independent) using many-body perturbation theory, but I'm unsure how to work out what values the parameter I'm expanding the perturbation series in ...
7
votes
3answers
268 views
How does the quantum path integral relate to the quantization of energy?
So, the quantum path integral is a generalization of the classical principle of least action- but here we know that all paths contribute something finite to the probability density. What confuses me ...
5
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2answers
279 views
Two paths having the same phase in the path integral approach
In the path integral approach to Quantum Mechanics, can two distinctly different paths of the possible infinite paths have the same phase, i.e can there be a bimodal distribution of the phases ...
6
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2answers
306 views
Lagrangians combining terms with 1 and 2 derivatives
How are field theory Langrangians treated when some terms have 2 derivatives but others have only 1? Because the number of derivatives in a Lagrangian term is more easily even than odd, the ...
5
votes
1answer
495 views
What is the meaning of the Fourier transform of Feynman propagator?
I know $K(a,b,t)$ is the probability amplitude of find a particle that starts at point a in b in a time t later. There is also an expression that sometimes is called green function:
...
8
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1answer
481 views
Questions about the Dyson equation
I'm studying finite temperature many-body perturbation theory, and am trying to understand The Dyson equation. In particular, I'm using Mattuck - A guide to Feynman diagrams in the many body problem.
...
4
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0answers
187 views
When can the source term of a partition function be put in?
More specifically, in quantum field theory books, we usually have this:
\begin{equation}
Z = \int D(\bar{\psi}, \psi) e^{-S + \int_0^\beta d\tau \sum_l [\bar{\eta}_l (\tau) \psi_l (\tau) + ...
4
votes
1answer
222 views
Have the correlation functions of the XY spin chain model been calculated using a functional partition function with source terms?
Have the correlation functions of the XY spin chain model,
\begin{equation}
H=-\sum_l (J_x \sigma_l^x \sigma_{l+1}^x+J_x \sigma_l^y \sigma_{l+1}^y)-B\sum_l \sigma_l^z
\end{equation}
been calculated ...
7
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3answers
851 views
Once a quantum partition function is in path integral form, does it contain any operators?
Once a quantum partition function is in path integral form, does it contain any operators?
I.e. The quantum partition function is $Z=tr(e^{-\beta H})$ where H is an operator, the Hamiltonian of the ...
8
votes
5answers
491 views
Why is the contribution of a path in Feynmans path integral formalism $\sim e^{(i/\hbar)S[x(t)]}$
In Feynmans book "Quantum Mechanics and Path Integrals" Feynman states that
the probability $P(b,a)$ to go from point $x_a$ at time $t_a$ to the point $x_b$ at the time $t_b$ is $P(b,a) = ...
7
votes
1answer
536 views
Question about a Limit of Gaussian Integrals and how it relates to Path Integration (if at all)?
I have come across a limit of Gaussian integrals in the literature and am wondering if this is a well known result.
The background for this problem comes from the composition of Brownian motion and ...
4
votes
1answer
545 views
Do derivatives anticommute with Grassmann variables and complex numbers in a many-body path integral?
I'm trying to learn how to do a many-body path integral for both fermions and bosons, and I'm stuck. I'm following Altland and Simons - Condensed Matter Field Theory, chapter 4. On page 167, equation ...
6
votes
2answers
717 views
Wheeler-Feynman theory, QED without fields, vacuum polarization
Initially Wheeler and Feynman postulated that, the electromagnetic field is just a set of bookkeeping variables required in a Hamiltonian description. This is very neat because makes the point of ...
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votes
5answers
1k views
Path integral vs. measure on infinite dimensional space
Coming from a mathematical background, I'm trying to get a handle on the path integral formulation of quantum mechanics.
According to Feynman, if you want to figure out the probability amplitude for ...
10
votes
1answer
1k views
The Concepts of Path Integral in Quantitative Finance
I realize that path integral techniques can be applied to quantitative finance such as option value calculation. But I don't quite understand how this is done.
Is it possible to explain this to me ...
