Path integral formulation (Due to Feynman) is a major formulation of Quantum Mechanics along with Matrix mechanics (Due to Heisenberg and Pauli), Wave Mechanics (Due to Schrodinger), and Variational Mechanics (Due to Dirac). DO NOT USE THIS TAG for line/contour integrals.

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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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What is the meaning of the Fourier transform of Feynman propagator?

I know $K(a,b,t)$ is the probability amplitude that a particle that starts at point $a$ is found at point $b$ at a time $t$ later. There is also an expression that sometimes is called green function: ...
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How is the path integral for light explained, or how does it arise?

In a Phys.SE question titled How are classical optics phenomena explained in QED (Snell's law)? Marek talked about the probability amplitude for photons of a given path. He said that it was ...
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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. ...
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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) + ...
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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 ...
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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 ...
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Why is the contribution of a path in Feynmans path integral formalism $\sim e^{(i/\hbar)S[x(t)]}$

In Feynman's 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) = ...
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1answer
698 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 ...
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9answers
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Rigor in quantum field theory

Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, ...
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1answer
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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 ...
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954 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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7answers
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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 ...
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The Concepts of Path Integral in Quantitative Finance [closed]

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 ...