Questions tagged [path-integral]
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.
1,656 questions
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Initial condition of the canonical density matrix in path integral formulation
The imaginary-time path-integral expression for the many-body density matrix of $N$ bosons is $$ \rho\left(R,R_{0};\beta\right)=\left\langle R\right|e^{-\beta\hat{H}}\left|R_{0}\right\rangle \propto\...
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Beginner friendly materials for functional method in QFT
When I ask questions on this site regarding Feynman diagram, I see a lot of answers using functional method in QFT (e.g. this post and this post). However, they seems quite confusing to me because I'...
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Experiment demonstrating light actually explores all the paths in a Veritasium YouTube video [duplicate]
This is the link to the Veritasium YouTube video where Derek and his friend show that light indeed explores all the paths. A laser beam is made to fall on a point say $P$ on a reflecting surface at an ...
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Infrared zeromodes and the physical status of infinite-wavelength photons in quantum field theory
In quantum field theory, photons are described as quantized excitations of the electromagnetic field, with energy given by $E = ℏω = hc/λ$. In the infrared (IR) limit, where the wavelength $λ$ tends ...
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Gaussian integral (Hubbard-Stratonovich) with complex field
I am trying to perform a Hubbard-Stratonovich transformation to decouple a quartic interaction, which technically is just a Gaussian integral over an extra field complex field \begin{equation} e^{V \...
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Why are free quantum fields said to be Gaussian?
This is perhaps a very elementary question, but it's something I was thinking about today and couldn't come up with a very good answer. The most general definition one can give for an object to be ...
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Decoherent histories for Young's experiment (with and without gas)
Lately I've been trying my hand at consistent/deconsistent histories. To measure my understanding, I'm trying to apply formalism to concrete cases - in this case, the sacrosanct double-slit experiment....
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Is it possible to demand a thermal initial state in the closed time contour Keldysh formalism?
The Keldysh path integral derived from a Lindblad-equation on a closed time contour in coherent state representation reads $$ Z = \int\mathcal{D}[\Psi_+,\Psi_-]e^{iS[\Psi_+,\Psi_-]}\langle\Psi_+(0)|\...
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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 $$\...
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Solutions to Schrodinger Equation with Feynman-Kac Formula
I am currently taking a course on stochastic differential equations, and part of the course is doing a project on applications of stochastic differential equations and I am curious if there is a ...
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Faddeev-Popov method, insertion of identity
Question 1: Understanding the Faddeev-Popov determinant in gauge theory In quantum field theory, we encounter difficulties when quantizing gauge theories because of redundancies in the path integral. ...
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Confusion about thermodynamic expectation value in path integral formalism
In the derivation of the average condensed particle count fluctuation of a double well from the effective action \begin{equation} S_\text{eff}[\phi,\delta N]=\int_0^\beta d\tau~i\frac{1}{2}\delta ...
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What is the point of the Pauli-Van Vleck-Morette determinant?
I wish to get a better feel for the Heat kernel ansatz below $$\hat{K}(s \mid x, y)=\frac{\Delta^{1 / 2}(x, y)}{(4 \pi s)^{d / 2}} g^{1 / 2}(y) e^{-\sigma(x, y) / 2 s-s m^2} \sum_{n=0}^{\infty} s^n \...
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How to relate $\langle 0| \phi(x) |0\rangle$ with Feynman diagrams to a $\phi^3$ theory without counterterms?
I am learning QFT on my own via Mark Srednicki's book, and I have a bit of trouble following the author in chapter 9, where the path integral for an interacting theory is introduced, as well as ...
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Gaussian integral in QFT
I would like to perform this (basic) integral in QFT: where $a$ is a constant $$ \int D\phi D\phi^*e^{-\int d^4x \phi^* M\phi+a(\phi+\phi^*)} $$ The general formula is $$ \int D \varphi^{\dagger} D \...
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