# Questions tagged [greens-functions]

A Green's function is the impulse response of an inhomogeneous differential equation defined on a domain, with specified initial conditions or boundary conditions, thereby restricting that equation's fundamental solution. In QFT, it is essentially the propagator.

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### Calculating a space and time dependant temeprature profile of a very long pipe in an infinite medium

I am trying to calculate the time and space depenadant temperature profile of an infinite medium after inserting a very long pipe into it using Green's function. The pipe serves as a heat source with ...
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### Given Green's function, can I find the corresponding operator? [migrated]

Green's function is the solution to the equation $L G(x;x') = \delta(x-x')$, where $L$ is a linear differential operator. Usually, we want to find the Green's function of a given $L$. Instead, if we ...
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### Photon propagator in path integral vs. operator formalism

I am self-studying the book "Quantum field theory and the standard model" by Schwartz, and I am really confused about the derivation of the Photon propagator on page 128-129. He starts ...
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### Are there exactly solvable problems in curved space, except for cases of constant curvature of space?

I have two questions. I know the expressions for geodesic distance in Minkowski, de Sitter and anti de Sitter space-time and their Euclidean analogues $R^n$, $S^n$ and $H^n$ [1]. For what other curved ...
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### Analytic continuation Matsubara/imaginary-time to retarded function in complex time domain

In linear response theory, one may either use the real-time retarded correlation function, or analytically continue to imaginary time/frequency to use the Matsubara Green's function instead. While ...
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### Green's function solution in 2D for the potential of solenoids in the Lorenz gauge

My main goal is to find a general expression for the potential in the Lorenz gauge of some solenoidal (not necessarily circular) current density using the Green's function. I assume that the current ...
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### The problem with derivation of an equation in a many-body book

In the corrected version (14 January 2016) of the book "Many-Body Quantum Theory in Condensed Matter Physics: An Introduction (Oxford Graduate Texts)" chapter 8, for the following time ...
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### Green function and probability amplitude

Consider the following Green function: $$G_{2}(x,t,x',t') = \langle \Omega_{0}, e^{itH_{0}}a_{x}e^{-itH_{0}}e^{it' H_{0}}a_{x'}^{*}e^{-it' H_{0}}\Omega_{0}\rangle$$ for $t' > t$. Here, $a_{x}^{*}$ ...
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### How does one rigorously define two-point functions?

Let $\mathscr{H}$ be a complex Hilbert space, and $\mathcal{F}^{\pm}(\mathscr{H})$ be its associated bosonic (+) and fermionic (-) Fock spaces. Given $f \in \mathscr{H}$, we can define rigorously the ...
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### Why do different contours give different answers in the limit $\epsilon \rightarrow 0$ when calculating propagators?

Let $\phi$ denote the Klein-Gordon field. Then its propagator $\langle 0 \mid [\phi(x), \phi(y)] \mid 0 \rangle$ can be calculated as \int \frac{d^4}{(2\pi)^3} \frac{-e^{-ip(x-y)}}{p^2 -m ^2}. \tag{...
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### How small is $\eta$ when we say $\eta\to 0^+$ in Green's functions

When we convert Matsubara's imaginary time Green's function to the retarded Green's function, we perform an analytical continuation by substituting $i\omega_n$ with $\omega + i\eta$, with $\eta\to0^+$....
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