All Questions
Tagged with quantum-field-theory greens-functions
371
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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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Retarded Green's function in Peskin & Schroeder
In an Introduction to Quantum Field Theory by M. E. Peskin & D. V. Schroeder (eq. 2.56 on page 30) the following relation for the retarded Green's function was established:
$$(\partial^2 + m^2) ...
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Questions about fundamental solutions and propagators for the Dirac operator
I thought that propagator is a synonym for fundamental solution. But that seems not to be the case since in this answer it is said that an expression with delta function on a surface has to be ...
- 101
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Intuition for imaginary time Greens function
I understand that $$G^M(0,0^+) = \operatorname{tr}\{\rho O_2 O_1\}$$ (I am not putting hats on the operators here because they don't render in the correct position) is simply the expectation value of ...
- 21
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Relation between time-ordered propagator in condensed matter and Feynman propagator
In particle physics I am used to the Feynman propagator being decomposed into positive and negative frequency Wightman functions. For example, this is the representation used in Eq. (6.2.13) of ...
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Self Consistency of Wave Function Given By Green Function ($\psi(r,t) = \psi^0(r,t) + \int dr'\int dt G_0(r,r',t,t') V(r')\psi(r',t') $)
In "Introduction to Many-body Quantum theory in condensed matter physics" by Bruus and Flensberg there is an exercise regarding Green functions.
We want to solve the time dependent ...
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Two-particle Green's function, possible typo in the book referred?
I'm trying to follow a computation in some QFT book, p64. The goal is to derive the equation of motion for the lesser Green's function $G^<$ defined as
$$
G^< = \mp i {\rm Tr}\left(\rho \Psi^\...
- 793
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51
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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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Invert operator to integrate heavy fields
We have a Lagrangian $$\mathcal{L}=\frac{1}{2} \partial_\mu \Phi \partial^\mu \Phi - \frac{1}{2} M^2 \Phi^2- \frac{\lambda}{4}\phi^2 \Phi^2 - \frac{g}{2} \Phi \phi^2+\cdots $$ where $\Phi$ denotes a ...
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Why are 2-point functions Green's functions?
I asked a question about this earlier but I think it was unfocused so I have rephrased it and asked it again.
The propagator/two-point function $\langle \phi(x_1)\phi(x_2)\rangle$ for any theory can ...
- 3,350
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Is there any intuitive reason why 2-point functions are inverse operators to the free Lagrangian? [duplicate]
To compute $n$-point functions in quantum field theory we use Wick's theorem to reduce this problem to computing 2-point functions. In many textbooks, such as Peskin & Schroeder, the 2-point ...
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Why does a singularity imply the need for a distribution?
I am following Section 11 of Prof. Etingof's MIT OpenCourseWare notes on "Geometry And Quantum Field Theory" in which he says:
...for $d = 1$, the Green's function $G(x)$ is continuous at $...
- 3,350
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Renormalization condition for field strength renormalization
I am studying $\phi^4$ theory and so far I understand the mass and coupling constant renormalizations. In these theories, once we expand a diagram in perturbation theory we "cancel" the ...
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Why $n-1$ point function vanishes in $D=0$ scalar theory?
If we consider a $D=0$ theory with the Lagrangian:
$$\mathcal{L}[\phi]=g\phi^n+J\phi$$
And its Green functions:
$$G_n=\langle\phi^n\rangle_{J=0}=\frac{1}{Z[0]}\frac{\delta^nZ[J]}{\delta J^n}|_{J\...
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