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.
Questions tagged [greens-functions]
974 questions
132
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3 answers
Differentiating Propagator, Green's function, Correlation function, etc
For the following quantities respectively, could someone write down the common definitions, their meaning, the field of study in which one would typically find these under their actual name, and most foremost the associated abuse of language as well…
Nikolaj-K
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75
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4 answers
Why correlation functions?
While this concept is widely used in physics, it is really puzzling (at least for beginners) that you just have to multiply two functions (or the function by itself) at different values of the parameter and then average over the domain of the…
Kostya
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3 answers
What do the poles of a Green function mean, physically?
Is there a physical interpretation of the existence of poles for a Green function? In particular how can we interpret the fact that a pole is purely real or purely imaginary? It's a general question but I would be interested in the interpretation in…
PanAkry
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How to interpret correlation functions in QFT?
I'm fairly new to the subject of quantum field theory (QFT), and I'm having trouble intuitively grasping what a n-point correlation function physically describes. For example, consider the 2-point correlation function between a (real) scalar field…
user35305
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33
votes
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Boundary conditions / uniqueness of the propagators / Green's functions
My question(s) concern the interpretation and uniqueness of the propagators / Green's functions for both classical and quantum fields.
It is well known that the Green's function for the Laplace equation
$$ \Delta_x G(x,x') = \delta^{(3)}(x-x')…
Greg Graviton
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How exactly is the propagator a Green's function for the Schrodinger equation?
Sakurai mentions (in various editions) that the propagator is a Green's function for the Schrodinger equation because it solves
$$\begin{align}&\left(H-i\hbar\frac{\partial}{\partial t}\right)K(x,t,x_0,t_0) \cr=…
Kasper
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Time ordering and time derivative in path integral formalism and operator formalism
In operator formalism, for example a 2-point time-ordered Green's function is defined as
$$\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{op}=\theta(x_1-x_2)\phi(x_1)\phi(x_2)+\theta(x_2-x_1)\phi(x_2)\phi(x_1),$$
where the subscript "op" and "pi"…
Jia Yiyang
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24
votes
4 answers
Two definitions of Green's function
In literature, usually two types of definition exist for Green's function.
$\hat{L}G=\delta(x-x')$. This equation states that Green's function is a solution to an ODE assuming the source is a delta function
$G=\langle…
atbug
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22
votes
2 answers
Particle/Pole correspondence in QFT Green's functions
The standard lore in relativistic QFT is that poles appearing on the real-axis in momentum-space Green's functions correspond to particles, with the position of the pole yielding the invariant mass of that particle. (Here, I disregard complications…
QuantumDot
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Benefit of using Matsubara Green function
Physicists often calculate Matsubara Green function and then perform an analytic continuation $i\omega_n \rightarrow \omega +i\eta$ to obtain the retarded Green function.
Why is doing so better than directly computing the retarded Green function?
leongz
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Green's function in path integral approach (QFT)
After having studied canonical quantization and feeling (relatively) comfortable with it, I have now been studying the path integral approach. But I don't feel entirely comfortable with.
I have the feeling that the main objective of the…
Hunter
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19
votes
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Dirac Delta in definition of Green function
For a inhomogeneous differential equation of the following form
$$\hat{L}u(x) = \rho(x) ,$$
the general solution may be written in terms of the Green function,
$$u(x) = \int dx' G(x;x')\rho(x'),$$
such that
$$\hat{L}G(x;x') = \delta(x-x') .$$
In…
WoofDoggy
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A curious issue about Dyson-Schwinger equation (DSE): why does it work so well?
This question comes out of my other question Time ordering and time derivative in path integral formalism and operator formalism, especially from the discussion with drake. The original post is somewhat badly composed because it contains too many…
Jia Yiyang
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18
votes
3 answers
How to obtain the explicit form of Green's function of the Klein-Gordon equation?
The definition of the green's function for the Klein-Gordon equation reads:
$$
(\partial_t^2-\nabla^2+m^2)G(\vec{x},t)=-\delta(t)\delta(\vec{x})
$$
According to these resources:
Green's function for the inhomogenous Klein-Gordon equation , the…
an offer can't refuse
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What information is contained in spectral density function in QFT?
I have been thinking lately about the following question. In quantum field theory, we define spectral density function $\rho(\mu^2)$ using two-point function as follows (Källén–Lehmann formula)
$$
\langle 0|T \phi(x) \phi(y)|0\rangle = \int…
