- #1
Orbb
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Hi,
I have a question about the relation between the propagator of a scalar field and the heat kernel. I'm not sure wether I should rather put this question into the math section: Given a Laplacian D on some manifold M, what I mean by heat kernel is just
[tex] K(x,y;s) = \langle x | \exp(-sD) | y \rangle [/tex]
where x, y are distinct points on M and s is the diffusion time (in the sense that K obeys the heat eqn.). Now the propagator of a scalar field can be determined from K via
[tex] D^{-1}(x,y) = \int_0^{\infty} ds K(x,y;s). [/tex]
What I want to ask now is wether there is a way to invert this expression such that given some propagator, I can determine the corresponding heat kernel. Can anyobdy help?
Cheers,
O
I have a question about the relation between the propagator of a scalar field and the heat kernel. I'm not sure wether I should rather put this question into the math section: Given a Laplacian D on some manifold M, what I mean by heat kernel is just
[tex] K(x,y;s) = \langle x | \exp(-sD) | y \rangle [/tex]
where x, y are distinct points on M and s is the diffusion time (in the sense that K obeys the heat eqn.). Now the propagator of a scalar field can be determined from K via
[tex] D^{-1}(x,y) = \int_0^{\infty} ds K(x,y;s). [/tex]
What I want to ask now is wether there is a way to invert this expression such that given some propagator, I can determine the corresponding heat kernel. Can anyobdy help?
Cheers,
O