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4 votes
1 answer
260 views

Are renormalizability and the criticality of a PDE synonymous?

In the physics literature a quantum field theory is qualitatively classified as renormalizable, super-renormalizable, or non-renormalizable. This heuristic is based on how many Feynman diagrams ...
CBBAM's user avatar
  • 721
0 votes
0 answers
55 views

Status of generalization of timelike tube theorem to algebras of causal completions

The timelike tube theorem states that the additive algebra $A_{\text{add}}(U)$ of operators in a spacetime region $U$ is equal to the additive algebra $A_{\text{add}}(E(U))$ of the timelike envelope $...
user avatar
10 votes
1 answer
436 views

Propagators and PDEs

I have already asked this at MSE but did not get an answer. In quantum field theory one encounters the retarded, advanced and Feynman propagators as certain solutions to a wave equation. ...
Bettina's user avatar
  • 113
3 votes
1 answer
2k views

Boundary conditions for Klein-Gordon equation

Let us consider the Klein-Gordon equation $$(\Box +m^2)u=0,$$ where $u$ is a scalar valued function, $m\geq 0$, $\Box=\frac{\partial^2}{\partial x_0^2}-\sum_{i=1}^d\frac{\partial^2}{\partial x_i^2}$. ...
asv's user avatar
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5 votes
2 answers
898 views

Is there a true many-body green's function for interacting systems?

I've recently been trying to compute the Green's function for a non-interacting system of fermions. Since this is a site for mathematicians, for context, let me provide the following definition: ...
David Roberts's user avatar