Timeline for Feynman rule in finite volume or at periodic boundary condition
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 29, 2020 at 15:48 | comment | added | Michael Engelhardt | The algebraic steps involved in a Wick decomposition are fairly simple: Introducing sources with respect to which you can take derivatives, and completing the square. Off the top of my head, I don't see how spatial boundary conditions would interact nontrivially with these operations - the boundary conditions will influence the propagator, not the combinatorics of Gaussian integrals. Of course, in practice, I'd quickly run through these steps for any particular model in question to make sure. | |
| Aug 29, 2020 at 13:55 | comment | added | Carlo Beenakker | see, for example, page 170 of these notes --- the only assumption is a bilinear Hamiltonian in the fermionic (or bosonic) fields. | |
| Aug 29, 2020 at 13:34 | comment | added | Simon Lentner | Carlo, that would be great - do you have a reference? I would somehow expect that, but the proofs I found where too involved for myself to easily include additional potential terms (e.g. the binomial formula for V(x+deltax) does not hold if I include a cut-off)? | |
| Aug 29, 2020 at 13:10 | comment | added | Carlo Beenakker | I thought that Wick's theorem holds for any quadratic Hamiltonian; a finite volume or periodic boundary conditions would be realized by a potential term, without spoiling the quadratic nature, so it should not invalidate Wick's theorem. | |
| Aug 29, 2020 at 13:06 | comment | added | Carlo Beenakker | also posted at physicsoverflow.org/43194 (it is best practice to disclose cross-postings, in order to avoid duplication of efforts) | |
| Aug 29, 2020 at 12:55 | history | asked | Simon Lentner | CC BY-SA 4.0 |