4
votes
1answer
197 views

From Minkowski to Euclidean Time in Path Integrals

I'm trying to prove the following equality: $$ <x_{f},\, it_{f}|x_{i},\, it_{i}>=\mathcal{N}\int_{\left\{ x\in\mathbb{R}^{\mathbb{R}}:\, x\left(t_{f}\right)=x_{f}\wedge ...
8
votes
2answers
381 views

Is the step of analytic continuation unavoidable or can you model around it?

One sometimes considers the analytic continuation of certain quantities in physics and take them seriously. More so than the direct or actual values, actually. For example if you use the procedure ...
4
votes
1answer
492 views

A confusion from Weinberg's QFT text (a vanishing term in Lippmann-Schwinger equation)

I was reviewing the first few chapters of Weinberg Vol I and found a hole in my understanding in page 112, where he tried to show in the asymptotic past $t=−∞$, the in states coincide with a free ...
4
votes
1answer
314 views

interpretation of Green function

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 ...
1
vote
2answers
648 views

Inverted Harmonic oscillator

what are the energies of the inverted Harmonic oscillator? $$ H=p^{2}-\omega^{2}x^{2} $$ since the eigenfunctions of this operator do not belong to any $ L^{2}(R)$ space I believe that the spectrum ...