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3

As alluded to in the quotation, the time-evolution of non-relativistic matter waves is given by Schrodinger's equation, which is a linear, first-order differential equation in time. As such the future state of the system is fully specified if we specify a single boundary condition. On the other hand, photons, being massless, cannot be treated in a ...

1

The main issue seems to be that BGV uses a supercommutator notation $$\tag{1} [a,b]~:=~ab-(-1)^{|a||b|}ba,$$ where $|a|$ and $|b|$ denote the $\mathbb{Z}_2$-grading of operators $a$ and $b$, respectively. So if $a$ and $b$ have odd gradings, then $[a,b]$ is actually the anticommutator. References: [BGV] N. Berline, E. Getzler & M. Vergne, Heat ...

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I see now that your question is about the interpretation. Well, the interpretation is that you now integrate over the space of all fields in momentum space. Of course, mathematically the region of integration is still the space of functions $\mathbb{R}^4\to\mathbb{R}$ (or whatever kind of field applies) and so the meaning of $\mathcal{D}\phi$ is more or less ...

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1) $\exp(-1/g)$ is not necessarily related to bound states. In the standard QM double well problem it is the splitting, not the binding energy, that is $O(\exp(-1/g))$. In conformal field theories instantons can give $\exp(-1/g)$ effects even though there are no bound states at all. 2) Instantons are one source of $\exp(-1/g)$ effects, but there are others. ...

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For QED this corresponds to bound states, and the solution is well known, if one is willing to admit that bound state calculations do not rely upon the assumption of detectors interacting only asymptotically. For example, some of the tricks employed involve substituting the asymptotically free electron states with electron states in a known external ...

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