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We consider expressions of the form of an exponential of the sum of two non-commuting operators of a single variable inside a path integration. We show that it is possible to shift one of the non-commuting operators from the exponential to other functions which are pre-factors and post-factors when the domain of integration of the argument of that function is from -infty to +infty. This shift theorem is useful to perform certain integrals and path integrals involving the exponential of sum of two non-commuting operators.
For a fixed Feynman graph one can consider Feynman integrals with all possible powers of propagators and try to reduce them, by linear relations, to a finite subset of integrals, the so-called master integrals. Up to now, there are numerous examples
A salient feature of the Schr{o}dinger equation is that the classical radial momentum term $p_{r}^{2}$ in polar coordinates is replaced by the operator $hat{P}^{dagger}_{r} hat{P}_{r}$, where the operator $hat{P}_{r}$ is not hermitian in general. Thi
Perturbative quantum field theory usually uses second quantisation and Feynman diagrams. The worldline formalism provides an alternative approach based on first quantised particle path integrals, similar in spirit to string perturbation theory. Here
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A number of irreducible master integrals for L-loop sunrise-type and bubble Feynman diagrams with generic values of masses and external momenta are explicitly evaluated via Mellin-Barnes representation.