Feynman path integrals over entangled states

Narayani Tyagi, K. B. Wharton

Andrew G. Green, C. Hooley, Jonathan Keeling +1 more

The saddle points of a conventional Feynman path integral are not entangled, since they comprise a sequence of classical field configurations. We combine insights from field theory and tensor networks by constructing a Feynman path integral over a sequence of matrix product states. The paths that dominate this path integral include some degree of entanglement. This new feature allows several insights and applications: i. A Ginzburg-Landau description of deconfined phase transitions. ii. The emergence of new classical collective variables in states that are not adiabatically continuous with product states. iii. Features that are captured in product-state field theories by proliferation of instantons are encoded in perturbative fluctuations about entangled saddles. We develop a general formalism for such path integrals and a couple of simple examples to illustrate their utility.

Wataru Ichinose

Convergence of a time-slicing approximation is studied in a general way of the Feynman path integral in phase space with an electromagnetic potential. In the present paper a new approximation of the Feynman path integral in phase space, different from the familiar one in physics, is proposed so that its convergence can be shown independently of the choice of electromagnetic potentials and that gauge invariance of the Feynman path integral defined by its limit can be shown directly. It is also shown that the Feynman path integral in phase space defined above can be expressed in the form of the Feynman path integral in configuration space defined in the familiar way in physics, which Feynman himself stated heuristically.

Jean-Louis Basdevant

Nancy Makri

María Guadalupe Morales, R. Gaitán

The motivation of this paper is to give mathematical formalism to the Feynman path integral using the Henstock integral. This integral saves some of Feynman's integral difficulties and justifies Feynman's intuition: to interpret the state function as "a sum of complex contributions, one from each path in the region".