A Future-Input Dependent Path Integral for Quantum Mechanics

TL;DR

This paper introduces a novel future-input dependent path integral over Hilbert space that exactly reproduces quantum mechanics, incorporating entangled states directly and allowing modifications for wave-function collapse.

Contribution

It presents a new path integral formulation that depends on future boundary conditions, providing a fresh perspective on quantum mechanics and entanglement.

Findings

Reproduces quantum mechanics exactly

Incorporates entangled states directly in paths

Allows modification to include wave-function collapse

Abstract

We here put forward a new path-integral over Hilbert space and show that it reproduces quantum mechanics exactly. This approach works by optimizing the generating functional under a variation of the final state; it is hence an example of a future-input dependent theory. The benefit of this method is that entangled states appear in the paths directly, and the generating functional can be modified to also include wave-function collapse.