2T Physics and Quantum Mechanics

TL;DR

This paper explores six different formulations of quantum mechanics in spaces with two time-like dimensions, unified by a common classical limit, and proposes a new approach to quantum mechanics in gravitational contexts.

Contribution

It introduces six novel formulations of quantum mechanics in two-time spaces, extending traditional theory and addressing quantum gravity.

Findings

All formulations share the same classical limit.

One formulation serves as a basis for quantum mechanics with gravity.

The approach generalizes quantum mechanics to higher-dimensional spacetime.

Abstract

We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit described by the same Hamiltonian. One of these formulations is used as a basis for a complementation of the usual quantum mechanics when in the presence of gravity.