Time and time functions in parametrized non-relativistic quantum mechanics

Time and Time Functions in Parametrized Non-Relativistic Quantum Mechanics

The “evolving constants” method of defining the quantum dynamics of time-reparametrization-invariant theories is investigated for a particular implementation of parametrized non-relativistic quantum mechanics (PNRQM). The wide range of time functions that are available to define evolving constants raises issues of interpretation, consistency, and the degree to which the resulting quantum theory...

Relativistic Non-Hermitian Quantum Mechanics

We develop relativistic wave equations in the framework of the new non-hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT -symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no cou...

On Relativistic Non-linear Quantum Mechanics

The possibility that quantum mechanics itself could be non-linear has run up against difficulties with relativistic covariance. Most of the schemes proposed up to now engender superluminal communication, and those that don’t, have been equivalent to linear theories. We show in a simplified model that a proposal based on the consistent histories approach to quantum mechanics avoids the usual dif...

Interacting relativistic quantum dynamics for multi-time wave functions

In this paper, we report on recent progress about a rigorous and manifestly covariant interacting model for two Dirac particles in 1+1 dimensions [9, 10]. It is formulated using the multi-time formalism of Dirac, Tomonaga and Schwinger. The mechanism of interaction is a relativistic generalization of contact interactions, and it is achieved going beyond the usual functional-analytic Hamiltonian...

Arrival Time in Quantum Mechanics