On the introduction of particle positions in relativistic quantum mechanics

Tommy Ohlsson B

Konstantin K. Likharev

R. Acharya, E. C. G. Sudarshan

The problem of introducing a Cartesian position operator canonically conjugate to the momentum operator into relativistic one-particle theories is investigated independent of any particular relativistic wave equation. The known result that such a description is possible for particles with nonvanishing mass is rederived. The general problem of introduction of canonical variables into relativistic theories is formulated and solved. The configurational indices so obtained correspond to directed plane wavefronts rather than point particles.

Francisco Ancelmo Pinheiro Ferreira

In this work we analyze some aspects related to the introduction, in the non-relativistic quantum mechanics,of a translation operator whose action is a function of the point of application. From the introduction of this operator, we derive a modified canonical commutation relation and a modified representation for the momentum operator and we show that such changes require a restructuring of the Hilbert space. We also see that the “new” Hilbert space can be associated with the case of a particle with position dependent mass and also that of a particle moving in a curved space. Still, we compare our formalism with the formalism of von Roos, we analyze the classical limit of this formalism,we solve the problem of a particle with position-dependent mass in two dimensions and we end up analyzing some quantities of information theory for the case of a one-dimensional harmonic particle.

Anastasios Kyprianidis