Relativistic quantum mechanics on the SL(2,R) spacetime
T. F\"ul\"op
TL;DR
This paper adapts the Schrödinger formalism of Klein-Gordon quantum mechanics to the SL(2,R) spacetime, solving for free particles, topologically nontrivial solutions, and antiparticle modes, providing new insights into the theory's physical content.
Contribution
It introduces a novel adaptation of Klein-Gordon quantum mechanics to SL(2,R) spacetime, including solutions and physical interpretation.
Findings
Reproduces known free particle solutions
Finds topologically nontrivial solutions
Identifies antiparticle modes
Abstract
The Schr\"odinger-type formalism of the Klein-Gordon quantum mechanics is adapted for the case of the spacetime. The free particle case is solved, the results of a recent work are reproduced while all the other, topologically nontrivial solutions and the antiparticle modes are also found, and a deeper insight into the physical content of the theory is given.
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