Abstract
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin-zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and spacelike intervals, are treated equally, which makes the new theory fully symmetric and consistent with the special theory of relativity. The theory correctly reproduces the classical action of a relativistic particle in the path integral formalism, and allows for the introduction of a new quantity called vector-mass, whose physical implications for nonlocality, the uncertainty principle, and quantum vacuum are described and discussed.
Highlights
Relativistic quantum mechanics (RQM) primarily concerns free relativistic fields [1,2] described by the Klein–Gordon [3,4], Dirac [5], Proca [6], and Rarita–Schwinger [7] wave equations, whereas the fundamental interactions and their unification are considered by the gauge invariant quantum field theory (QFT) [8,9]
The developed RQM theory preserves causality, is self-consistent, and is formulated using the path integral formalism, which correctly reproduces the classical action of a relativistic particle; the theory does not allow for tachyons [31,32]
Standard RQM that is based on the timelike intervals is reformulated by taking into account both the timelike and spacelike intervals
Summary
Relativistic quantum mechanics (RQM) primarily concerns free relativistic fields [1,2] described by the Klein–Gordon [3,4], Dirac [5], Proca [6], and Rarita–Schwinger [7] wave equations, whereas the fundamental interactions and their unification are considered by the gauge invariant quantum field theory (QFT) [8,9].
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