Tachyons or Antiparticles?
J.N. Pecina-Cruz
Department of Physics
The University of Texas-Pan American
1201 West University Drive
Edinburg, Texas 78541-2999
jpecina2@panam.edu
This article proves that elementary particles can violate the second postulate of the
Special Theory of Relativity. According to Heisenberg’s principle, superluminal particles
are allowed in the theoretical framework of Quantum Mechanics. In this paper the
tachyons, are identified with the unitary irreducible representations of the “full” Poincare
group (Poincare group plus space-time reflections.) on the past time-like cone.
Introduction
Einstein’s theory of relativity demands that exist a symmetry that leaves invariant the
laws of physics [1], under the relative motion of reference frames. Einstein also claims
that the time coordinate rests on the same footing than the space coordinates. Therefore
the Poincare group must be enlarged to include space-time inversions. Ne’eman et al [2]
have conjectured that a theory of quantum gravity could be the result of enhancing the
Poincare group to SA(r,4). Schwinger already intended to introduce the strong reflections
in quantum field theory [3]. Section 1 is devoted to explaining the tunnelling of a particle
from the future time-like region to the past time-like region of the space-time. In sections
2 to 6 the unitary irreducible representations of the “full” Poincare group are constructed.
ARXIV.ORG
