On superluminal fermions within the second derivative equation
Abstract
We postulate the second-order derivative equation with four parameters for spin-1/2 fermions possessing two mass states. For some choice of parameters fermions propagate with the superluminal speed. Thus, the novel tachyonic equation is suggested. The relativistic 20-component first-order wave equation is formulated and projection operators extracting states with definite energy and spin projections are obtained. The Lagrangian formulation of the first-order equation is presented and the electric current and energy-momentum tensor are found. The minimal and non-minimal electromagnetic interactions of fermions are considered and Schr\"{o}dinger's form of the equation and the quantum-mechanical Hamiltonian are obtained. The canonical quantization of the field in the first-order formalism is performed and we find the vacuum expectation of chronological pairing of operators.
Cite
@article{arxiv.1201.2391,
title = {On superluminal fermions within the second derivative equation},
author = {S. I. Kruglov},
journal= {arXiv preprint arXiv:1201.2391},
year = {2012}
}
Comments
21 pages, minor corrections, journal version, accepted in IJMPA