Eur. Phys. J. C (2012) 72: 1894
https://doi.org/10.1140/epjc/s10052-012-1894-4

Regular Article - Theoretical Physics

Localizability of tachyonic particles and neutrinoless double beta decay

¹ Department of Physics, Missouri University of Science and Technology, Rolla, MO, 65409-0640, USA
² Institut für Theoretische Physik, Philosophenweg 16, 69020, Heidelberg, Germany

^* e-mail: ulj@mst.edu

Received: 19 December 2011
Revised: 9 January 2012
Published online: 15 February 2012

Abstract

The quantum field theory of superluminal (tachyonic) particles is plagued by a number of problems, which include the Lorentz non-invariance of the vacuum state, the ambiguous separation of the field operator into creation and annihilation operators under Lorentz transformations, and the necessity of a complex reinterpretation principle for quantum processes. Another unsolved question concerns the treatment of subluminal components of a tachyonic wave packet in the field-theoretical formalism, and the calculation of the time-ordered propagator. After a brief discussion on related problems, we conclude that rather painful choices have to be made in order to incorporate tachyonic spin- particles into field theory. We argue that the field theory needs to be formulated such as to allow for localizable tachyonic particles, even if that means that a slight unitarity violation is introduced into the S matrix, and we write down field operators with unrestricted momenta. We find that once these choices have been made, the propagator for the neutrino field can be given in a compact form, and the left-handedness of the neutrino as well as the right-handedness of the antineutrino follow naturally. Consequences for neutrinoless double beta decay and superluminal propagation of neutrinos are briefly discussed.