Localizability of tachyonic particles and neutrinoless double beta decay

Abstract

The quantum field theory of superluminal (tachyonic) particles is plagued with 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 packets 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-1 2 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.

Weighing the neutrino

“…[22] and recently subject to a few more investigations reported in Refs. [52][53][54][55]. It is based on the Lagrangian…”

“…Quite recently [52,53,55], it has been shown that the solutions of Eq. (A2) have an convenient structure in helicity basis [55].…”

“…Furthermore, they fulfill projector sum rules, discussed in Refs. [52,55], permitting the evaluation of the tachyonic Dirac propagator as the inverse of the kinetic operator (Dirac Hamiltonian), which is crucial in formulating the corresponding field theory. In view of the structure of the Lagrangian (A1), the role of the Dirac adjoint in the tachyonic sector is assumed by the pseudoscalar adjoint ψ γ 5 , and the generalized Dirac propagator is calculated as the time-ordered product S T (x, y) = 0 T ψ(x) ψ(y)γ 5 0 .…”

Ultrarelativistic decoupling transformation for generalized Dirac equations

“…The ultrarelativistic transform leads to a form which asymptotically is equal to the Weyl Hamiltonian (helicity basis) of a massless particle, as it should be (in the ultrarelativistic limit). Here, we shall make the point that, unlike the original Foldy-Wouthuysen transform, which can only be applied to tardyons, the ultrarelativistic decoupling can also be used for Lorentz-invariant tachyons [12,19,20], whose velocity remains superluminal upon Lorentz transformation [13][14][15][16][17].…”

“…The accepted generalized Dirac Hamiltonian for a free tachyonic Dirac particle is given as [12,19,20] …”