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arXiv:1201.1341

Wave Packet for Massless Fermions and its Implication to the Superluminal Velocity Statistics of Neutrino

K. Wang, Zexian Cao

Published Jan 6, 2012• 3 citations
arXivHTMLPDF

Abstract

Non-dispersive wave packet for massless fermions is formulated on the basis of squeezed coherent states that are put in a form of common eigenfunction for the Hamiltonian and the helicity operator, starting from the Dirac equation. The wave packet thus constructed is demonstrated to propagate at a constant velocity as that of light. This explicit expression of wave packet for the massless fermions can facilitate theoretical analysis of problems where a wave packet is of formal significance. Furthermore, extensive wave packet may result in a superluminal velocity statistics if determined from the time-of-flight measurement, as recently done on muon neutrinos, when a threshold particle flux or energy transfer, which is eventually referred to the propagation of wave packet, to invoke a detection event is assumed.

DOI
10.48550/arxiv.1201.1341

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Non-dispersive wave packet for massless fermions is formulated on the basis of squeezed coherent states that are put in a form of common eigenfunction for the Hamiltonian and the helicity operator, starting from the Dirac equation. The wave packet thus constructed is demonstrated to propagate at a constant velocity as that of light. This explicit expression of wave packet for the massless fermions can facilitate theoretical analysis of problems where a wave packet is of formal significance. Furthermore, extensive wave packet may result in a superluminal velocity statistics if determined from the time-of-flight measurement, as recently done on muon neutrinos, when a threshold particle flux or energy transfer, which is eventually referred to the propagation of wave packet, to invoke a detection event is assumed.
An explanation for superluminal phenomena based on wave-particle duality of photons is suggested. A single photon may be regarded as a wave packet, whose spatial extension is its coherence volume. As a photon propagates as a wave train in vacuum, its velocity is just the speed of light. When it tunnels through a barrier as a particle, its wave function collapses and it will travel faster than light. Superluminal motion can occur only within the coherence length and the time constrained by uncertainty principle. A massive particle cannot be superluminal during the tunneling process. So superluminality does not violate causality. As for the superluminal and negative group velocities in anomalously dispersive medium, they are merely reshaping effect of the pulse, and they will become subluminal at large distances. A couple of experiments are proposed to test the superluminal phenomena.
Majorana neutrino oscillations in a magnetic field are considered using the wave packets formalism. The modified Dirac equation for Majorana neutrinos with non-zero transition magnetic moments propagating in a magnetic field is solved analytically in the two flavour case. The expressions for the oscillations probabilities are derived accounting for the decoherence effect emerging at distances exceeding the coherence length. It is shown that for Majorana neutrinos propagating in a magnetic field the coherence length coincides with the coherence length for neutrino oscillations in vacuum when the vacuum frequency is much greater than the magnetic frequency (ωvac≫ωBω_{vac} \gg ω_Bωvac​≫ωB​), while it is proportional to the cube of the average neutrino momentum if (ωvac≪ωBω_{vac} \ll ω_Bωvac​≪ωB​). We show that the decoherence effect may appear during neutrino propagation in a magnetic field of supernova.
Dynamical Localized Wave Packet Theory (DLWPT) is a theoretical framework that extends conventional quantum mechanics by interpreting the wavefunction as a physically real coherence field rather than a purely probabilistic object. In this approach, quantum particles correspond to dynamically stable, localized wave packets whose evolution is governed by modified dynamical equations incorporating a fundamental coherence scale. In its relativistic formulation, DLWPT modifies the standard Dirac dynamics by introducing a nonlocal coherence operator. This operator captures the finite spacetime coherence region associated with localized fermionic wave packets. As a result, the theory naturally describes fermions as extended but localized structures with Planck-scale coherence tails, rather than strictly pointlike particles. The DLWPT framework provides a deterministic description of wave packet evolution while maintaining compatibility with relativistic covariance. At energies far below the Planck scale, the modified dynamics reduce smoothly to the standard Dirac equation, ensuring consistency with established quantum field theory. However, at ultra-high energies the coherence operator introduces Planck-suppressed corrections to the dispersion relation and particle propagation. Several conceptual implications follow from this formulation. The nonlocal structure of the coherence operator provides a natural interpretation of quantum non-separability through overlapping coherence regions. Localized fermions arise as stable eigenmodes of the coherence operator, and the theory suggests that internal orientation degrees of freedom of these coherence packets may underlie the emergence of gauge symmetries. Within this framework, gravity can be interpreted as an emergent phenomenon associated with gradients in the coherence energy density of localized wave packets. The Planck scale therefore appears not merely as a parameter of quantum gravity but as the fundamental coherence scale governing the structure of matter fields. DLWPT thus proposes a unified conceptual picture in which particles are self-coherent spacetime wave packets, interactions arise from coherence structures and their orientation modes, and spacetime geometry reflects the collective behavior of coherence energy at the Planck scale. The present work develops the relativistic fermionic sector of the theory, deriving the modified Dirac equation, associated dispersion relations, and propagator structure. Potential observational signatures include Planck-suppressed deviations in high-energy particle propagation and coherence-induced modifications to scattering processes.
On the base of the photon’s wave function (wave packet) in Schrodinger coordinate representation developed in previous papers the modeling of the propagation in space and in time of a wave packet of the photon corresponding to a separate laser impulse of radiation of femtosecond diapason is carried out. The development is proceeded from single-particle approach with the usage of the basis eigenfunctions of energy, momentum and helicity operators in continuous momentum spectrum case. The wave packet is constructed in the form of superposition of these eigenfunctions as the integral over the all momentum space. In the case of Gaussian momentum distribution the character of an extension of a form of this wave packet is established. The essence of wave-particle duality of light and microparticles is specified. The hypothesis is formulated, however, that the photon is a quasi-particle corresponding to the propagation of spin wave in physical vacuum. It is claimed that this question is related to the structure of the leptons and other particles on the Planck distances.