Information and Particle Physics

Abstract

Information measures for relativistic quantum spinors are constructed to satisfy various postulated properties such as normalisation invariance and positivity. Those measures are then used to motivate generalised Lagrangians meant to probe shorter distance physics within the maximum uncertainty framework. The modified evolution equations that follow are necessarily nonlinear and simultaneously violate Lorentz invariance, supporting previous heuristic arguments linking quantum nonlinearity with Lorentz violation. The nonlinear equations also break discrete symmetries. We discuss the implications of our results for physics in the neutrino sector and cosmology.

The nonlinear dirac equation in Bose–Einstein condensates: vortex solutions and spectra in a weak harmonic trap

“…In a previous paper we derived a BEC version of the nonlinear Dirac equation (NLDE) for the case of weak interparticle interactions [12]. This has attracted attention from diverse fields of research [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41]. Solutions of the NLDE are effectively long wavelength limit lattice envelopes, and so can cover a large number of sites.…”

Constraining Non-linear Dirac Equations with Neutrino Oscillations

“…We can interpret these non-linear Dirac equations as encoding potential new physics at higher energies. We then proceed to apply constraints to the information measure to obtain various forms of F as in [3]. It is important to note that the non-linearity here is not demanded but a result of information theoretic generalisation [3].…”

“…We assume that ψ andψ contract in the natural way in F to give us scalars. The information measure should satisfy the following conditions [3]:…”

Information and cosmological physics

“…In passing we note that nonlinear generalisations of the Dirac equation using informationtheoretic measures have been discussed in [6].…”