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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.
We review the noncommutative approach to the standard model. We start with the introduction if the mathematical concepts necessary for the definition of noncommutative spaces, and manifold in particular. This defines the framework of spectral geometr
We review pedagogically non-Abelian discrete groups, which play an important role in the particle physics. We show group-theoretical aspects for many concrete groups, such as representations, their tensor products. We explain how to derive, conjugacy
We clearly formulate and study further a conjecture of effective field theory interaction with gravity in the cosmological context. The conjecture stems from the fact that the melding of quantum theory and gravity typically indicates the presence of
In this review I discuss the role of chiral extrapolations for the determination of several phenomenologically relevant quantities, including light quark masses, meson decay constants and the axial charge of the nucleon. In particular, I investigate
Today, both particle physics and cosmology are described by few parameter Standard Models, i.e. it is possible to deduce consequence of particle physics in cosmology and vice verse. The former is examined in this lecture, in light of the recent syste