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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.
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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 geometry. This is applied to the standard model of particle interaction, discussing the fermionic and bosonic spectral action. The issues relating to the calculation of the mass of the Higgs are discussed, as well as the role of neutrinos and Wick rotations. Finally, we present the possibility of solving the problem of the Higgs mass by considering a pregeometric grand symmetry.
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 classes, characters, representations, and tensor products for these groups (with a finite number). We discussed them explicitly for $S_N$, $A_N$, $T$, $D_N$, $Q_N$, $Sigma(2N^2)$, $Delta(3N^2)$, $T_7$, $Sigma(3N^3)$ and $Delta(6N^2)$, which have been applied for model building in the particle physics. We also present typical flavor models by using $A_4$, $S_4$, and $Delta (54)$ groups. Breaking patterns of discrete groups and decompositions of multiplets are important for applications of the non-Abelian discrete symmetry. We discuss these breaking patterns of the non-Abelian discrete group, which are a powerful tool for model buildings. We also review briefly about anomalies of non-Abelian discrete symmetries by using the path integral approach.
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 an inherent UV cutoff. Taking note of the physical origin of this UV cutoff, that the background metric fluctuations does not allow QFT to operate with a better precision than the background space resolution, we conjecture that the converse statement might also be true. That is, an effective field theory could not perceive the background space with a better precision than it is allowed by its intrinsic UV scale. Some of the subtleties and cosmological implications of this conjecture are explored.
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 whether chiral extrapolations are sufficiently controlled in order to rightfully claim the accuracy which is quoted in recent compilations of these quantities. While this is the case for the masses of the light quarks and the ratio fK/fpi of decay constants, small inconsistencies in the chiral and continuum behaviour of individual decay constants fK and fpi, as well as the hadronic radii r0, r1 remain and must be clarified. In the case of the nucleon axial charge, gA, the chiral behaviour is still poorly understood due to the presence of other systematic effects.
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 systematic exploration of the electroweak scale by the LHC experiments. The two main results of the first phase of the LHC, the discovery of a Higgs-like particle and the absence so far of new particles predicted by natural theories beyond the Standard Model (supersymmetry, extra-dimension and composite Higgs) are put in a historical context to enlighten their importance and then presented extensively. To be complete, a short review from the neutrino physics, which can not be probed at LHC, is also given. The ability of all these results to resolve the 3 fundamental questions of cosmology about the nature of dark energy and dark matter as well as the origin of matter-antimatter asymmetry is discussed in each case.
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