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Noncommutative Geometry and Particle Physics
Abstract: Transverse gauge invariance is the minimal condition necessary for a theory of spin 2 in flat space to lower the number of independent polarizations, from five for a massive field, down to two for a massless one. It will be pointed out that there is another theory, besides the one given by the Fierz-Pauli Lagrangian, that unitarily propagates only spin 2, in flat space. The nonlinear version of it is unimodular gravity. This will be embedded in the general context of dilaton gravity (pseudo Weyl invariant gravity), as well.
Abstract: We discuss the emergence of the generalized Wilson loop space in the quantum field-theoretical description of the high-energy hadron collisions. We show, in particular, how the geometrical properties of the loop space can be used in the study of the most general properties of the nonperturbative parton distribution functions inside the nucleon.