Minimal Z' models and the early LHC

We consider a class of minimal extensions of the Standard Model with an extra massive neutral gauge boson Z'. They include both family-universal models, where the extra U(1) is associated with (B-L), and non-universal models where the Z' is coupled to a non-trivial linear combination of B and the lepton flavours. After giving an estimate of the range of parameters compatible with a Grand Unified Theory, we present the current experimental bounds, discussing the interplay between electroweak precision tests and direct searches at the Tevatron. Finally, we assess the discovery potential of the early LHC.Comment: 6 pages, 2 figures. Talk given at the 2nd Young Researchers Workshop "Physics Challenges in the LHC Era", Frascati, May 10 and 13, 201

Classical and quantum mechanics via supermetrics in time

Koopman-von Neumann in the 30's gave an operatorial formululation of Classical Mechanics. It was shown later on that this formulation could also be written in a path-integral form. We will label this functional approach as CPI (for classical path-integral) to distinguish it from the quantum mechanical one, which we will indicate with QPI. In the CPI two Grassmannian partners of time make their natural appearance and in this manner time becomes something like a three dimensional supermanifold. Next we introduce a metric in this supermanifold and show that a particular choice of the supermetric reproduces the CPI while a different one gives the QPI.Comment: To appear in the proceedings of the conference held in Trieste in October 2008 with title: "Theoretical and Experimental aspects of the spin statistics connection and related symmetries

Cartan-Calculus and its Generalizations via a Path-Integral Approach to Classical Mechanics

In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical variables entering this formulation and show that they are essentially a basis of the cotangent bundle to the tangent bundle to phase-space. In this space we introduce an extended Poisson brackets structure which allows us to re-do all the usual Cartan calculus on symplectic manifolds via these brackets. We also briefly sketch how the Schouten-Nijenhuis, the Fr\"olicher- Nijenhuis and the Nijenhuis-Richardson brackets look in our formalism.Comment: 6 pages, amste