Understanding flavor mixing in Quantum Field Theory

We report on recent results showing that a rich non-perturbative vacuum structure is associated with flavor mixing in Quantum Field Theory. We treat explicitly the case of mixing among three generations of Dirac fermions. Exact oscillation formulas are presented exhibiting new features with respect to the usual ones. CP and T violation are also discussed.Comment: 9 pages. Presented at the "International Conference on Flavor Physics", Zhang-Jia-Jie, China, May 31 - June 6 200

Group theoretical aspects of neutrino mixing in Quantum Field Theory

By resorting to recent results on the Quantum Field Theory of mixed particles, we discuss some aspects of three flavor neutrino mixing. Particular emphasis is given to the related algebraic structures and their deformation in the presence of CP violation. A novel geometric phase related to CP violation is introduced.Comment: 10 pages, 2 figures. Presented at the XII International Baksan School "Particles and Cosmology", Baksan Valley, Kabardino-Balkaria, Russian Federation - April 21 - 26, 200

A new perspective in the dark energy puzzle from particle mixing phenomenon

We report on recent results on particle mixing and oscillations in quantum field theory. We discuss the role played in cosmology by the vacuum condensate induced by the neutrino mixing phenomenon. We show that it can contribute to the dark energy of the universe.Comment: 11 pages, to be published on the review book "Dark Energy-Current Advances and Ideas

Dissipation and quantization for composite systems

In the framework of 't Hooft's quantization proposal, we show how to obtain from the composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be interpreted as a particle in an effective magnetic field, interacting through a spin-orbit interaction term. In the limit of a large separation from the interaction region one can describe the system in terms of two irreducible elementary subsystems which correspond to two independent quantum harmonic oscillators.Comment: 9 page

Dissipation and Topologically Massive Gauge Theories in Pseudoeuclidean Plane

In the pseudo-euclidean metrics Chern-Simons gauge theory in the infrared region is found to be associated with dissipative dynamics. In the infrared limit the Lagrangian of 2+1 dimensional pseudo-euclidean topologically massive electrodynamics has indeed the same form of the Lagrangian of the damped harmonic oscillator. On the hyperbolic plane a set of two damped harmonic oscillators, each other time-reversed, is shown to be equivalent to a single undamped harmonic oscillator. The equations for the damped oscillators are proven to be the same as the ones for the Lorentz force acting on two particles carrying opposite charge in a constant magnetic field and in the electric harmonic potential. This provides an immediate link with Chern-Simons-like dynamics of Bloch electrons in solids propagating along the lattice plane with hyperbolic energy surface. The symplectic structure of the reduced theory is finally discussed in the Dirac constrained canonical formalism.Comment: 22 pages, LaTe

On Normal ordering and Canonical transformations in Thermal Field Theory

We look at a real scalar field in thermal equilibrium in the context of the new normal ordering and field split defined by Evans and Steer. We show that the field split defines a natural canonical transformation, but that this transformation differs from others known in thermal field theory.Comment: 13 pages, LaTeX. (Revisions made to discussion and various small errors in equations corrected

Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics

By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg ($q$-WH) algebra into the theory of entire analytic functions. The main tool is the realization of the $q$--WH algebra in terms of finite difference operators. The physical relevance of our study relies on the fact that coherent states (CS) are indeed formulated in the space of entire analytic functions where they can be rigorously expressed in terms of theta functions on the von Neumann lattice. The r\^ole played by the finite difference operators and the relevance of the lattice structure in the completeness of the CS system suggest that the $q$--deformation of the WH algebra is an essential tool in the physics of discretized (periodic) systems. In this latter context we define a quantum mechanics formalism for lattice systems.Comment: 22 pages, TEX file, DFF188/9/93 Firenz