Neutrino mixing contribution to the cosmological constant

We show that the non-perturbative vacuum structure associated with neutrino mixing leads to a non-zero contribution to the value of the cosmological constant. Such a contribution comes from the specific nature of the mixing phenomenon. Its origin is completely different from the one of the ordinary contribution of a massive spinor field. We estimate this neutrino mixing contribution by using the natural cut--off appearing in the quantum field theory formalism for neutrino mixing and oscillation.Comment: 7 page

Nonassociative strict deformation quantization of C*-algebras and nonassociative torus bundles

In this paper, we initiate the study of nonassociative strict deformation quantization of C*-algebras with a torus action. We shall also present a definition of nonassociative principal torus bundles, and give a classification of these as nonassociative strict deformation quantization of ordinary principal torus bundles. We then relate this to T-duality of principal torus bundles with $H$-flux. We also show that the Octonions fit nicely into our theory.Comment: 15 pages, latex2e, exposition improved, to appear in LM

Fermion mixing in quasi-free states

Quantum field theoretic treatments of fermion oscillations are typically restricted to calculations in Fock space. In this letter we extend the oscillation formulae to include more general quasi-free states, and also consider the case when the mixing is not unitary.Comment: 10 pages, Plain Te

Mixing and oscillations of neutral particles in Quantum Field Theory

We study the mixing of neutral particles in Quantum Field Theory: neutral boson field and Majorana field are treated in the case of mixing among two generations. We derive the orthogonality of flavor and mass representations and show how to consistently calculate oscillation formulas, which agree with previous results for charged fields and exhibit corrections with respect to the usual quantum mechanical expressions.Comment: 8 pages, revised versio

Quantisation of twistor theory by cocycle twist

We present the main ingredients of twistor theory leading up to and including the Penrose-Ward transform in a coordinate algebra form which we can then `quantise' by means of a functorial cocycle twist. The quantum algebras for the conformal group, twistor space CP^3, compactified Minkowski space CMh and the twistor correspondence space are obtained along with their canonical quantum differential calculi, both in a local form and in a global *-algebra formulation which even in the classical commutative case provides a useful alternative to the formulation in terms of projective varieties. We outline how the Penrose-Ward transform then quantises. As an example, we show that the pull-back of the tautological bundle on CMh pulls back to the basic instanton on S^4\subset CMh and that this observation quantises to obtain the Connes-Landi instanton on \theta-deformed S^4 as the pull-back of the tautological bundle on our \theta-deformed CMh. We likewise quantise the fibration CP^3--> S^4 and use it to construct the bundle on \theta-deformed CP^3 that maps over under the transform to the \theta-deformed instanton.Comment: 68 pages 0 figures. Significant revision now has detailed formulae for classical and quantum CP^

T-duality for principal torus bundles

In this paper we study T-duality for principal torus bundles with H-flux. We identify a subset of fluxes which are T-dualizable, and compute both the dual torus bundle as well as the dual H-flux. We briefly discuss the generalized Gysin sequence behind this construction and provide examples both of non T-dualizable and of T-dualizable H-fluxes.Comment: 9 pages, typos removed and minor corrections mad

Fermion Quasi-Spherical Harmonics

Spherical Harmonics, $Y_\ell^m(\theta,\phi)$, are derived and presented (in a Table) for half-odd-integer values of $\ell$ and $m$. These functions are eigenfunctions of $L^2$ and $L_z$ written as differential operators in the spherical-polar angles, $\theta$ and $\phi$. The Fermion Spherical Harmonics are a new, scalar and angular-coordinate-dependent representation of fermion spin angular momentum. They have $4\pi$ symmetry in the angle $\phi$, and hence are not single-valued functions on the Euclidean unit sphere; they are double-valued functions on the sphere, or alternatively are interpreted as having a double-sphere as their domain.Comment: 16 pages, 2 Tables. Submitted to J.Phys.

Quantizing the damped harmonic oscillator

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.Comment: 4 pages, no figure

Dark energy and particle mixing

We show that the vacuum condensate due to particle mixing is responsible of a dynamically evolving dark energy. In particular, we show that values of the adiabatic index close to -1 for vacuum condensates of neutrinos and quarks imply, at the present epoch, contributions to the vacuum energy compatible with the estimated upper bound on the dark energy.Comment: 11 page

Neutrino oscillations from relativistic flavor currents

By resorting to recent results on the relativistic currents for mixed (flavor) fields, we calculate a space-time dependent neutrino oscillation formula in Quantum Field Theory. Our formulation provides an alternative to existing approaches for the derivation of space dependent oscillation formulas and it also accounts for the corrections due to the non-trivial nature of the flavor vacuum. By exploring different limits of our formula, we recover already known results. We study in detail the case of one-dimensional propagation with gaussian wavepackets both in the relativistic and in the non-relativistic regions: in the last case, numerical evaluations of our result show significant deviations from the standard formula.Comment: 16 pages, 4 figures, RevTe