Physical flavor neutrino states

The problem of representation for flavor states of mixed neutrinos is discussed. By resorting to recent results, it is shown that a specific representation exists in which a number of conceptual problems are resolved. Phenomenological consequences of our analysis are explored.Comment: Presented at 5th International Workshop DICE2010: Space-Time-Matter - Current Issues in Quantum Mechanics and Beyon

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

Boundary conformal fields and Tomita--Takesaki theory

Motivated by formal similarities between the continuum limit of the Ising model and the Unruh effect, this paper connects the notion of an Ishibashi state in boundary conformal field theory with the Tomita--Takesaki theory for operator algebras. A geometrical approach to the definition of Ishibashi states is presented, and it is shownthat, when normalisable the Ishibashi states are cyclic separating states, justifying the operator state correspondence. When the states are not normalisable Tomita--Takesaki theory offers an alternative approach based on left Hilbert algebras, opening the way to extensions of our construction and the state-operator correspondence.Comment: 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

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

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

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.

Noncommutative Burgers Equation

We present a noncommutative version of the Burgers equation which possesses the Lax representation and discuss the integrability in detail. We find a noncommutative version of the Cole-Hopf transformation and succeed in the linearization of it. The linearized equation is the (noncommutative) diffusion equation and exactly solved. We also discuss the properties of some exact solutions. The result shows that the noncommutative Burgers equation is completely integrable even though it contains infinite number of time derivatives. Furthermore, we derive the noncommutative Burgers equation from the noncommutative (anti-)self-dual Yang-Mills equation by reduction, which is an evidence for the noncommutative Ward conjecture. Finally, we present a noncommutative version of the Burgers hierarchy by both the Lax-pair generating technique and the Sato's approach.Comment: 24 pages, LaTeX, 1 figure; v2: discussions on Ward conjecture, Sato theory and the integrability added, references added, version to appear in J. Phys.

Lectures on Nongeometric Flux Compactifications

These notes present a pedagogical review of nongeometric flux compactifications. We begin by reviewing well-known geometric flux compactifications in Type II string theory, and argue that one must include nongeometric "fluxes" in order to have a superpotential which is invariant under T-duality. Additionally, we discuss some elementary aspects of the worldsheet description of nongeometric backgrounds. This review is based on lectures given at the 2007 RTN Winter School at CERN.Comment: 31 pages, JHEP