40 research outputs found
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, , are derived and presented (in a
Table) for half-odd-integer values of and . These functions are
eigenfunctions of and written as differential operators in the
spherical-polar angles, and . The Fermion Spherical Harmonics
are a new, scalar and angular-coordinate-dependent representation of fermion
spin angular momentum. They have symmetry in the angle , 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