arXiv subjects

F. Scheck

Publications and source records attributed to F. Scheck.

9 recordsLinked to original sources

arXiv2006

The spin-statistics relation in nonrelativistic quantum mechanics and projective modules

In this work we consider non-relativistic quantum mechanics, obtained from a classical configuration space Q of indistinguishable particles. Following an approach proposed by one of the authors, wave functions are regarded as elements of suitable projective modules over C(Q). We take furthermore into account the G-Theory point of view, where the role of group action is particularly emphasized. As an example illustrating the method, the case of two particles is worked out in detail. Previous works aiming at a proof of a spin-statistics theorem for non-relativistic quantum mechanics are re-considered from the point of view of our approach, enabling us to clarify several points.

quant-ph↗

arXiv2000

Tau neutrinos from muon storage rings

Charged tau leptons emerging in a long baseline experiment with a muon storage ring and a far-away detector will positively establish neutrino oscillations. We study the conversion of $\nu_\mu$ ($\bar{\nu}_\mu$) and of $\bar{\nu}_e$ ($\nu_e$) to $\nu_\tau$ or $\bar{\nu}_\tau$ for neutrinos from a 20 GeV muon storage ring, within the strong mixing scheme and on the basis of the squared mass differences which are compatible with all reported neutrino anomalies, including the LSND data. In contrast to other solutions which ignore the Los Alamos anomaly, we find charged tau production rates which should be measurable in a realistic set up. As a consequence, determining the complete mass spectrum of neutrinos as well as all three mixing angles seems within reach. Matter effects are discussed thoroughly but are found to be small in this situation.

hep-ph↗

arXiv2000

CP Violation with Three Oscillating Neutrino Flavours

We explore the prospects of observing leptonic CP violation in a neutrino factory in the context of a scenario with three strongly oscillating neutrinos able to account for the solar, the atmospheric and the LSND results. We address also the problems related with the fake asymmetries induced by the experimental device and by the presence of matter.

hep-ph↗

arXiv1999

Oscillations, Neutrino Masses and Scales of New Physics

We show that all the available experimental information involving neutrinos can be accounted for within the framework of already existing models where neutrinos have zero mass at tree level, but obtain a small Dirac mass by radiative corrections.

hep-ph↗

arXiv1997

Leptonic Generation Mixing, Noncommutative Geometry and Solar Neutrino Fluxes

Triangular mass matrices for neutrinos and their charged partners contain full information on neutrino mixing in a most concise form. Although the scheme is general and model independent, triangular matrices are typical for reducible but indecomposable representations of graded Lie algebras which, in turn, are characteristic for the standard model in noncommutative geometry. The mixing matrix responsible for neutrino oscillations is worked out analytically for two and three lepton families. The example of two families fixes the mixing angle to just about what is required by the Mikheyev-Smirnov-Wolfenstein resonance oscillation of solar neutrinos. In the case of three families we classify all physically plausible choices for the neutrino mass matrix and derive interesting bounds on some of the moduli of the mixing matrix.

hep-ph↗

arXiv1997

Triangular mass matrices of quarks and Cabibbo-Kobayashi-Maskawa mixing

Every nonsingular fermion mass matrix, by an appropriate unitary transformation of right-chiral fields, is equivalent to a triangular matrix. Using the freedom in choosing bases of right-chiral fields in the minimal standard model, reduction to triangular form reduces the well-known ambiguities in reconstructing a mass matrix to trivial phase redefinitions. Furthermore, diagonalization of the quark mass sectors can be shifted to one charge sector only, without loosing the concise and economic triangular form. The corresponding effective triangular mass matrix is reconstructed, up to trivial phases, from the moduli of the CKM matrix elements, and vice versa, in a unique way. A new formula for the parametrization independent CP-measure in terms of observables is derived and discussed.

hep-ph↗

arXiv1997

The Standard model within noncommutative geometry: a comparison of models

Algebraic Yang-Mills-Higgs theories based on noncommutative geometry have brought forth novel extensions of gauge theories with interesting applications to phenomenology. We sketch the model of Connes and Lott, as well as variants of it, and the model developed by a Mainz-Marseille group, by comparing them in a schematic way. The role of fermion masses and mixings is discussed, and the question of possible parameter relations is briefly touched.

hep-th↗

arXiv1994

Models of Electroweak Interactions in Non-Commutative Geometry: A Comparison

Alain Connes' construction of the standard model is based on a generalized Dirac-Yukawa operator and the K-cycle $(\HD ,D)$, with $\HD$ a fermionic Hilbert space. If this construction is reformulated at the level of the differential algebra then a direct comparison with the alternative approach by the Marseille-Mainz group becomes possible. We do this for the case of the toy model based on the structure group $U(1)\times U(1)$ and for the $SU(2)\times U(1)$ of electroweak interactions. Connes' results are recovered without the somewhat disturbing $γ_{5}$-factors in the fermion mass terms and Yukawa couplings. We discuss both constructions in the same framework and, in particular, pinpoint the origin of the difference in the Higgs potential obtained by them.

hep-th↗

arXiv1993

Algebraic connections on parallel universes

For any manifold $M$, we introduce a $\ZZ $-graded differential algebra $Ξ$, which, in particular, is a bi-module over the associative algebra $C(M\cup M)$. We then introduce the corresponding covariant differentials and show how this construction can be interpreted in terms of Yang-Mills and Higgs fields. This is a particular example of noncommutative geometry. It differs from the prescription of Connes in the following way: The definition of $Ξ$ does not rely on a given Dirac-Yukawa operator acting on a space of spinors.

hep-th↗