Casimir-Polder intermolecular forces in minimal length theories

Generalized uncertainty relations are known to provide a minimal length $\hbar\sqrt{\beta}$. The effect of such minimal length in the Casimir-Polder interactions between neutral atoms (molecules) is studied. The first order correction term in the minimal uncertainty parameter is derived and found to describe an attractive potential scaling as $r^{-9}$ as opposed to the well known $r^{-7}$ long range retarded potential.Comment: 1 Figure. Version published by Physical Review D. Few references added, typos correcte

Mass Mixing, the Fourth Generation, and the Kinematic Higgs Mechanism

We describe how to construct chiral fermion mass terms using Dirac-Kahler (DK) spinors. Classical massive DK spinors are shown to be equivalent to four generations of Dirac spinors with equal mass coupled to a background U(2,2) gauge field. Quantization breaks U(2,2) to U(2)xU(2), lifts mass spectrum degeneracy, and generates a non-trivial mass mixing matrix.Comment: 12 pages. No figures. Phys Lett B version. Minor typos fixe

The Spectrum of the 4-Generation Dirac-Kaehler Extension of the SM

We compute the mass spectrum of the fermionic sector of the Dirac-Kaehler extension of the SM (DK-SM) by showing that there exists a Bogoliubov transformation that transforms the DK-SM into a flavor U(4) extension of the SM (SM-4) with a particular choice of masses and mixing textures. Mass relations of the model allow determination of masses of the 4th generation. Tree level prediction for the mass of the 4th charged lepton is 370 GeV. The model selects the normal hierarchy for neutrino masses and reproduces naturally the near tri-bimaximal and quark mixing textures. The electron neutrino and the 4th neutrino masses are related via a see-saw-like mechanism.Comment: 14 pages. Phys Lett B versio

Cosmological Constraints on a Dynamical Electron Mass

Motivated by recent astrophysical observations of quasar absorption systems, we formulate a simple theory where the electron to proton mass ratio $\mu =m_{e}/m_{p}$ is allowed to vary in space-time. In such a minimal theory only the electron mass varies, with $\alpha$ and $m_{p}$ kept constant. We find that changes in $\mu$ will be driven by the electronic energy density after the electron mass threshold is crossed. Particle production in this scenario is negligible. The cosmological constraints imposed by recent astronomical observations are very weak, due to the low mass density in electrons. Unlike in similar theories for spacetime variation of the fine structure constant, the observational constraints on variations in $\mu$ imposed by the weak equivalence principle are much more stringent constraints than those from quasar spectra. Any time-variation in the electron-proton mass ratio must be less than one part in $10^{9}$since redshifts $z\approx 1.$This is more than one thousand times smaller than current spectroscopic sensitivities can achieve. Astronomically observable variations in the electron-proton must therefore arise directly from effects induced by varying fine structure 'constant' or by processes associated with internal proton structure. We also place a new upper bound of $2\times 10^{-8}$ on any large-scale spatial variation of $\mu$ that is compatible with the isotropy of the microwave background radiation.Comment: New bounds from weak equivalence principle experiments added, conclusions modifie

Faddeev-Niemi Conjecture and Effective Action of QCD

We calculate a one loop effective action of SU(2) QCD in the presence of the monopole background, and find a possible connection between the resulting QCD effective action and a generalized Skyrme-Faddeev action of the non-linear sigma model. The result is obtained using the gauge-independent decomposotion of the gauge potential into the topological degrees which describes the non-Abelian monopoles and the local dynamical degrees of the potential, and integrating out all the dynamical degrees of QCD.Comment: 6 page

Relativistic Green functions in a plane wave gravitational background

We consider a massive relativistic particle in the background of a gravitational plane wave. The corresponding Green functions for both spinless and spin 1/2 cases, previously computed by A. Barducci and R. Giachetti \cite{Barducci3}, are reobtained here by alternative methods, as for example, the Fock-Schwinger proper-time method and the algebraic method. In analogy to the electromagnetic case, we show that for a gravitational plane wave background a semiclassical approach is also sufficient to provide the exact result, though the lagrangian involved is far from being a quadratic one.Comment: Last paper by Professor Arvind Narayan Vaidya, 18 pages, no figure

Graphene and non-Abelian quantization

In this article we employ a simple nonrelativistic model to describe the low energy excitation of graphene. The model is based on a deformation of the Heisenberg algebra which makes the commutator of momenta proportional to the pseudo-spin. We solve the Landau problem for the resulting Hamiltonian which reduces, in the large mass limit while keeping fixed the Fermi velocity, to the usual linear one employed to describe these excitations as massless Dirac fermions. This model, extended to negative mass, allows to reproduce the leading terms in the low energy expansion of the dispersion relation for both nearest and next-to-nearest neighbor interactions. Taking into account the contributions of both Dirac points, the resulting Hall conductivity, evaluated with a $\zeta$-function approach, is consistent with the anomalous integer quantum Hall effect found in graphene. Moreover, when considered in first order perturbation theory, it is shown that the next-to-leading term in the interaction between nearest neighbor produces no modifications in the spectrum of the model while an electric field perpendicular to the magnetic field produces just a rigid shift of this spectrum. PACS: 03.65.-w, 81.05.ue, 73.43.-fComment: 23 pages, 4 figures. Version to appear in the Journal of Physics A. The title has been changed into "Graphene and non-Abelian quantization". The motivation and presentation of the paper has been changed. An appendix and Section 6 on the evaluation of the Hall conductivity have been added. References adde