Binding Threshold for the Pauli–Fierz Operator

For the Pauli–Fierz operator with a short range potential we study the binding threshold ₁() as a function of the fine structure constant and show that it converges to the binding threshold for the Schrödinger operator in the limit 0.This work was supported in part by Fondecyt (Chile), Project #102-0844. Work partially supported by HPRN-CT-2002-00277, and the Volkswagen Stiftung through a cooperation grant.     

Fierz–Pauli equation for massive gravitons from Induced Matter theory of gravity

Starting with a 5D physical vacuum described by a 5D Ricci-flat background metric, we study the emergence of gravitational waves (GW) from the Induce Matter (IM) theory of gravity. We obtain the equation of motion for GW on a 4D curved spacetime which has the form of a Fierz–Pauli one. In our model the mass of gravitons mg is induced by a static foliation on the noncompact space-like extra dimension and the source-term is originated in the interaction of the GW with the induced connections of the background 5D metric. Here, relies the main difference of this formalism with the original Fierz–Pauli one.     

Fierz bilinear formulation of the Maxwell–Dirac equations and symmetry reductions

We study the Maxwell–Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The internally produced vector potential is expressed via algebraic manipulation of the Dirac equation, as a rational function of the Fierz bilinears and first derivatives (valid on the support of the scalar density), which allows a gauge invariant vector potential to be defined. This leads to a Fierz bilinear formulation of the Maxwell tensor and of the Maxwell–Dirac equations, without any reference to gauge dependent quantities. We show how demanding invariance of tensor fields under the action of a fixed (but arbitrary) Lie subgroup of the Poincaré group leads to symmetry reduced equations. The procedure is illustrated, and the reduced equations worked out explicitly for standard spherical and cylindrical cases, which are coupled third order nonlinear PDEs. Spherical symmetry necessitates the existence of magnetic monopoles, which do not affect the coupled Maxwell–Dirac system due to magnetic terms cancelling. In this paper we do not take up numerical computations. As a demonstration of the power of our approach, we also work out the symmetry reduced equations for two distinct classes of dimension 4 one-parameter families of Poincaré subgroups, one splitting and one non-splitting. The splitting class yields no solutions, whereas for the non-splitting class we find a family of formal exact solutions in closed form.     

Wolfgang Pauli 1900–1958

A review of The New Physics. Edited by P. C. W. Davies. (Cambridge University Press, 1989.) [Pp. 5161 £30 hardback. ISBN 0 521 30420 2. Scope: Multiauthor survey. Level: General readerfundergraduate.     

Newton–Hooke-type symmetry of anisotropic oscillators

Rotation-less Newton–Hooke-type symmetry, found recently in the Hill problem, and instrumental for explaining the center-of-mass decomposition, is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter system is shown, by the orbit method, to be the most general one with such a symmetry. Full Newton–Hooke symmetry is recovered in the isotropic case. Star escape from a galaxy is studied as an application.     

Tri-bimaximal mixing from twisted Friedberg–Lee symmetry

We investigate the Friedberg–Lee (FL) symmetry and its promotion to include the μ–τ symmetry, and call this the twisted FL symmetry. Based on the twisted FL symmetry, two possible schemes are presented toward the realistic neutrino mass spectrum and the tri-bimaximal mixing. In the first scheme, we suggest the semi-uniform translation of the FL symmetry. The second one is based on the S ₃ permutation family symmetry. The breaking terms, which are twisted FL symmetric, are introduced. Some viable models in each scheme are also presented.     

BRST symmetry for Regge–Teitelboim-based minisuperspace models

The Einstein–Hilbert action in the context of higher derivative theories is considered for finding their BRST symmetries. Being a constraint system, the model is transformed in the minisuperspace language with the FRLW background and the gauge symmetries are explored. Exploiting the first order formalism developed by Banerjee et al. the diffeomorphism symmetry is extracted. From the general form of the gauge transformations of the field, the analogous BRST transformations are calculated. The effective Lagrangian is constructed by considering two gauge-fixing conditions. Further, the BRST (conserved) charge is computed, which plays an important role in defining the physical states from the total Hilbert space of states. The finite field-dependent BRST formulation is also studied in this context where the Jacobian for the functional measure is illustrated specifically.     

Noether symmetry for Gauss–Bonnet dilatonic gravity

Noether symmetry for Gauss–Bonnet Dilatonic interaction exists for a constant dilatonic scalar potential and a linear functional dependence of the coupling parameter on the scalar field. The symmetry with the same form of the potential and coupling parameter exists all in the vacuum, radiation and matter dominated era. The late time acceleration is driven by the effective cosmological constant rather than the Gauss–Bonnet term, while the later compensates for the large value of the effective cosmological constant giving a plausible answer to the well-known coincidence problem.     

Influence of s± symmetry on unconventional superconductivity in pnictides above the Pauli limit – two-band model study

The theoretical analysis of the Cooper pair susceptibility shows the two-band Fe-based superconductors (FeSC) to support the existence of the phase with nonzero Cooper pair momentum (called the Fulde-Ferrel-Larkin-Ovchinnikov phase or shortly FFLO), regardless of the order parameter symmetry. Moreover this phase for the FeSC model with s _± symmetry is the ground state of the system near the Pauli limit. This article discusses the phase diagram h-T for FeSC in the two-band model and its physical consequences. We compare the results for the superconducting order parameter with s-wave and s _±-wave symmetry – in first case the FFLO phase can occur in both bands, while in second case only in one band. We analyze the resulting order parameter in real space – showing that the FeSC with s _±-wave symmetry in the Pauli limit have typical properties of one-band systems, such as oscillations of the order parameter in real space with constant amplitude, whereas with s-wave symmetry the oscillations have an amplitude modulation. Discussing the free energy in the superconducting state we show that in absence of orbital effects, the phase transition from the BCS to the FFLO state is always first order, whereas from the FFLO phase to normal state is second order.     

Dynamics of multiparticle systems with non–abelian symmetry

We consider the dynamics governing the evolution of a many body system constrained by a nonabelian local symmetry. We obtain explicit forms of the global macroscopic condition assuring that at the microscopic level the evolution respects the overall symmetry constraint. We demonstrate the constraint mechanisms for the case of SU(2) system comprising particles in fundamental, and adjoint representations (‘nucleons’ and ‘pions’). Received: 10 March 2000 / Revised version: 7 July 2000/ Published online: 8 December 2000     

Optical solitons with Chen–Lee–Liu equation by Lie symmetry

This paper avails of classical Lie symmetry analysis to exhibit optical solitons to Chen–Lee–Liu model. By the aid of the proposed method, we secure symmetries that transform the model to a system of ordinary differential equations which are subsequently investigated by a number of methods to recover bright, dark and singular solitons.     

Universal seesaw from left–right and Peccei–Quinn symmetry breaking

To generate the lepton and quark masses in the left–right symmetric models, we can consider a universal seesaw scenario by integrating out heavy fermion singlets which have the Yukawa couplings with the fermion and Higgs doublets. The universal seesaw scenario can also accommodate the leptogenesis with Majorana or Dirac neutrinos. We show that the fermion singlets can obtain their heavy masses from the Peccei–Quinn symmetry breaking.     

Ultrarelativistic Bose–Einstein gas on Lorentz symmetry violation

In this paper, we study the effects of Lorentz Symmetry Breaking on the thermodynamic properties of ideal gases. Inspired by the dispersion relation coming from the Carroll–Field–Jackiw model for Electrodynamics with Lorentz and CPT violation term, we compute the thermodynamics quantities for a Boltzmann, Fermi–Dirac and Bose–Einstein distributions. Two regimes are analyzed: the large and the small Lorentz violation. In the first case, we show that the topological mass induced by the Chern–Simons term behaves as a chemical potential. For Bose–Einstein gases, a condensation in both regimes can be found.     

Painlevé analysis,infinite dimensional symmetry group and symmetry reductions for the(2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

The(2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani(KdVSKR) equation is studied by the singularity structure analysis. It is proven that it admits the Painlevé property. The Lie algebras which depend on three arbitrary functions of time t are obtained by the Lie point symmetry method. It is shown that the KdVSKR equation possesses an infinite-dimensional Kac–Moody–Virasoro symmetry algebra. By selecting first-order polynomials in t, a finitedimensional subalgebra of physical transformati...