Boson mass spectrum in SU(4)L⊗U(1)YSU(4)_L\otimes U(1)_Y model with exotic electric charges

The boson mass spectrum of the electro-weak \textbf{$SU(4)_{L}\otimes U(1)_{Y}$} model with exotic electric charges is investigated by using the algebraical approach supplied by the method of exactly solving gauge models with high symmetries. Our approach predicts for the boson sector a one-parameter mass scale to be tuned in order to match the data obtained at LHC, LEP, CDF.Comment: 12 pages, 1 Table with numerical estimates and 1 Figure added, mistaken results correcte

Canonical and Lie-algebraic twist deformations of κ\kappa-Poincare and contractions to κ\kappa-Galilei algebras

We propose canonical and Lie-algebraic twist deformations of $\kappa$-deformed Poincare Hopf algebra which leads to the generalized $\kappa$-Minkowski space-time relations. The corresponding deformed $\kappa$-Poincare quantum groups are also calculated. Finally, we perform the nonrelativistic contraction limit to the corresponding twisted Galilean algebras and dual Galilean quantum groups.Comment: 16 pages, no figures, v3: few changes provided - version for journal, v2: submitted incidentally, v4: the page numbers for all references in preprint version are provide

Kinematics and hydrodynamics of spinning particles

In the first part (Sections 1 and 2) of this paper --starting from the Pauli current, in the ordinary tensorial language-- we obtain the decomposition of the non-relativistic field velocity into two orthogonal parts: (i) the "classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM), and (ii) the so-called "quantum" part, that is, the 3-velocity V of the motion IN the CM frame (namely, the internal "spin motion" or zitterbewegung). By inserting such a complete, composite expression of the velocity into the kinetic energy term of the non-relativistic classical (i.e., newtonian) lagrangian, we straightforwardly get the appearance of the so-called "quantum potential" associated, as it is known, with the Madelung fluid. This result carries further evidence that the quantum behaviour of micro-systems can be adirect consequence of the fundamental existence of spin. In the second part (Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it being now necessary to pass to relativistic (classical) physics; and we show that the proper time entering the definition of the four-velocity v^mu for spinning particles has to be the proper time tau of the CM frame. Inserting the correct Lorentz factor into the definition of v^mu leads to completely new kinematical properties for v_mu v^mu. The important constraint p_mu v^mu = m, identically true for scalar particles, but just assumed a priori in all previous spinning particle theories, is herein derived in a self-consistent way.Comment: LaTeX file; needs kapproc.st

Nullification of multi-Higgs threshold amplitudes in the Standard Model

We show that nullification of all tree-order threshold amplitudes involving Higgs particles in the Standard Model occurs, provided that certain equations relating the masses of all existing elementary particles to the mass of the Higgs scalar are satisfied. The possible role of these relations in restoring the high-multiplicity unitarity and their phenomenological relevance are briefly discussed.Comment: CERN-TH.6853/93, 9 pages, Late

Operator Transformations Between Exactly Solvable Potentials and Their Lie Group Generators

One may obtain, using operator transformations, algebraic relations between the Fourier transforms of the causal propagators of different exactly solvable potentials. These relations are derived for the shape invariant potentials. Also, potentials related by real transformation functions are shown to have the same spectrum generating algebra with Hermitian generators related by this operator transformation.Comment: 13 pages with one Postscript figure, uses LaTeX2e with revte

Unified description of 0+ states in a large class of nuclear collective models

A remarkably simple regularity in the energies of 0+ states in a broad class of collective models is discussed. A single formula for all 0+ states in flat-bottomed infinite potentials that depends only on the number of dimensions and a simpler expression applicable to all three IBA symmetries in the large boson number limit are presented. Finally, a connection between the energy expression for 0+ states given by the X(5) model and the predictions of the IBA near the critical point is explored.Comment: 4 pages, 3 postscript figures, uses revTe

Decomposition of time-covariant operations on quantum systems with continuous and/or discrete energy spectrum

Every completely positive map G that commutes which the Hamiltonian time evolution is an integral or sum over (densely defined) CP-maps G_\sigma where \sigma is the energy that is transferred to or taken from the environment. If the spectrum is non-degenerated each G_\sigma is a dephasing channel followed by an energy shift. The dephasing is given by the Hadamard product of the density operator with a (formally defined) positive operator. The Kraus operator of the energy shift is a partial isometry which defines a translation on R with respect to a non-translation-invariant measure. As an example, I calculate this decomposition explicitly for the rotation invariant gaussian channel on a single mode. I address the question under what conditions a covariant channel destroys superpositions between mutually orthogonal states on the same orbit. For channels which allow mutually orthogonal output states on the same orbit, a lower bound on the quantum capacity is derived using the Fourier transform of the CP-map-valued measure (G_\sigma).Comment: latex, 33 pages, domains of unbounded operators are now explicitly specified. Presentation more detailed. Implementing the shift after the dephasing is sometimes more convenien

On the shape of tachyons

We study some aspects of the experimental behaviour of tachyons, in particular by finding out their « apparent » shape. A Superluminal particle, which in its own rest frame is spherical or ellipsoidal (and with an infinite lifetime), would « appear » to a laboratory frame as occupying the whole region of space bound by a double cone and a twosheeted hyperboloid. Such a structure (the tachyon « shape ») rigidly travels with the speed of the tachyon. However, if the Superluminal particle has a finite lifetimein its rest frame, then in the laboratory frame it gets afinite space extension. As a by-product, we are able to interpret physically the imaginary units entering—as is well known—the transverse co-ordinates in the Superluminal Lorentz transformations. The various particular or limiting cases of the tachyon shape are thoroughly considered. Finally, some brief considerations concerning possible experiments to look for tachyons are added

Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics

In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based upon the complex Lie algebra sl(2, C). This extends to the complex domain the well-known relationship between SUSYQM and potential algebras for Hermitian Hamiltonians, resulting from their common link with the factorization method and Darboux transformations. In the same framework, we also generate for the first time a pair of elliptic partner potentials of Weierstrass $\wp$ type, one of them being real and the other imaginary and PT symmetric. The latter turns out to be quasiexactly solvable with one known eigenvalue corresponding to a bound state. When the Weierstrass function degenerates to a hyperbolic one, the imaginary potential becomes PT non-symmetric and its known eigenvalue corresponds to an unbound state.Comment: 20 pages, Latex 2e + amssym + graphics, 2 figures, accepted in Int. J. Mod. Phys.

Heat Kernel Asymptotics on Homogeneous Bundles

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal solution correctly reproduces the exact heat kernel diagonal after a suitable regularization and analytical continuation.Comment: 29 pages, Proceedings of the 2007 Midwest Geometry Conference in Honor of Thomas P. Branso