Advances in High Energy Physics The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Quantum Speed Limit for Relativistic Spin-0 and Spin-1 Bosons on Commutative and Noncommutative Planes Sun, 22 Oct 2017 07:10:35 +0000 Quantum speed limits of relativistic charged spin-0 and spin-1 bosons in the background of a homogeneous magnetic field are studied on both commutative and noncommutative planes. We show that, on the commutative plane, the average speeds of wave packets along the radial direction during the interval in which a quantum state is evolving from an initial state to the orthogonal final one can not exceed the speed of light, regardless of the intensities of the magnetic field. However, due to the noncommutativity, the average speeds of the wave packets on noncommutative plane will exceed the speed of light in vacuum provided the intensity of the magnetic field is strong enough. It is a clear signature of violating Lorentz invariance in the relativistic quantum mechanics region. Kang Wang, Yu-Fei Zhang, Qing Wang, Zheng-Wen Long, and Jian Jing Copyright © 2017 Kang Wang et al. All rights reserved. Irreversible Thermodynamic Description of Dark Matter and Radiation Creation during Inflationary Reheating Wed, 18 Oct 2017 00:00:00 +0000 We investigate matter creation processes during the reheating period of the early Universe, by using the thermodynamic of open systems. The Universe is assumed to consist of the inflationary scalar field, which, through its decay, generates relativistic matter and pressureless dark matter. The inflationary scalar field transfers its energy to the newly created matter particles, with the field energy decreasing to near zero. The equations governing the irreversible matter creation are obtained by combining the thermodynamics description of the matter creation and the gravitational field equations. The role of the different inflationary scalar field potentials is analyzed by using analytical and numerical methods. The values of the energy densities of relativistic matter and dark matter reach their maximum when the Universe is reheated up to the reheating temperature, which is obtained as a function of the scalar field decay width, the scalar field particle mass, and the cosmological parameters. Particle production leads to the acceleration of the Universe during the reheating phase, with the deceleration parameter showing complex dynamics. Once the energy density of the scalar field becomes negligible with respect to the matter densities, the expansion of the Universe decelerates, and inflation has a graceful exit. Juntong Su, Tiberiu Harko, and Shi-Dong Liang Copyright © 2017 Juntong Su et al. All rights reserved. Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space Tue, 17 Oct 2017 00:00:00 +0000 We study the (2 + 1)-dimensional Dirac oscillator in the noncommutative phase space and the energy eigenvalues and the corresponding wave functions of the system are obtained through the sl() algebraization. It is shown that the results are in good agreement with those obtained previously via a different method. H. Panahi and A. Savadi Copyright © 2017 H. Panahi and A. Savadi. All rights reserved. Cosmic Microwave Background as a Thermal Gas of SU(2) Photons: Implications for the High- Cosmological Model and the Value of Mon, 16 Oct 2017 00:00:00 +0000 Presently, we are facing a tension in the most basic cosmological parameter, the Hubble constant . This tension arises when fitting the Lambda-cold-dark-matter model (CDM) to the high-precision temperature-temperature (TT) power spectrum of the Cosmic Microwave Background (CMB) and to local cosmological observations. We propose a resolution of this problem by postulating that the thermal photon gas of the CMB obeys an SU() rather than U() gauge principle, suggesting a high- cosmological model which is void of dark-matter. Observationally, we rely on precise low-frequency intensity measurements in the CMB spectrum and on a recent model independent (low-) extraction of the relation between the comoving sound horizon at the end of the baryon drag epoch and (). We point out that the commonly employed condition for baryon-velocity freeze-out is imprecise, judged by a careful inspection of the formal solution to the associated Euler equation. As a consequence, the above-mentioned tension actually transforms into a discrepancy. To make contact with successful low-  CDM cosmology we propose an interpolation based on percolated/depercolated vortices of a Planck-scale axion condensate. For a first consistency test of such an all- model we compute the angular scale of the sound horizon at photon decoupling. Steffen Hahn and Ralf Hofmann Copyright © 2017 Steffen Hahn and Ralf Hofmann. All rights reserved. AdS Black Hole with Phantom Scalar Field Sun, 15 Oct 2017 06:40:55 +0000 We present an AdS black hole solution with Ricci flat horizon in Einstein-phantom scalar theory. The phantom scalar fields just depend on the transverse coordinates and , which are parameterized by the parameter . We study the thermodynamics of the AdS phantom black hole. Although its horizon is a Ricci flat Euclidean space, we find that the thermodynamical properties of the black hole solution are qualitatively the same as those of AdS Schwarzschild black hole. Namely, there exists a minimal temperature and the large black hole is thermodynamically stable, while the smaller one is unstable, so there is a so-called Hawking-Page phase transition between the large black hole and the thermal gas solution in the AdS space-time in Poincare coordinates. We also calculate the entanglement entropy for a strip geometry dual to the AdS phantom black holes and find that the behavior of the entanglement entropy is qualitatively the same as that of the black hole thermodynamical entropy. Limei Zhang, Xiaoxiong Zeng, and Zhonghua Li Copyright © 2017 Limei Zhang et al. All rights reserved. Response to: Comment on “Does the Equivalence between Gravitational Mass and Energy Survive for a Composite Quantum Body?” Tue, 10 Oct 2017 00:00:00 +0000 We have recently shown that both passive and active gravitational masses of a composite body are not equivalent to its energy due to some quantum effects. We have also suggested idealized and more realistic experiments to detect the above-mentioned inequivalence for a passive gravitational mass. The suggested idealized effect is as follows. A spacecraft moves protons of a macroscopic ensemble of hydrogen atoms with constant velocity in the Earth’s gravitational field. Due to nonhomogeneous squeezing of space by the field, electron ground state wave function experiences time-dependent perturbation in each hydrogen atom. This perturbation results in the appearance of a finite probability for an electron to be excited at higher energy levels and to emit a photon. The experimental task is to detect such photons from the ensemble of the atoms. More realistic variants of such experiment can be realized in solid crystals and nuclei, as first mentioned by us. In his recent comment on our paper, Crowell has argued that the effect, suggested by us, contradicts the existing experiments and, in particular, astronomic data. We show here that this conclusion is incorrect and based on the so-called “free fall” experiments, where our effect does not have to be observed. A. G. Lebed Copyright © 2017 A. G. Lebed. All rights reserved. Impact of Scalar Leptoquarks on Heavy Baryonic Decays Mon, 09 Oct 2017 00:00:00 +0000 We present a study on the impact of scalar leptoquarks on the semileptonic decays of ,, and . To this end, we calculate the differential branching ratio and lepton forward-backward asymmetry defining the processes , , and , with being or , using the form factors calculated via light cone QCD in full theory. In calculations, the errors of form factors are taken into account. We compare the results obtained in leptoquark model with those of the standard model as well as the existing lattice QCD predictions and experimental data. K. Azizi, A. T. Olgun, and Z. Tavukoğlu Copyright © 2017 K. Azizi et al. All rights reserved. The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential Sun, 08 Oct 2017 00:00:00 +0000 We first present the exact solutions of the single ring-shaped Coulomb potential and then realize the visualizations of the space probability distribution for a moving particle within the framework of this potential. We illustrate the two-dimensional (contour) and three-dimensional (isosurface) visualizations for those specifically given quantum numbers (,,) essentially related to those so-called quasi-quantum numbers (,,) through changing the single ring-shaped Coulomb potential parameter . We find that the space probability distributions (isosurface) of a moving particle for the special case and the usual case are spherical and circularly ring-shaped, respectively, by considering all variables in spherical coordinates. We also study the features of the relative probability values of the space probability distributions. As an illustration, by studying the special case of the quantum numbers (,,) = (6, 5, 1), we notice that the space probability distribution for a moving particle will move towards the two poles of the -axis as the relative probability value increases. Moreover, we discuss the series expansion of the deformed spherical harmonics through the orthogonal and complete spherical harmonics and find that the principal component decreases gradually and other components will increase as the potential parameter increases. Yuan You, Fa-Lin Lu, Dong-Sheng Sun, Chang-Yuan Chen, and Shi-Hai Dong Copyright © 2017 Yuan You et al. All rights reserved. A Study of Confinement for Potentials on D3, M2, and M5 Branes Tue, 03 Oct 2017 00:00:00 +0000 We study analytically and numerically the interaction potentials between a pair of quark and antiquark on D3, M2, and M5 branes. These potentials are obtained using Maldacena’s method involving Wilson loops and present confining and nonconfining behaviours in different situations that we explore in this work. In particular, at the near horizon geometry, the potentials are nonconfining in agreement with conformal field theory expectations. On the other side, far from horizon, the dual field theories are no longer conformal and the potentials present confinement. This is in agreement with the behaviour of strings in flat space where the string mimics the expected flux tube of QCD. A study of the transition between the confining/nonconfining regimes in the three different scenarios (D3, M2, and M5) is also performed. Edward Quijada and Henrique Boschi-Filho Copyright © 2017 Edward Quijada and Henrique Boschi-Filho. All rights reserved. Note on Relation between Bottom-Up Holographic Models and Large- QCD Mon, 02 Oct 2017 07:30:29 +0000 We discuss a derivation of the quadratic in fields part of action of bottom-up holographic models from some general properties of the large- limit in QCD. The importance of rescaling of five-dimensional fields is emphasized using the soft wall model as an example. S. S. Afonin Copyright © 2017 S. S. Afonin. All rights reserved. Bulk Local Operators, Conformal Descendants, and Radial Quantization Mon, 02 Oct 2017 00:00:00 +0000 We establish a construction of the bulk local operators in AdS by considering CFT at finite energy scale. Without assuming any prior knowledge about the bulk, the solution to the bulk free field equation automatically appears in the field theory arguments. In the radial quantization formalism, we find a properly regularized version of our initial construction. Possible generalizations beyond pure AdS are also discussed. Zhao-Long Wang and Yi Yan Copyright © 2017 Zhao-Long Wang and Yi Yan. All rights reserved. Van der Waals-Like Phase Transition from Holographic Entanglement Entropy in Lorentz Breaking Massive Gravity Mon, 02 Oct 2017 00:00:00 +0000 Phase transition of AdS black holes in Lorentz breaking massive gravity has been studied in the framework of holography. We find that there is a first-order phase transition (FPT) and second-order phase transition (SPT) both in Bekenstein-Hawking entropy- (BHE-) temperature plane and in holographic entanglement entropy- (HEE-) temperature plane. Furthermore, for the FPT, the equal area law is checked and for the SPT, the critical exponent of the heat capacity is also computed. Our results confirm that the phase structure of HEE is similar to that of BHE in Lorentz breaking massive gravity, which implies that HEE and BHE have some potential underlying relationship. Xian-Ming Liu, Hong-Bo Shao, and Xiao-Xiong Zeng Copyright © 2017 Xian-Ming Liu et al. All rights reserved. Massive Fluctuations in Deconfining SU(2) Yang-Mills Thermodynamics Wed, 27 Sep 2017 09:24:43 +0000 We review how vertex constraints inherited from the thermal ground state strongly reduce the integration support of loop four-momenta associated with massive quasiparticles in bubble diagrams constituting corrections to the free thermal quasiparticle pressure. In spite of the observed increasingly suppressing effect when increasing 2-particle-irreducible (2PI) loop order, a quantitative analysis enables us to disprove the conjecture voiced in hep-th/0609033 that the loop expansion would terminate at a finite order. This reveals the necessity to investigate exact expressions of (at least some) higher-loop order diagrams. Explicit calculation shows that although the behaviour of the 2PI three-loop contribution at low temperatures displays hierarchical suppression compared to lower loop orders, its high-temperature expression instead dominates all lower orders. However, an all-loop-order resummation of a class of 2PI bubble diagrams is shown to yield an analytic continuation of the low-temperature hierarchy to all temperatures in the deconfining phase. Ingolf Bischer Copyright © 2017 Ingolf Bischer. All rights reserved. Effective Models of Quantum Gravity Induced by Planck Scale Modifications in the Covariant Quantum Algebra Tue, 26 Sep 2017 10:02:10 +0000 We introduce modified covariant quantum algebra based on the so-called Quesne-Tkachuk algebra. By means of a deformation procedure we arrive at a class of higher-derivative models of gravity. The study of the particle spectra of these models reveals equivalence with the physical content of the well-known higher-derivative gravities. The particle spectrum exhibits the presence of spurious complex ghosts and, in light of this problem, we suggest an interesting interpretation in the context of minimal length theories. Also, a discussion regarding the nonrelativistic potential energy is proposed. G. P. de Brito, P. I. C. Caneda, Y. M. P. Gomes, J. T. Guaitolini Junior, and V. Nikoofard Copyright © 2017 G. P. de Brito et al. All rights reserved. Asymptotic Behaviour of the QED Perturbation Series Tue, 19 Sep 2017 00:00:00 +0000 I will summarize the present state of a long-term effort to obtain information on the large-order asymptotic behaviour of the QED perturbation series through the effective action. Starting with the constant-field case, I will discuss the Euler-Heisenberg Lagrangian in various dimensions and up to the three-loop level. This Lagrangian holds the information on the N-photon amplitudes in the low-energy limit, and combining it with Spinor helicity methods explicit all-N results can be obtained at the one-loop and, for the “all +” amplitudes, also at the two-loop level. For the imaginary part of the Euler-Heisenberg Lagrangian, an all-loop formula has been conjectured independently by Affleck, Alvarez, and Manton for Scalar QED and by Lebedev and Ritus for Spinor QED. This formula can be related through a Borel dispersion relation to the leading large-N behaviour of the N-photon amplitudes. It is analytic in the fine structure constant, which is puzzling and suggests a diagrammatic investigation of the large-N limit in perturbation theory. Preliminary results of such a study for the dimensional case throw doubt on the validity of the conjecture. Idrish Huet, Michel Rausch de Traubenberg, and Christian Schubert Copyright © 2017 Idrish Huet et al. All rights reserved. Collectivity in High Energy Heavy-Ion Collisions Tue, 19 Sep 2017 00:00:00 +0000 Md. Nasim, Shusu Shi, Sandeep Chatterjee, Subhash Singha, and Victor Roy Copyright © 2017 Md. Nasim et al. All rights reserved. -Deformed Morse and Oscillator Potential Tue, 19 Sep 2017 00:00:00 +0000 We studied the -deformed Morse and harmonic oscillator systems with appropriate canonical commutation algebra. The analytic solutions for eigenfunctions and energy eigenvalues are worked out using time-independent Schrödinger equation and it is also noted that these wave functions are sensitive to variation in the parameters involved. H. Hassanabadi, W. S. Chung, S. Zare, and S. B. Bhardwaj Copyright © 2017 H. Hassanabadi et al. All rights reserved. Probing the Anomalous FCNC Couplings at Large Hadron Electron Collider Thu, 14 Sep 2017 07:24:53 +0000 We investigate the anomalous flavour changing neutral current (FCNC) interactions of top quark through the process . We calculate the signal and background cross sections in electron-proton collisions at Large Hadron electron Collider (LHeC) with a 7 TeV proton beam from the LHC and a new 60 GeV electron beam from energy recovery linac (ERL). We study the relevant background processes including one electron and three jets in the final state. The distributions of the invariant mass of two jets and an additional jet tagged as -jet are used to account for signal and background events after the analysis cuts. We find upper bounds on anomalous FCNC couplings of the order of at LHeC for a luminosity projection of   together with the fast simulation of detector effects. As a matter of interest, we analyze the sensitivity to the couplings , and find an enhanced sensitivity to at the LHeC when compared to the results from the HERA. I. Turk Cakir, A. Yilmaz, H. Denizli, A. Senol, H. Karadeniz, and O. Cakir Copyright © 2017 I. Turk Cakir et al. All rights reserved. A Quantum Space behind Simple Quantum Mechanics Mon, 11 Sep 2017 08:51:12 +0000 In physics, experiments ultimately inform us about what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles). This configuration space (as well as phase space) can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity) symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold and provides a crucial first link for any theoretical model of quantum space-time at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective. Chuan Sheng Chew, Otto C. W. Kong, and Jason Payne Copyright © 2017 Chuan Sheng Chew et al. All rights reserved. Phase Transition of Black Holes in Brans–Dicke Born–Infeld Gravity through Geometrical Thermodynamics Mon, 11 Sep 2017 00:00:00 +0000 Using the geometrical thermodynamic approach, we study phase transition of Brans–Dicke Born–Infeld black holes. We apply introduced methods and describe their shortcomings. We also use the recently proposed new method and compare its results with those of canonical ensemble. By considering the new method, we find that its Ricci scalar diverges in the places of phase transition and bound points. We also show that the bound point can be distinguished from the phase transition points through the sign of thermodynamical Ricci scalar around its divergencies. S. H. Hendi, M. S. Talezadeh, and Z. Armanfard Copyright © 2017 S. H. Hendi et al. All rights reserved. Coulomb-Type Interaction under Lorentz Symmetry Breaking Effects Wed, 06 Sep 2017 08:37:28 +0000 Based on models of confinement of quarks, we analyse a relativistic scalar particle subject to a scalar potential proportional to the inverse of the radial distance and under the effects of the violation of the Lorentz symmetry. We show that the effects of the Lorentz symmetry breaking can induce a harmonic-type potential. Then, we solve the Klein-Gordon equation analytically and discuss the influence of the background of the violation of the Lorentz symmetry on the relativistic energy levels. R. L. L. Vitória, H. Belich, and K. Bakke Copyright © 2017 R. L. L. Vitória et al. All rights reserved. Neutrino Physics in the Frontiers of Intensities and Very High Sensitivities 2016 Wed, 30 Aug 2017 09:06:18 +0000 Theocharis Kosmas, Hiroyasu Ejiri, and Athanasios Hatzikoutelis Copyright © 2017 Theocharis Kosmas et al. All rights reserved. Supersymmetry across the Hadronic Spectrum Wed, 30 Aug 2017 06:27:29 +0000 Semiclassical light-front bound-state equations for hadrons are presented and compared with experiment. The essential dynamical feature is the holographic approach; that is, the hadronic equations in four-dimensional Minkowski space are derived as holograms of classical equations in a 5-dimensional anti-de Sitter space. The form of the equations is constrained by the imposed superconformal algebra, which fixes the form of the light-front potential. If conformal symmetry is strongly broken by heavy quark masses, the combination of supersymmetry and the classical action in the 5-dimensional space still fixes the form of the potential. By heavy quark symmetry, the strength of the potential is related to the heavy quark mass. The contribution is based on several recent papers in collaboration with Stan Brodsky and Guy de Téramond. Hans Günter Dosch Copyright © 2017 Hans Günter Dosch. All rights reserved. Exact Computations in Topological Abelian Chern-Simons and BF Theories Wed, 30 Aug 2017 00:00:00 +0000 We introduce Deligne cohomology that classifies fibre bundles over 3 manifolds endowed with connections. We show how the structure of Deligne cohomology classes provides a way to perform exact (nonperturbative) computations in Chern-Simons theory (BF theory, resp.) at the level of functional integrals. The partition functions (and observables) of these theories are strongly related to topological invariants well known to the mathematicians. Philippe Mathieu Copyright © 2017 Philippe Mathieu. All rights reserved. Mixing in the Minimal Flavor-Violating Two-Higgs-Doublet Models Tue, 29 Aug 2017 09:40:41 +0000 The two-Higgs-doublet model (2HDM), as one of the simplest extensions of the Standard Model (SM), is obtained by adding another scalar doublet to the SM and is featured by a pair of charged Higgs, which could affect many low-energy processes. In the “Higgs basis” for a generic 2HDM, only one scalar doublet gets a nonzero vacuum expectation value and, under the criterion of minimal flavor violation, the other one is fixed to be either color-singlet or color-octet, which are named as type III and type C 2HDM, respectively. In this paper, we study the charged-Higgs effects of these two models on the mixing, an ideal process to probe New Physics (NP) beyond the SM. Firstly, we perform a complete one-loop computation of the box diagrams relevant to the mixing, keeping the mass and momentum of the external strange quark up to the second order. Together with the up-to-date theoretical inputs, we then give a detailed phenomenological analysis, in the cases of both real and complex Yukawa couplings of the charged Higgs to quarks. The parameter spaces allowed by the current experimental data on the mass difference and the CP-violating parameter are obtained and the differences between these two 2HDMs are investigated, which are helpful to distinguish them from each other from a phenomenological point of view. Natthawin Cho, Xin-Qiang Li, Fang Su, and Xin Zhang Copyright © 2017 Natthawin Cho et al. All rights reserved. Nonequilibrium Dynamics of the -Model Modes on the de Sitter Space Tue, 29 Aug 2017 07:10:30 +0000 The two-dimensional -model with the de Sitter target space is locally canonic in the north pole diamond of the Penrose diagram in the cosmological gauge. The left and right moving modes on the cylindrical base space are entangled among themselves and interact with the de Sitter metric. Firstly, we show that the untangled oscillators can be obtained from the entangled operators by applying a set of Bogoliubov transformations constrained by the requirement that the partial evolution generator be diagonal. Secondly, we determine the nonequilibrium dynamics of the untangled modes in the nonequilibrium thermofield dynamics formalism. The thermal modes are represented as thermal doublet oscillators that satisfy partial evolution equations of Heisenberg-type. From these we compute the local free one-body propagator of an arbitrary mode between two times. Thirdly, we discuss the field representation of the thermal modes. We show that there is a set of thermal doublet fields that satisfy the equal time canonical commutation relations, are solutions to the -model equations of motion, and can be decomposed in terms of thermal doublet oscillators. Finally, we construct a local partial evolution functional of Hamilton-like form for the thermal doublet fields. Ion V. Vancea Copyright © 2017 Ion V. Vancea. All rights reserved. Top Partner Production at Collider in the Littlest Higgs Model with -Parity Wed, 23 Aug 2017 00:00:00 +0000 In the framework of the littlest Higgs Model with -parity, we discuss the top partner production at future collider. We calculate the cross sections of the top partner production processes and associated production processes of Higgs and top partner under current constraints. Then, we investigate the observability of the -odd top partner pair production through the process in the dilepton channel for two -odd top partner masses  GeV at  TeV. We analyze the signal significance depending on the integrated luminosity and find that this signal is promising at the future high energy collider. Haiyan Wang and Bingfang Yang Copyright © 2017 Haiyan Wang and Bingfang Yang. All rights reserved. Dreibein as Prepotential for Three-Dimensional Yang-Mills Theory Tue, 22 Aug 2017 08:02:44 +0000 We advocate and develop the use of the dreibein (and the metric) as prepotential for three-dimensional SO() Yang-Mills theory. Since the dreibein transforms homogeneously under gauge transformation, the metric is gauge invariant. For a generic gauge potential, there is a unique dreibein on fixing the boundary condition. Topologically nontrivial monopole configurations are given by conformally flat metrics, with scalar fields capturing the monopole centres. Our approach also provides an ansatz for the gauge potential covering the topological aspects. Indrajit Mitra and H. S. Sharatchandra Copyright © 2017 Indrajit Mitra and H. S. Sharatchandra. All rights reserved. Big Bang as a Critical Point Tue, 22 Aug 2017 00:00:00 +0000 This article addresses the issue of possible gravitational phase transitions in the early universe. We suggest that a second-order phase transition observed in the Causal Dynamical Triangulations approach to quantum gravity may have a cosmological relevance. The phase transition interpolates between a nongeometric crumpled phase of gravity and an extended phase with classical properties. Transition of this kind has been postulated earlier in the context of geometrogenesis in the Quantum Graphity approach to quantum gravity. We show that critical behavior may also be associated with a signature change in Loop Quantum Cosmology, which occurs as a result of quantum deformation of the hypersurface deformation algebra. In the considered cases, classical space-time originates at the critical point associated with a second-order phase transition. Relation between the gravitational phase transitions and the corresponding change of symmetry is underlined. Jakub Mielczarek Copyright © 2017 Jakub Mielczarek. All rights reserved. Charges and Electromagnetic Radiation as Topological Excitations Tue, 22 Aug 2017 00:00:00 +0000 We discuss a model with stable topological solitons in Minkowski space with only three degrees of freedom, the rotational angles of a spatial Dreibein. This model has four types of solitons differing in two topological quantum numbers which we identify with electric charge and spin. The vacuum has a two-dimensional degeneracy leading to two types of massless excitations, characterised by a topological quantum number which could have a physical equivalent in the photon number. Manfried Faber Copyright © 2017 Manfried Faber. All rights reserved.