Wave solutions of Hopf theories

We present a class of plane-wave solutions for some Hopf theories defined on the symmetric space SU(2)/U(1) in 3 + 1 space-time dimensions, using a recently proposed ansatz by Hirayama and Yamashita. These solutions are not solitonic, but they provide us with an example of how plane-wave solutions arise in non-linear field theories.Received: 12 July 2003, Revised: 24 July 2003, Published online: 26 September 2003     

Cancelling Jüttner distributions for space-like freeze-out

We study the freeze-out process of particles across a three-dimensional space-time hypersurface with space-like normal. The problem of negative contribution is discussed with respect to conservation laws, and a simple and practical new one-particle distribution for the post-FO side is introduced, the Cancelling Jüttner (CJ) distribution.Received: 1 May 2003, Revised: 15 September 2003, Published online: 3 February 2004PACS: 25.75.-q Relativistic heavy-ion collisions - 25.75.Ld Collective flow - 24.85. + p Quarks, gluons, and QCD in nuclei and nuclear processes     

Convergence properties of the cluster expansion for equal- time Green functions in scalar theories

We investigate the convergence properties of the cluster expansion of equal-time Green functions in scalar theories with quartic self-coupling in (0 + 1), (1 + 1), and (2 + 1) space-time dimensions. The computations are carried out within the equal-time correlation dynamics approach, which consists in a closed set of coupled equations of motion for connected Green functions as obtained by a truncation of the BBGKY hierarchy. We find that the cluster expansion shows good convergence as long as the system is in a localized state (single phase configuration) and that it breaks down in a non-localized state (two phase configuration), as one would naively expect. Furthermore, in the case of dynamical calculations with a time dependent Hamiltonian for the evaluation of the effective potential we find two timescales determining the adiabaticity of the propagation; these are the time required for adiabaticity in the single phase region and the time required for tunneling into the non-localized lowest energy state in the two phase region. Our calculations show a good convergence for the effective potentials in (1 + 1) and (2+1) space-time dimensions since tunneling is suppressed in higher space-time dimensions.     

Periodic instantons and domain structure in a ferromagnetic film

We in this paper study periodic instantons and domain structures in a theoretical film consisting of biaxial-anisotropic ferromagnets. In a proper approximation the equation of motion of the magnetization vector as a space-time function in the film is reduced to the 1 + 2-dimensional sine-Gordon field equation in strong anisotropy limit. Static periodic instantons, which are solutions of Euclidean field equantion, and various new domain structures are obtained analytically. We also investigate the energy density and stability of the periodic instantons.Received: 6 August 2003, Published online: 8 December 2003PACS: 05.45.Yv Solitons - 75.70.Kw Domain structure (including magnetic bubbles)     

Strong and electroweak interactions and their unification with non-commutative space-time

Quantum field theories based on non-commutative space-time (NCQFT) have been extensively studied recently. However no NCQFT model which can uniquely describe the strong and electroweak interactions has been constructed. This prevents one to make a consistent and systematic study of non-commutative space-time. In this work we construct a NCQFT model based on the trinification gauge group . A unique feature of this model, that all matter fields (fermions and Higgs bosons) are assigned to (anti-) fundamental representations of the factor SU(3) groups, allows us to construct a NCQFT model for strong and electroweak interactions and their unification without ambiguities. This model provides an example which allows one to make a consistent and systematic study of non-commutative space-time phenomenology. We also comment on some related issues regarding extensions to E₆ and models. Received: 18 September 2002 / Revised version: 21 February 2003 / Published online: 5 May 2003     

Solutions to Class of Linear and Nonlinear Fractional Differential Equations

In this paper, the fractional auxiliary sub-equation expansion method is proposed to solve nonlinear fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional Kd V equation, the space-time fractional RLW equation, the space-time fractional Boussinesq equation, and the(3+1)-spacetime fractional ZK equation. The solutions are expressed in terms of fractional hyperbolic and fractional trigonometric functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The analytical solution of homogenous linear FDEs with constant coefficients are obtained by using the series and the Mittag–Leffler function methods. The obtained results recover the well-know solutions when α = 1.     

Cayley parametrization of semisimple lie groups and its application to physical laws in a (3+1)-dimensional cubic lattice

The assumption of a discrete space-time is expressed mathematically by restricting the space-time variables to the field of integer numbers, and by restricting to the field of rational numbers the functions describing the laws of motion. This rational character must be preserved under the transformations connecting different systems of reference. The Cayley parametrization of semisimple Lie groups, and in particular of the Lorentz group, satisfies this condition if we require these parameters to take only integer values. The rational points of the most frequently used transcendental functions are obtained with the help of the integer complex and hypercomplex numbers. Some applications are made concerning the laws of motion in special relativity defined over a (3+1)-dimensional cubic lattice.     

Testing non-commutative QED \gamma\gamma\gamma and \gamma\gamma\gamma\gamma couplings at LHC

In this work, we investigate the sensitivity of the process at LHC for the photonic 3- and 4-point functions that appear in non-commutative QED. We show that this process serves to study the behavior of the space-space as well as of the space-time non-commutativity. We also show that this process can probe the non-commutative scale in the range of a few TeV.Received: 9 February 2004, Revised: 27 February 2004, Published online: 8 April 2004     

Numerical experiment of anharmonic oscillators by using the symplectic scheme-shooting method

Symplectic scheme-shooting method (SSSM) is applied to solve the energy eigenvalues of anharmonic oscillators characterized by the potentials V(x)=λx4 and V(x)=(1/2)x2+λx2α with α=2,3,4 and doubly anharmonic oscillators characterized by the potentials V(x)=(1/2)x2+λ1x4+λ2x6, and a high order symplectic scheme tailored to the "time"-dependent Hamiltonian function is presented. The numerical results illustrate that the energy eigenvalues of anharmonic oscillators with the symplectic scheme-shooting method are in good agreement with the numerical accurate ones obtained from the non-perturbative method by using an appropriately scaled basis for the expansion of each eigenfunction; and the energy eigenvalues of doubly anharmonic oscillators with the sympolectic scheme-shooting method are in good agreement with the exact ones and are better than the results obtained from the four-term asymptotic series. Therefore, the symplectic scheme-shooting method, which is very simple and is easy to grasp, is a good numerical algorithm.     

Exact solutions of （3＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

The symmetries and the exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the (3+1)-dimensional INHB system.     

Path-integral quantization of Galilean Fermi fields

The Galilei-covariant fermionic field theories are quantized by using the path-integral method and five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. First, we review the five-dimensional approach to the Galilean Dirac equation, which leads to the Lévy-Leblond equations, and define the Galilean generating functional and Green’s functions for positive- and negative-energy/mass solutions. Then, as an example of interactions, we consider the quartic self-interacting potential , and we derive expressions for the 2- and 4-point Green’s functions. Our results are compatible with those found in the literature on non-relativistic many-body systems. The extended manifold allows for compact expressions of the contributions in (3 + 1) space-time. This is particularly apparent when we represent the results with diagrams in the extended (4 + 1) manifold, since they usually encompass more diagrams in Galilean (3 + 1) space-time.     

Multiplicity correlations of intermediate-mass fragments with pions and fast protons in <Superscript>12</Superscript>C + <Superscript>197</Superscript>Au

Low-energy ( MeV) from ¹² C + ¹⁹⁷ Au collisions at incident energies from 300 to 1800 MeV per nucleon were detected with the Si-Si(Li)-CsI(Tl) calibration telescopes of the INDRA multidetector. The inclusive angular distributions are approximately isotropic, consistent with multiple rescattering in the target spectator. The multiplicity correlations of the low-energy pions and of energetic protons ( MeV) with intermediate-mass fragments were determined from the measured coincidence data. The deduced correlation functions for inclusive event samples reflect the strong correlations evident from the common impact parameter dependence of the considered multiplicities. For narrow impact parameter bins (based on charged-particle multiplicity), the correlation functions are close to unity and do not indicate strong additional correlations. Only for pions at high particle multiplicities (central collisions) a weak anticorrelation is observed, probably due to a limited competition between these emissions. Overall, the results are consistent with the equilibrium assumption made in statistical multifragmentation scenarios. Predictions obtained with intranuclear-cascade models coupled to the Statistical Multifragmentation Model are in good agreement with the experimental data.Received: 9 December 2003, Revised: 18 February 2004, Published online: 31 August 2004PACS: 25.70.Mn Projectile and target fragmentation - 25.70.Pq Multifragment emission and correlations - 25.75.Dw Particle and resonance production - 25.75.Gz Particle correlations     

Deep inelastic scattering of leptons on nuclei: Hadron formation, cumulative particles production

We introduce a space-time model for propagation of quark and gluon jets in nuclear matter, taking into account the formation zone phenomena (Landau-Pomeranchuk-Migdal, LPM, effect) and cascading of soft particles in a nucleus. The measured final-state hadrons, including cumulative nucleons produced in neutrino interactions with nuclei are investigated and the formation length of hadrons is obtained.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.60.Le Meson production - 13.15. + g Neutrino interactions - 25.30.Pt Neutrino scattering     

Total Quantum Statistical Entropy of Reissner-Nordstrom Black Holes: in Dirac Field Case

The total quantum statistical entropy of Reissner-Nordstrom black holes in Dirac field case is evaluated in this article. The space-time of the black holes is divided into three regions: region 1 (r>r_o), region 2 ( r_o > r > r_i), and region 3 (r_i >r>0), where r_o is the radius of the outer event horizon, and r_i is the radius of the inner event horizon. The total quantum statistical entropy of Reissner-Nordstrom black holes is S=S₁+S₂+S₃, where S_i (i=1,2,3) is the entropy, contributed by regions 1,2,3. The detailed calculation shows that S₂ is neglectfully small. S₁=w_t(π²/45)k_b(A_o/ε²β³), S₃=-w_t(π²/45)k_b(A_i/ε²β³), where A_o and A_i are, respectively, the areas of the outer and inner event horizons, w_t=2^s[1- 2^-(s+1)], s=d/2, d is the space-time dimension, here d=4, s=2. As r_i approaches r_o in the extreme case the total quantum statistical entropy of Reissner-Nordstrom black holes approaches zero.     

2-Dimensional polymers confined in a strip

Single two dimensional polymers confined to a strip are studied by Monte Carlo simulations. They are described by N-step self-avoiding random walks on a square lattice between two parallel hard walls with distance ( is the Flory exponent). For the simulations we employ the pruned-enriched-Rosenbluth method (PERM) with Markovian anticipation. We measure the densities of monomers and of end points as functions of the distance from the walls, the longitudinal extent of the chain, and the forces exerted on the walls. Their scaling with D and the universal ratio between force and monomer density at the wall are compared to theoretical predictions.Received: 14 August 2003, Published online: 8 December 2003PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 07.05.Tp Computer modeling and simulation - 61.41. + e Polymers, elastomers, and plastics     

Fixing a hole

Movements in space-time: the author composes a hole diffeomorphism for a 3+1-dimensional space-time manifold, which is required in the so-called Hole Argument. The composition applies directly to the universe.     

Four-cluster chimera state in non-locally coupled phase oscillator systems with an external potential

Dynamics of a one-dimensional array of non-locally coupled Kuramoto phase oscillators with an external potential is studied. A four-cluster chimera state is observed for the moderate strength of the external potential. Different from the clustered chimera states studied before, the instantaneous frequencies of the oscillators in a synchronized cluster are different in the presence of the external potential. As the strength of the external potential increases, a bifurcation from the two-cluster chimera state to the four-cluster chimera states can be found. These phenomena are well predicted analytically with the help of the Ott-Antonsen ansatz.     

(3+1)-dimensional relativistic hydrodynamical expansion of hot and dense matter in ultra-relativistic nuclear collision

A full (3+1)-dimensional calculation using Lagrangian hydrodynamics is proposed for relativistic nuclear collisions. This calculation enables us to evaluate the anisotropic flow of the hadronic matter which appears in non-central and/or asymmetrical relativistic nuclear collisions. Applying hydrodynamical calculations to the deformed uranium collisions in the AGS energy region, we discuss the nature of the space-time structure and particle distributions in detail. Received: 18 July 2000 / Published online: 23 October 2000     

Quantum Instantons with Classical Moduli Spaces

 We introduce a quantum Minkowski space-time based on the quantum group SU(2) _q extended by a degree operator and formulate a quantum version of the anti-self-dual Yang-Mills equation. We construct solutions of the quantum equations using the classical ADHM linear data, and conjecture that, up to gauge transformations, our construction yields all the solutions. We also find a deformation of Penrose's twistor diagram, giving a correspondence between the quantum Minkowski space-time and the classical projective space ℙ³. Received: 10 May 2002 / Accepted: 10 January 2003 Published online: 5 May 2003 Communicated by L. Takhtajan     

No UV/IR mixing in unitary space-time non-commutative field theory

In this article we calculate several divergent amplitudes in -theory on non-commutative space-time ( ) in the framework of interaction-point time-ordered perturbation theory (IPTOPT), continuing work done in hep-th/0209253. On the ground of these results we find corresponding Feynman rules that allow for a much easier diagrammatic calculation of amplitudes. The most important feature of the present theory is the absence of the UV/IR mixing problem in all amplitudes calculated so far. Although we are not yet able to give a rigorous proof, we provide a strong argument for this result to hold in general. Together with the Feynman rules we found, this opens promising vistas onto the systematic renormalization of non-commutative field theories.Received: 26 August 2003, Published online: 20 November 2003V. Putz: Work supported by the Fonds zur Förderung der Wissenschaften (FWF) under contract P15015-TPH.