Gauge theory of massless spin-(3/2) field in de Sitter space-time

On several levels of theoretical physics, especially particle physics and early universe cosmology, de Sitter space-time has become an attractive possibility. The principle of local gauge invariance governs all known fundamental interactions of elementary particles, from electromagnetism and weak interactions to strong interactions and gravity. This paper presents a procedure for defining the gauge-covariant derivative and gauge invariant Lagrangian density in de Sitter ambient space-time formalism. The gauge invariant field equation is then explicitly calculated in detail for a massless spin-(3/2) gauge field.     

Casimir Effect for a Massless Spin-3/2 Field in Minkowski Spacetime

The Casimir effect has been studied for various quantum fields in both fiat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimlr effect for massless spin-3/2 field with periodic boundary condition imposed in four-dimensional Minkowski spacetime. The corresponding results with Dirichlet and Neumann boundary conditions are also discussed.     

Casimir Effect for a Massless Spin-3/2 Field in Minkowski Spacetime

The Casimir effect has been studied for various quantum fields in both flat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimir effect for massless spin-3/2 field with periodic boundary condition imposed in four-dimensional Minkowski spacetime. The corresponding results with Dirichlet ard Neumann boundary conditions are also discussed.     

ADM Mass for Asymptotically de Sitter Space-Time

In this paper, an ADM mass formula for asymptotically de Sitter（dS） space-time is derived from the energy-momentum tensor. We take the vacuum dS space as the background and investigate the ADM mass of the （d ＋ 3）-dimensional sphere-symmetric space with a positive cosmological constant, and find that the ADM mass of asymptotically dS space is based on the ADM mass of Schwarzschild field and the cosmological background brings some small mass contribution as well.     

Letter: Casimir Stress for Cylindrical Shell in de Sitter Space

The Casimir stress on a cylindrical shell in the de Sitter background for a massless scalar field satisfying Dirichlet boundary conditions on the cylinder is calculated. The metric is written in conformally flat form to make maximal use of the Minkowski space calculations. In the framework of a toy model, we have considered the quantum vacuum effect in the evolution of a domain wall between a cylindrical or in fact circle region around the z axis in which vacuum is _in and the remaining part of space where vacuum is _out .     

Scalar massless field in de Sitter space

A method for quantizing a scalar massless field in the de Sitter space is demonstrated; the method is based on the conformai invariance of the field equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 19–24, July, 1972.The author would like to thank Professor N. A. Chernikov for his aid and É. A. Tagirov for helpful criticism.     

Thermodynamics of de Sitter Black Holes in Massive Gravity

In this paper, by taking de Sitter space-time as a thermodynamic system, we study the effective thermodynamic quantities of de Sitter black holes in massive gravity, and furthermore obtain the effective thermodynamic quantities of the space-time. Our results show that the entropy of this type of space-time takes the same form as that in Reissner-Nordstr¨om-de Sitter space-time, which lays a solid foundation for deeply understanding the universal thermodynamic characteristics of de Sitter space-time in the future. Moreover, our analysis indicates that the effective thermodynamic quantities and relevant parameters play a very important role in the investigation of the stability and evolution of de Sitter space-time.     

第五讲暗能量和德西特时空

最近的天文观测表明，宇宙是在加速膨胀，而不是原来认为的减速膨胀．为解释加速膨胀，必须在宇宙的物质能量中引入暗能量这一成分，文章讨论了暗能量的可能侯选者，特别强调了宇宙常数问题、德西特时空问题以及和德西特时空相关的一些基本问题．     

Entropic uncertainty relation in de Sitter space

The uncertainty principle restricts our ability to simultaneously predict the measurement outcomes of two incompatible observables of a quantum particle. However, this uncertainty could be reduced and quantified by a new Entropic Uncertainty Relation (EUR). By the open quantum system approach, we explore how the nature of de Sitter space affects the EUR. When the quantum memory A$A$ freely falls in the de Sitter space, we demonstrate that the entropic uncertainty acquires an increase resulting from a thermal bath with the Gibbons–Hawking temperature. And for the static case, we find that the temperature coming from both the intrinsic thermal nature of the de Sitter space and the Unruh effect associated with the proper acceleration of A$A$ also brings effect on entropic uncertainty, and the higher the temperature, the greater the uncertainty and the quicker the uncertainty reaches the maximal value. And finally the possible mechanism behind this phenomenon is also explored.     

Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive (ferromagnetic interaction) and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative (ferromagnetic or anti-ferromagnetic interaction). The temperature dependence of the layer magnetizations of the system is examined to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the phase transition temperatures. The system exhibits both second-and first-order phase transitions besides triple point (T P ), critical end point (E), multicritical point (A), isolated critical point (C) and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in N′eel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.     

Relaxation theory of spin-3/2 Ising system near phase transition temperatures

<正>Dynamics of a spin-3/2 Ising system Hamiltonian with bilinear and biquadratic nearest-neighbour exchange interactions is studied by a simple method in which the statistical equilibrium theory is combined with the Onsager's theory of irreversible thermodynamics.First,the equilibrium behaviour of the model in the molecular-field approximation is given briefly in order to obtain the phase transition temperatures,i.e.the first- and second-order and the tricritical points.Then,the Onsager theory is applied to the model and the kinetic or rate equations are obtained.By solving these equations three relaxation times are calculated and their behaviours are examined for temperatures near the phase transition points.Moreover,the z dynamic critical exponent is calculated and compared with the z values obtained for different systems experimentally and theoretically,and they are found to be in good agrement.     

Dirac Fields in 3D de Sitter Spacetime

We show that the Dirac equation is separable in the circularly symmetric metric in three dimensions and when the background spacetime is de Sitter we find exact solutions to the radial equations. Using these results we show that the de Sitter horizon has a cross section equal to zero for the massless Dirac field, as in the case of the scalar field. Also, using the improved brick wall model we calculate the fermionic entropy associated with the de Sitter horizon and we compare it with some results previously published.     

Quadrupole effects of spin-3/2 nuclei on the solid-state magic-angle spinning nuclear magnetic resonance spectra of spin-1/2 nuclei Deviations from first-order theory and implications concerning the sign of the indirect coupling constant

The effect of the interaction between spin-3/2 and spin-1/2 nuclei on solid-state magic-angle spinning nuclear magnetic resonance (MAS NMR) spectra of the latter is studied in cases where deviations from first-order theory are expected. A comparison is made between the exact and first-order perturbation approaches. Both dipolar and indirect (iso- and anisotropic) coupling interactions are considered. Implications regarding ¹³C,^35,37Cl, ³¹P,^63,65Cu and ¹¹⁹Sn,^35,37Cl cases are discussed. It is shown that in the latter two cases the sign of the indirect coupling constant J can be derived.     

Doubly special relativity in de Sitter spacetime

We discuss the generalization of Doubly Special Relativity to a curved de Sitter background. The model has three fundamental observer‐independent scales, the velocity of light c, the de Sitter radius α, and the Planck energy κ, and can be realized through a nonlinear action of the de Sitter group on a noncommutative position space. We consider different choices of coordinates on the de Sitter hyperboloid that, although equivalent, may be more suitable for treating different problems. Also the momentum space can be described as a hyperboloid embedded in a five‐dimensional space, but in this case different choices of coordinates lead to inequivalent models. We investigate the kinematics and the Hamiltonian dynamics of some specific models and describe some of their phenomenological consequences. Finally, we show that it is possible to construct a model exhibiting a duality for the interchange of positions and momenta together with the interchange of α and κ.     

Dynamic magnetic properties in the kinetic mixed spin-2 and spin-5/2 Ising model under a time-dependent magnetic field

We extend the recent paper [W. Jiang, V-C. Lo, B-D. Bai, J. Yang, Physica A 389 (2010) 2227-2233] to present a study, within a mean-field approach, the dynamic magnetic properties of the mixed spin-2 and spin-5/2 Ising ferrimagnetic system, which corresponds the molecular-based magnetic materials AFe^IIFe^III(C₂O₄)₃ [ A=N(n-C_nH_2n+1)₄, n=3-5], by using the Glauber-type stochastic dynamics. This mixed Ising ferrimagnetic system is used on a layered honeycomb lattice in which Fe^II (S=5/2) and Fe^III (σ=2) occupy sites. First, we investigate the time variations of average order parameters to find the phases in the system and then the thermal behavior of the dynamic order parameters to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (first-or second-order) phase transitions. We also present the dynamic phase diagrams and study the dynamic magnetic hysteresis loop behaviors of the kinetic mixed spin-2 and spin-5/2 Ising ferrimagnetic system. The results are compared with some experimental and theoretical works and a good overall agreement is found.     

Spinning Particles in Reissner-Nordström-de Sitter Spacetime

We study the geodesic motion of pseudo-classical spinning particles in the Reissner-Nordström-de Sitter spacetime. We investigate the generalized Killing equations for spinning space and derive the constants of motion in terms of the solutions of these equations. We discuss bound state orbits in a plane.     

On 3+1 Anti-de Sitter and de Sitter Lie Bialgebras with Dimensionful Deformation Parameters

We analyze among all possible quantum deformations of the 3+1 (anti)de Sitter algebras, so(3,2) and so(4,1), which have two specific non-deformed or primitive commuting operators: the time translation/energy generator and a rotation. We prove that under these conditions there are only two families of two-parametric (anti)de Sitter Lie bialgebras. All the deformation parameters appearing in the bialgebras are dimensionful ones and they may be related to the Planck length. Some properties conveyed by the corresponding quantum deformations (zero-curvature and non-relativistic limits, space isotropy, . . . ) are studied and their dual (first-order) non-commutative spacetimes are also presented.     

Gravitational field of a tachyon in a de Sitter universe

An exact solution of Einstein’s equations is interpreted as describing the gravitational field of a tachyon in a de Sitter universe. Switching off the cosmological constant yields the gravitational field of a tachyon in flat spacetime background.     

Analytical Solutions of the Gravitational Field Equations in de Sitter and Anti-de Sitter Spacetimes

The generalized Laplace partial differential equation, describing gravitational fields, is investigated in de Sitter spacetime from several metric approaches—such as the Riemann, Beltrami, Börner-Dürr, and Prasad metrics—and analytical solutions of the derived Riccati radial differential equations are explicitly obtained. All angular differential equations trivially have solutions given by the spherical harmonics and all radial differential equations can be written as Riccati ordinary differential equations, which analytical solutions involve hypergeometric and Bessel functions. In particular, the radial differential equations predict the behavior of the gravitational field in de Sitter and anti-de Sitter spacetimes, and can shed new light on the investigations of quasinormal modes of perturbations of electromagnetic and gravitational fields in black hole neighborhood. The discussion concerning the geometry of de Sitter and anti-de Sitter spacetimes is not complete without mentioning how the wave equation behaves on such a background. It will prove convenient to begin with a discussion of the Laplace equation on hyperbolic space, partly since this is of interest in itself and also because the wave equation can be investigated by means of an analytic continuation from the hyperbolic space. We also solve the Laplace equation associated to the Prasad metric. After introducing the so called internal and external spaces—corresponding to the symmetry groups SO(3,2) and SO(4,1) respectively—we show that both radial differential equations can be led to Riccati ordinary differential equations, which solutions are given in terms of associated Legendre functions. For the Prasad metric with the radius of the universe independent of the parametrization, the internal and external metrics are shown to be of AdS-Schwarzschild-like type, and also the radial field equations arising are shown to be equivalent to Riccati equations whose solutions can be written in terms of generalized Laguerre polynomials and hypergeometric confluent functions.