Gibbons-Hawking effect in the sonic de Sitter space-time of an expanding Bose-Einstein-condensed gas

We propose an experimental scheme to observe the Gibbons-Hawking effect in the acoustic analog of a (1+1)-dimensional de Sitter universe, produced in an expanding, cigar-shaped Bose-Einstein condensate. It is shown that a two-level system created at the center of the trap, an atomic quantum dot interacting with phonons, observes a thermal Bose distribution at the de Sitter temperature.     

Poisson's equation in de Sitter space-time

The form of gravitation's law in projective relativity is examined, based on a suitable generalization of Poisson's equation in de Sitter space-time; it is found that, in the interior case, a small difference with the customary Newtonian law arises. This difference, of a repulsive character, can be very important in cosmological problems.     

Reissner-Nordstroem de Sitter黑洞的量子隧穿效应

运用Parikh的量子隧穿模型，研究了Reissner—Nordstrom de Sitter黑洞的量子隧穿效应。结果表明，在能量守恒的条件下，黑洞外视界和宇宙视界处的粒子出射率与Bekenstein—Hawking熵有关，辐射谱不再是严格的纯热谱。     

Hawking effect in Vaidya-de Sitter space-time

The solutions of both the Klein-Gordon equation and the Dirac equation near the event horizons are given in the Vaidya-de Sitter space-time. With a new method the locations of the black hole event horizon and universe horizon, as well as their Hawking temperatures, are shown automatically and easily.     

Snyder''s quantized space-time and de Sitter special relativity

There is a one-to-one correspondence between Snyder’s model in de Sitter space of momenta and the dS-invariant special relativity as well as a minimum uncertainty-like relation. This indicates that physics at the Planck length ℓ _P and the scale R = (3/Λ)^1/2 should be dual to each other and there is in-between gravity of local dS-invariance characterized by a dimensionless coupling constant g = ℓ _P /R ∼ 10⁻⁶¹.      

Evidence for special relativity with de Sitter space-time symmetry

I show the formulation of de Sitter Special Relativity (dS-SR) based on Dirac-Lu-Zou-Guo's discussions, dS-SR quantum mechanics is formulated, and the dS-SR Dirac equation for hydrogen is suggested. The equation in the earth-QSO framework reference is solved by means of the adiabatic approach. It's found that the fine-structure "constant" α in dS-SR varies with time. By means of the t-z relation of the ACDM model, α's time-dependency becomes redshift z-dependent. The dS-SR's predictions of △α/α agree with data of spectra of 143 quasar absorption systems, the dS-space-time symmetry is SO(3,2) (i.e., anti-dS group) and the universal parameter R (de Sitter ratio) in dS-SR is estimated to be R ≈ 2.73 x 10<'12> ly. The effects of dS-SR become visible at the cosmic space-time scale (i.e., the distance≥ 10<'9> ly). At that scale, dS-SR is more reliable than Einstein SR. The α-variation with time is evidence of SR with de Sitter symmetry.     

Evidence for special relativity with de Sitter space-time symmetry

I show the formulation of de Sitter Special Relativity (dS-SR) based on Dirac-Lu-Zou-Guo's discussions. dS-SR quantum mechanics is formulated, and the dS-SR Dirac equation for hydrogen is suggested. The equation in the earth-QSO framework reference is solved by means of the adiabatic approach. It's found that the fine-structure "constant" α in dS-SR varies with time. By means of the t-z relation of the ΛCDM model, α's time-dependency becomes redshift z-dependent. The dS-SR's predictions of Δα/α agree with data of spectra of 143 quasar absorption systems, the dS-space-time symmetry is SO(3,2) (i.e., anti-dS group) and the universal parameter R (de Sitter ratio) in dS-SR is estimated to be R≈2.73×10¹² ly. The effects of dS-SR become visible at the cosmic space-time scale (i.e., the distance ≥ 10⁹ ly). At that scale, dS-SR is more reliable than Einstein SR. The α-variation with time is evidence of SR with de Sitter symmetry.     

Reissner-Nordstr?m de Sitter黑洞的量子隧穿效应

运用Parikh的量子隧穿模型，研究了Reissner-Nordstrm de Sitter黑洞的量子隧穿效应.结果表明，在能量守恒的条件下，黑洞外视界和宇宙视界处的粒子出射率与Bekenstein-Hawking熵有关，辐射谱不再是严格的纯热谱.     

Positive-energy irreps of the quantum anti de Sitter algebra

We obtain positive-energy irreducible representations of theq-deformed anti de Sitter algebraU _q (so(3, 2)) by deformation of the classical ones. When the deformation parameterq isN-th root of unity, all these irreducible representations become unitary and finite-dimensional. Generically, their dimensions are smaller than those of the corresponding finite-dimensional non-unitary representations ofso(3, 2). We discuss in detail the singleton representations, i.e. the Di and Rac. WhenN is odd, the Di has dimension 1/2(N ²–1) and the Rac has dimension 1/2(N ²+1), while ifN is even, both the Di and Rac have dimension 1/2N ². These dimensions are classical only forN=3 when the Di and Rac are deformations of the two fundamental non-unitary representations ofso(3, 2).Presented at the 4th Colloquium Quantum groups and integrable systems, Prague, 22–24 June 1995.On leave from Bulgarian Acad. Sci., Institute of Nuclear Research and Nuclear Energy, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria.On leave from Pennsylvania State University (Fulbright scholar).     

Reissner-Nordström de Sitter黑洞的量子隧穿效应

运用Parikh的量子隧穿模型,研究了Reissner-Nordstr(o)m de Sitter黑洞的量子隧穿效应.结果表明,在能量守恒的条件下,黑洞外视界和宇宙视界处的粒子出射率与Bekenstein-Hawking熵有关,辐射谱不再是严格的纯热谱.     

Adiabatic invariants and scalar fields in a de Sitter space-time

The method of adiabatic invariants for time dependent Hamiltonians is applied to a massive scalar field in a de Sitter space-time. The scalar field ground state, its Fock space and coherent states are constructed and related to the particle states. Diverse quantities of physical interest are illustrated and compared with previous results.     

Snyder’s quantized space-time and de Sitter special relativity

There is a one-to-one correspondence between Snyder’s model in de Sitter space of momenta and the dS-invariant special relativity as well as a minimum uncertainty-like relation. This indicates that physics at the Planck length ? _P and the scale R = (3/Λ)^1/2 should be dual to each other and there is in-between gravity of local dS-invariance characterized by a dimensionless coupling constant g = ? _P /R ～ 10^?61.     

Remarks on quantum field theory on de Sitter and anti-de Sitter space-times

This is a short review of work done in common with Jacques Bros, Michel Gaudin, Ugo Moschella, and Vincent Pasquier. Among results are explicit K?llén?CLehmann representations for products of two free-field two-point functions in the de Sitter and the anti-de Sitter spaces and applications to particle decay.     

Open quantum system approach for heavy quark thermalization

We treat heavy quark as an open quantum system in a hot medium and rederive the stochastic Schr?dinger equation (SSE) from the full Schr?dinger equation for both heavy quarks and the medium. We apply the SSE to the dynamical evolutions of a heavy quark (as a system) in the static hot medium (as an environment). Heavy quarks interact with the medium via random scatterings, which exchange the momentum and phase factor randomly between two wave functions of the system and the environment. The exchange of momentum and phase factor results in the transition between different eigenstates of the system. These are included via an external stochastic potential in the Hamiltonian of SSE. Stochastic wave functions of a heavy quark are evolved with the stochastic external potential. The mean wave functions and corresponding momentum distributions of heavy quarks are obtained after the ensemble average over a large set of stochastic wave functions. We present the thermalization of heavy quarks in the static medium with different coupling strengths.     

Scheme dependence of quantum gravity on de Sitter background

We extend our investigation of the IR effects on the local dynamics of matter fields in quantum gravity. Specifically we clarify how the IR effects depend on the change of the quantization scheme: different parametrization of the metric and the matter field redefinition. Conformal invariance implies effective Lorentz invariance of the matter system in de Sitter space. An arbitrary choice of the parametrization of the metric and the matter field redefinition does not preserve the effective Lorentz invariance of the local dynamics. As for the effect of different parametrization of the metric alone, the effective Lorentz symmetry breaking term can be eliminated by shifting the background metric. In contrast, we cannot compensate the matter field redefinition dependence by such a way. The effective Lorentz invariance can be retained only when we adopt the specific matter field redefinitions where all dimensionless couplings become scale invariant at the classical level. This scheme is also singled out by unitarity as the kinetic terms are canonically normalized.     

Reissner-Nordstr(o)m de Sitter黑洞的量子隧穿效应

运用Parikh的量子隧穿模型,研究了Reissner-Nordstr(o)m de Sitter黑洞的量子隧穿效应.结果表明,在能量守恒的条件下,黑洞外视界和宇宙视界处的粒子出射率与Bekenstein-Hawking熵有关,辐射谱不再是严格的纯热谱.     

Nonlinear de Sitter symmetry and restricted space-time regions in gravity and supergravity

I discuss the frame-independent geometric structure of gravity and supergravity theories, and their nonlinear Poincaré and super-Poincaré invariances. Then I consider their generalizations to nonlinear de Sitter and super de Sitter invariances. I point out how these generalizations imply restrictions on the universe of propagation of basic fields. Related ideas are also discussed.