Zobrazeno 1 - 10
of 98
pro vyhledávání: '"Bachelot, Alain"'
Autor:
Bachelot, Alain
Publikováno v:
J. Math. Phys. 63, 022102 (2022)
We give a rigorous construction of the Dirac Sea for the fermionic quantization in the non-separable Hilbert spaces. These CAR-representations depend on the Axiom of Choice, hence are not unique, nevertheless they are unitarily equivalent to the clas
Externí odkaz:
http://arxiv.org/abs/2108.02629
Autor:
Bachelot, Alain
Publikováno v:
Comm. Math. Phys., 380, 973-1001, 2020
We investigate the linear and semilinear massive Klein-Gordon equations in geometrical frameworks of type "Conformal Cyclic Cosmology" of R. Penrose, or "Singular Bouncing Scenario" as well. We give sufficient conditions on the decay of the mass to t
Externí odkaz:
http://arxiv.org/abs/2003.03356
Autor:
Bachelot, Alain
Publikováno v:
Comm. Math. Phys., 369(3), 973-1020, 2019
We investigate the propagation of the scalar waves in the FLRW universes beginning with a Big Bang and ending with a Big Crunch, a Big Rip, a Big Brake or a Sudden Singularity. We obtain the sharp description of the asymptotics for the solutions of t
Externí odkaz:
http://arxiv.org/abs/1806.01543
Autor:
Bachelot-Motet, Agnes, Bachelot, Alain
Publikováno v:
Class. Quantum Gravity, 34 (2017) 055010 (39pp)
We investigate the wave propagation on a compact 3-manifold of constant positive curvature with a non trivial topology, the Poincar\'e dodecahedral space, when the scale factor is exponentially increasing. We prove the existence of a limit state as t
Externí odkaz:
http://arxiv.org/abs/1609.00806
Autor:
Bachelot, Alain
Publikováno v:
Comm. Math. Phys., 351 (2017), 599-651
We investigate the propagation of the scalar waves in the Witten space-time called "bubble of nothing" and in its remarkable sub-manifold, the Lorentzian Hawking wormhole. Due to the global hyperbolicity, the global Cauchy problem is well-posed in th
Externí odkaz:
http://arxiv.org/abs/1601.03682
Autor:
Bachelot, Alain
Publikováno v:
J. Math. Pures Appl., 105, 165-197, 2016
In this paper we investigate the Klein-Gordon equation in the past causal domain of a De Sitter brane imbedded in a Anti-de Sitter bulk. We solve the global mixed hyperbolic problem. We prove that any finite energy solution can be expressed as a Kalu
Externí odkaz:
http://arxiv.org/abs/1402.1071
Autor:
Bachelot, Alain
Publikováno v:
Comm. Math. Phys., 320 (2013), 723-759
This paper deals with the propagation of the gravitational waves in the Poincar\'e patch of the 5-dimensional Anti-de Sitter universe. We construct a large family of unitary dynamics with respect to some high order energies that are conserved and pos
Externí odkaz:
http://arxiv.org/abs/1112.6138
Autor:
Bachelot, Alain
Publikováno v:
J. Math. Pures Appl. (9) 96 (2011), no. 6, 527-554
This paper deals with the Klein-Gordon equation on the Poincar\'e chart of the 5-dimensional Anti-de Sitter universe. When the mass $\mu$ is larger than $-{1}{4}$, the Cauchy problem is well posed despite the loss of global hyperbolicity due to the t
Externí odkaz:
http://arxiv.org/abs/1010.1925
Autor:
Bachelot, Alain
Publikováno v:
J.H.D.E. 6(4) (2009), 809-861
We study the wave equation for the gravitational waves in the Randal-Sundrum brane cosmology model. We solve the global Cauchy problem and we establish that the solutions are the sum of a slowly decaying massless wave localized near the brane, and a
Externí odkaz:
http://arxiv.org/abs/0812.4197
Autor:
Bachelot, Alain
Publikováno v:
Commun.Math.Phys.283:127-167,2008
We investigate the global solutions of the Dirac equation on the Anti-de-Sitter Universe. Since this space is not globally hyperbolic, the Cauchy problem is not, {\it a priori}, well-posed. Nevertheless we can prove that there exists unitary dynamics
Externí odkaz:
http://arxiv.org/abs/0706.1315