40 citations · 62 across the 7 of their papers we have counts for
9 papers · 1 filter
The Dirac Sea for the Non-Separable Hilbert Spaces
Alain Bachelot
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…
Propagation of Massive Scalar Fields in Pre-Big Bang Cosmologies
Alain Bachelot
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…
Wave asymptotics at a cosmological time-singularity: classical and quantum scalar fields
Alain Bachelot
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…
Waves on accelerating dodecahedral universes
Agnes Bachelot-Motet, Alain Bachelot
We investigate the wave propagation on a compact 3-manifold of constant positive curvature with a non trivial topology, the Poincaré dodecahedral space, when the scale factor is ex…
Waves in the Witten Bubble of Nothing and the Hawking Wormhole
Alain Bachelot
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 t…
On the Klein-Gordon equation near a De Sitter brane in an Anti-de Sitter bulk
Alain Bachelot
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 proble…
The Klein-Gordon Equation in Anti-de Sitter Cosmology
Alain Bachelot
This paper deals with the Klein-Gordon equation on the Poincaré chart of the 5-dimensional Anti-de Sitter universe. When the mass is larger than , the Cauchy problem i…
Wave Propagation and Scattering for the RS2 Brane Cosmology Model
Alain Bachelot
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 s…
The Dirac system on the Anti-de Sitter Universe
Alain Bachelot
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}, we…