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Seeable matter; unseeable antimatter

Geoffrey Dixon (2014)

Commentationes Mathematicae Universitatis Carolinae

The universe we see gives every sign of being composed of matter. This is considered a major unsolved problem in theoretical physics. Using the mathematical modeling based on the algebra 𝐓 : = 𝐂 ⊗ 𝐇 ⊗ 𝐎 , an interpretation is developed that suggests that this seeable universe is not the whole universe; there is an unseeable part of the universe composed of antimatter galaxies and stuff, and an extra 6 dimensions of space (also unseeable) linking the matter side to the antimatter—at the very least.

Semibounded Unitary Representations of Double Extensions of Hilbert–Loop Groups

K. H. Neeb (2014)

Annales de l’institut Fourier

A unitary representation π of a, possibly infinite dimensional, Lie group G is called semibounded if the corresponding operators i d π ( x ) from the derived representation are uniformly bounded from above on some non-empty open subset of the Lie algebra 𝔤 of G . We classify all irreducible semibounded representations of the groups ℒ ^ φ ( K ) which are double extensions of the twisted loop group ℒ φ ( K ) , where K is a simple Hilbert–Lie group (in the sense that the scalar product on its Lie algebra is invariant) and φ is...

Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator

Bernard Helffer, Thierry Ramond (2000)

Journées équations aux dérivées partielles

We continue the study started by the first author of the semiclassical Kac Operator. This kind of operator has been obtained for example by M. Kac as he was studying a 2D spin lattice by the so-called “transfer operator method”. We are interested here in the thermodynamical limit Λ ( h ) of the ground state energy of this operator. For Kac’s spin model, Λ ( h ) is the free energy per spin, and the semiclassical regime corresponds to the mean-field approximation. Under suitable assumptions, which are satisfied...

Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I) Trace formula

Frédéric Faure (2007)

Annales de l’institut Fourier

We consider a nonlinear area preserving Anosov map M on the torus phase space, which is the simplest example of a fully chaotic dynamics. We are interested in the quantum dynamics for long time, generated by the unitary quantum propagator M ^ . The usual semi-classical Trace formula expresses T r M ^ t for finite time t , in the limit ℏ → 0 , in terms of periodic orbits of M of period t . Recent work reach time t ≪ t E / 6 where t E = log ( 1 / ℏ ) / λ is the Ehrenfest time, and λ is the Lyapounov coefficient. Using a semi-classical normal form...

Semiclassical Limit of the cubic nonlinear Schrödinger Equation concerning a superfluid passing an obstacle

Fanghua Lin, Ping Zhang (2004/2005)

Séminaire Équations aux dérivées partielles

In this paper, we study the semiclassical limit of the cubic nonlinear Schrödinger equation with the Neumann boundary condition in an exterior domain. We prove that before the formation of singularities in the limit system, the quantum density and the quantum momentum converge to the unique solution of the compressible Euler equation with the slip boundary condition as the scaling parameter approaches 0 .

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