Spectral Theory of the Dirac Operator.
Spectre de l'équation de Schrödinger, application à la stabilité de la matière
Spectre de l'opérateur de Schrödinger magnétique avec symétrie d'ordre six
Spectrum generating functions for oscillators in Wigner's quantization
The n-dimensional (isotropic and non-isotropic) harmonic oscillator is studied as a Wigner quantum system. In particular, we focus on the energy spectrum of such systems. We show how to solve the compatibility conditions in terms of 𝔬𝔰𝔭(1|2n) generators, and also recall the solution in terms of 𝔤𝔩(1|n) generators. A method is described for determining a spectrum generating function for an element of the Cartan subalgebra when working with a representation of any Lie (super)algebra. Here, the...
Spectrum of the laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions
We consider the laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one...
Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions
We consider the Laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one...
Spectrum of the Laplacian in narrow tubular neighbourhoods of hypersurfaces with combined Dirichlet and Neumann boundary conditions
We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the hypersurfaces tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the area of the Neumann...
Spin chain connected to the quantum superalgebra .
Spinor equations in Weyl geometry
This paper deals with Dirac, twistor and Killing equations on Weyl manifolds with -spin structures. A conformal Schrödinger-Lichnerowicz formula is presented and used to derive integrability conditions for these equations. It is shown that the only non-closed Weyl manifolds of dimension greater than 3 that admit solutions of the real Killing equation are 4-dimensional and non-compact. Any Weyl manifold of dimension greater than 3, that admits a real Killing spinor has to be Einstein-Weyl.
Spinor types in infinite dimensions.
Spinorial matter and general relativity theory
Spinors in braided geometry
Let V be a ℂ-space, be a pre-braid operator and let This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra . If and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...
Splitting of the Dirac operator in the nonrelativistic limit
Splitting the conservation process into creation and annihilation parts
The aim of this paper is the study of a non-commutative decomposition of the conservation process in quantum stochastic calculus. The probabilistic interpretation of this decomposition uses time changes, in contrast to the spatial shifts used in the interpretation of the creation and annihilation operators on Fock space.
Spontaneously broken symmetries
Square integrability of group representations on homogeneous spaces. II. Coherent and quasi-coherent states. The case of the Poincaré group
Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames
Stability and semiclassics in self-generated fields
We consider non-interacting particles subject to a fixed external potential and a self-generated magnetic field . The total energy includes the field energy and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical...
Stability of matter for the Hartree-Fock functional of the relativistic electron-positron field.
Stability of matter in classical and quantized fields.