We give a relativistic generalization of the Gutzwiller-Duistermaat-Guillemin trace formula for wave group compact Riemannian manifold to globally hyperbolic stationary space-times with Cauchy hypersurfaces. introduce several (essentially equivalent) notions self-adjoint operators on null-space ker⁡□ operator and define U(t) be translation by flow etZ timelike Killing vector field Z □. The spec...

In this paper, we exploit the formal equivalence of Solution Manifold two distinct physical systems to create enough symmetries so as characterize them by Noether Invariants, thus favoring their future quantization. doing, somehow generalize Arnold Transformation for non-necessarily linear systems. Very particularly, algorithm applies case motion on de Sitter space-time providing a finite-dimen...

Let G be a semisimple algebraic group over [Formula: see text]. For reduced word text] of the longest element in Weyl and dominant integral weight text], one can construct string polytope whose lattice points encode character irreducible representation The is singular general combinatorics polytopes heavily depends on choice In this paper, we study when present sufficient condition such that to...

in the first part of this paper, some theorems are given for a riemannian manifold with semi-symmetric metric connection. in the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. we obtain some properties of this manifold having the vectors mentioned above.

‎In this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular Sturm-Liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎Also Weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

We propose a reduction procedure for symplectic connections with symmetry. This is applied to coadjoint orbits whose isotropy is reductive. Key-words: Marsden-Weinstein reduction, symplectic connections, Hamiltonian group actions MSC 2000: 53C15, 53D20 1 e-mail: [email protected] 2 Research supported by the Marie Curie Fellowship Nr. HPMF-CT-1999-00062 3 e-mail: [email protected] 4 Research supp...

In this paper we show how deformation quantization of line bundles over a Poisson manifold M produces a canonical action Φ of the Picard group Pic(M) ∼= H(M,Z) on the moduli space of equivalence classes of differential star products on M , Defdiff(M). The orbits of Φ characterize Morita equivalent star products on M . We describe the semiclassical limit of Φ in terms of the characteristic class...

Motivated by deformation quantization, we consider in this paper -algebras A over rings C = R(i), where R is an ordered ring and i = −1, and study the deformation theory of projective modules over these algebras carrying the additional structure of a (positive) A-valued inner product. For A = C(M), M a manifold, these modules can be identified with Hermitian vector bundles E overM . We show tha...

We extend the Kontsevich formality L∞-morphism U : T • poly(R ) → D poly(R ) to an L∞-morphism of an L∞-modules over T • poly(R ), Û : C•(A, A) → Ω(R), A = C(R). The construction of the map Û is given in Kontsevich-type integrals. The conjecture that such an L∞-morphism exists is due to Boris Tsygan [Ts]. As an application, we obtain an explicit formula for isomorphism A∗/[A∗, A∗] ∼ → A/{A, A} ...