ar X iv : m at h - ph / 0 10 30 34 v 1 2 5 M ar 2 00 1 MZ - TH 01 - 09 LPT - ORSAY 01 - 28 MULTIPLE NONCOMMUTATIVE TORI

ar X iv : h ep - t h / 01 03 09 3 v 1 1 3 M ar 2 00 1 Physical Aspects of the Space - Time Torsion

ar X iv : m at h . D S / 06 01 70 1 v 1 28 J an 2 00 6 HYPERBOLICITY VERSUS PARTIAL - HYPERBOLICITY AND THE TRANSVERSALITY - TORSION PHENOMENON

— In this paper, we describe a process to create hyperbolicity in the neighbourhood of a homoclinic orbit to a partially hyperbolic torus for three degrees of freedom Hamiltonian systems: the transversality-torsion phenomenon. keywords: Hyperbolicity, Partially hyperbolic tori, Hamiltonian systems.

ar X iv : m at h - ph / 0 31 10 01 v 4 3 N ov 2 00 4 Clifford Valued Differential Forms , Algebraic Spinor Fields

ar X iv : h ep - t h / 05 01 01 7 v 1 4 J an 2 00 5 Lorentz invariance of scalar field action on κ - Minkowski space - time

We construct field theory on noncommutative κ-Minkowski spacetime. Having the Lorentz action on the noncommutative space-time coordinates we show that the field lagrangian is invariant. We show that noncommutativity requires replacing the Leibnitz rule with the coproduct one.

ar X iv : h ep - t h / 01 01 05 9 v 2 1 4 M ay 2 00 1

We consider the complex scalar field coupled to background NC U(1) YM and calculate the correlator of two gauge invariant composite operators. We show how the noncommutative gauge invariance is restored for higher correlators (though the Green's function itself is not invariant). It is interesting that the recently discovered noncommutative solitons appear in the calculation.