ar X iv : m at h - ph / 0 40 40 70 v 2 1 6 D ec 2 00 4 Spectral Theory of Time Dispersive and Dissipative Systems

ar X iv : m at h - ph / 0 40 40 70 v 1 2 8 A pr 2 00 4 Spectral Theory of Time Dispersive and Dissipative Systems

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system – which we show is essentially ...

ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications

ar X iv : m at h - ph / 0 40 40 26 v 1 8 A pr 2 00 4 THE DE RHAM - HODGE - SKRYPNIK THEORY OF DELSARTE TRANSMUTATION OPERATORS IN MULTIDIMENSION AND ITS APPLICATIONS

Spectral properties od Delsarte transmutation operators are studied , their differential geometrical and topological structure in multidimension is analyzed, the relationships with De Rham-Hodge-Skrypnik theory of generalized differential complexes is stated.

ar X iv : m at h - ph / 0 40 70 25 v 6 2 J un 2 00 6 Clifford Valued Differential Forms , and Some Issues in Gravitation , Electromagnetism and ”

This version includes some corrections of misprints and of some formulas appearing in the original text.

ar X iv : m at h - ph / 0 40 60 11 v 4 2 2 D ec 2 00 4 PATH INTEGRALS FOR PARASTATISTICS

We demonstrate that parastatistics can be quantized using path integrals by calculating the generating functionals for time-ordered products of both free and interacting parabose and parafermi fields in terms of path integrals. We also give a convenient form of the commutation relations for the Green components of the parabose and parafermi operators in both the canonical and path integral form...