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Particles, phases, fields

L. Wojtczak, A. Urbaniak-Kucharczyk, I. Zasada, J. Rutkowski (1996)

Banach Center Publications

The physical properties of particles and phasesare considered in connection with their description by means of the deformation of space-time. The analogy between particle trajectories and phase boundaries is discussed. The geometry and its curvature is related to the Clifford algebraic structure whose construction in terms of the theory of deformation leads to the expected solutions for correlation functions referring to spectroscopy and scattering problems. The stochastic nature of space-time is...

Principal bundles, groupoids, and connections

Anders Kock (2007)

Banach Center Publications

We clarify in which precise sense the theory of principal bundles and the theory of groupoids are equivalent; and how this equivalence of theories, in the differentiable case, reflects itself in the theory of connections. The method used is that of synthetic differential geometry.

Pseudogroupes complexes quasi parallélisés de dimension un

Vincent Cavalier (1994)

Annales de l'institut Fourier

L’objet de ce travail est la classification, à équivalence près, des pseudogroupes de transformations holomorphes, en dimension un, qui laissent invariant un champ de vecteurs méromorphe; on les suppose en outre de génération compacte, au sens de A. Haefliger. Ces pseudogroupes apparaissent dans l’étude des feuilletages transversalement holomorphes, sur des variétés compactes, pourvus d’un champ feuilleté méromorphe. Les principaux résultats sont les théorèmes 3.2 et 4.11, qui en donnent une classification...

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