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Simple omega-categories and chain complexes
The category of strict omega-categories has an important full subcategory
whose objects are the simple omega-categories freely generated by planar trees
or by globular cardinals. We give a simple description of this subcategory in
terms of chain complexes, and we give a similar description of the opposite
category, the category of finite discs, in terms of cochain complexes. Berger
has shown that the category of simple omega-categories has a filtration by
iterated wreath products of the simplex category. We generalise his result by
considering wreath products of categories of chain complexes over the simplex
category.Comment: 14 pages; v2 has minor corrections and a little additional materia
Light-Cone Expansion of the Dirac Sea in the Presence of Chiral and Scalar Potentials
We study the Dirac sea in the presence of external chiral and
scalar/pseudoscalar potentials. In preparation, a method is developed for
calculating the advanced and retarded Green's functions in an expansion around
the light cone. For this, we first expand all Feynman diagrams and then
explicitly sum up the perturbation series. The light-cone expansion expresses
the Green's functions as an infinite sum of line integrals over the external
potential and its partial derivatives.
The Dirac sea is decomposed into a causal and a non-causal contribution. The
causal contribution has a light-cone expansion which is closely related to the
light-cone expansion of the Green's functions; it describes the singular
behavior of the Dirac sea in terms of nested line integrals along the light
cone. The non-causal contribution, on the other hand, is, to every order in
perturbation theory, a smooth function in position space.Comment: 59 pages, LaTeX (published version
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