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On an easy transition from operator dynamics to generating functionals by Clifford algebras
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RENORMALIZATION: A NUMBER THEORETICAL MODEL
No full textABSTRACT. We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals
Vertex normal ordering as a consequence of nonsymmetric bilinear forms in Clifford algebras
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GEOMETRIC CONSTRUCTIONS PRESERVE FIBRATIONS
No full textABSTRACT. Let C be a representable 2-category, and T • a 2-endofunctor of the arrow 2-category C ↓ such that (i) codT • = cod and (ii) T • preserves proneness of morphisms in C ↓. Then T• preserves fibrations and opfibrations in C. The proof takes Street’s characterization of (e.g.) opfibrations as pseudoalgebras for 2-monads LB on slice categories C/B and develops it by defining a 2-monad L • on C ↓ that takes change of base into account, and uses known results on the lifting of 2-functors to pseudoalgebras. 1
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