Free Fermions on a Piecewise Linear Four-Manifold. I: Exotic Chain Complex
| Autor: | Igor G. Korepanov |
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| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Basis (linear algebra) Applied Mathematics 010102 general mathematics FOS: Physical sciences Mathematical Physics (math-ph) Fermion 57R56 (Primary) 57Q99 (Secondary) 01 natural sciences Manifold Exponential function Piecewise linear function Chain (algebraic topology) Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Algebraic Topology (math.AT) Quantum Algebra (math.QA) Mathematics - Algebraic Topology 010307 mathematical physics 0101 mathematics Algebraic number Realization (systems) Mathematical Physics Mathematics |
| Zdroj: | Advances in Applied Clifford Algebras. 27:1411-1430 |
| ISSN: | 1661-4909 0188-7009 |
| DOI: | 10.1007/s00006-016-0746-y |
| Popis: | Recently, an algebraic realization of the four-dimensional Pachner move 3--3 was found in terms of Grassmann--Gaussian exponentials, and a remarkable nonlinear parameterization for it, going in terms of a $\mathbb C$-valued 2-cocycle. Here we define, for a given triangulated four-dimensional manifold and a 2-cocycle on it, an `exotic' chain complex intimately related to the mentioned parameterization, thus providing a basis for algebraic realizations of all four-dimensional Pachner moves. Comment: 23 pages. v2: new and better `gauge' for operators proposed, and many small improvements |
| Databáze: | OpenAIRE |
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