Twisted Homotopy: A Group Theoretic Approach

Details Twisted Homotopy: A Group Theoretic Approach Twisted Homotopy: A Group Theoretic Approach

1996-06-14

arxiv.org/abs/hep-th/9606085v1

Physics

High Energy Physics

High Energy Physics - Theory

7 pages,Latex,no figures

Scientific paper

After summarising the physical approach leading to twisted homotopy and after developing the cohomological approach further with respect to our previous work we propose a third alternative approach to twisted homotopy based on group theoretic considerations. In this approach the fundamental group $\Pi (m) $ isomorphic to Z which describes homotopic loops on the punctured plane$ R^2/(0) $ is enhanced in a special way to the continuous SO(2) group . This is performed by letting the parameter of the group $ m \rightarrow \lambda $ while keeping its generator unchanged .It is shown that such non-trivial procedure has the effect of introducing well defined self-interactions among loops which are at the basis of twisted homotopy where the angle $ \lambda $ plays the role of the self coupling constant. KEYWORDS: Homotopy, Group Theory, Quantum Mechanics MSC:55Q35; PACS:02.20.Fh ; 03.65.Fd

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