Nonlinear connections for conformal gauge theories on path-spaces and duality | Zendy

Mircea Crâșmăreanu | Zendy

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Nonlinear connections for conformal gauge theories on path-spaces and duality

Author(s) -

Mircea Crâșmăreanu

Publication year - 2012

Publication title -

publicationes mathematicae debrecen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.468

H-Index - 37

eISSN - 2064-2849

pISSN - 0033-3883

DOI - 10.5486/pmd.2012.5178

Subject(s) - mathematics , conformal map , duality (order theory) , gauge (firearms) , path (computing) , pure mathematics , nonlinear system , gauge theory , mathematical analysis , algebra over a field , mathematical physics , quantum mechanics , physics , computer science , geography , archaeology , programming language

Weyl structures and compatible nonlinear connections are introduced in the ge-ometry of semisprays as a natural generalization of similar notions from Riemanniangeometry. The existence and formula for the set of all compatible nonlinear connec-tions are derived by using the Obata tensors naturally associated to a xed metricin the given conformal class; this formula is also expressed in terms of dual non-linear connections which generalize the Norden's notion of dual linear connections.A geometric meaning for pairs (Weyl structure, compatible nonlinear connection) isprovided in terms of gauge conformal invariance.

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