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Geometry of space-time and generalised Lagrange gauge theory. (English) Zbl 0796.53020

Summary: The authors present the Einstein and Maxwell equations for the generalised Lagrange space \[ GL^ n= (M,g_{ij}(x,y)= e^{2\sigma(x,y)}\gamma_{ij}(x)), \] and characterize the case of vanishing mixed curvature tensor field of the canonical linear \(d\)- connection. Then the Lagrangian gauge theory in G. S. Asanov’s sense [G. S. Asanov and S. F. Ponomarenko, Finsler bundles over space-time, associated gauge fields and connections (1989; Zbl 0708.53001)] is developed for the tangent bundle endowed with \((h,v)\)- metrics, obtaining the generalized Einstein-Yang Mills equations with respect to the metric gauge tensor fields and to the gauge field \(\sigma(x,y)\) for three remarkable cases in which the metrics are derived from the fundamental tensor field \(g_{ij}(x,y)\). Proofs are, in most cases, mechanical but rather tedious calculations. They are omitted.

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
81T13 Yang-Mills and other gauge theories in quantum field theory

Citations:

Zbl 0708.53001
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