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Jet extension of Finslerian gauge approach. (English) Zbl 0744.53035

Summary: The gauge field figures as a key concept in the modern theory of fundamental physical fields. Various deep and intimate relationships between the gauge field theory properties and the methods of differential geometry of fibered spaces have been recognized for a long time. In the present survey article the author makes an attempt to reach a higher step of gauge generality by getting over the proper Yang-Mills ansatz that the group character of the fibre must be a steed concept from the very beginning. Instead, it looks quite accessible to begin the gauge analysis with a more primary starting point where some appropriate, and motivated in a physical sense, geometrical space is treated as a fibre. Such a generalized program proves to be quite feasible if the notion of diffeomorphisms of fibres in themselves is invoked to serve as the required generalized gauge transformations. Such a way of extending the gauge transformation concept seems to be sufficiently natural and fundamental for all.

MSC:

53Z05 Applications of differential geometry to physics
81T13 Yang-Mills and other gauge theories in quantum field theory
53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)