Jet Extension of Finslerian Gauge Approach

Abstract

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 proper and the methods of differential geometry of fibered spaces have been recognized for a long time. Usually, such relationships are established in terms of group fibrations such that the fibres are implied to be some of Lie groups (see, e.g., [1–4]). In the present servey-article, which extends basic tools elaborated in the preceding publications [5, 6], 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 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 way of extending the gauge transformation concept seems to be sufficiently natural and fundamental for all.