Abstract

where ~ = dxa/dt (t is an arbitrary parameter) and L is called the fundamental function. The independent variables in Finsler space arc the line elements (x, ~), and the ~'s are regarded as the independent internal variables associated with each point (x) 0). Therefore, since the ~'s are vectorial, the theory of fields in Finsler spaces belongs to the so-called nonlocal field theory (3,4). In the Finslerian unified field theory (~,5), the &'s are often adopted as the electromagnetic potential. And it has also been proposed (4) that the ~'s represent some (~ anisotropic ~> property underlying the field, so that they may be related to some kinds of broke~l symmetries within the range of the unified theory of gauge fields (s). Now, in the Finslerian field theory, two kinds of gauge (or spin gauge) fields, i.e. r~a and C~x (or F . and B.) appear through the absolute differential as follows:

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