Spinors and field interactions in higher order anisotropic spaces

We formulate the theory of field interactions with higher order anisotropy.The concepts of higher order anisotropic space and locally anisotropic space(in brief, ha-space and la-space) are introduced as general ones for varioustypes of higher order extensions of Lagrange and Finsler geometry and higherdimension (Kaluza-Klein type) spaces. The spinors on ha-spaces are defined inthe framework of the geometry of Clifford bundles provided with compatiblenonlinear and distinguished connections and metric structures (d-connection andd-metric). The spinor differential geometry of ha-spaces is constructed. Thereare discussed some related issues connected with the physical aspects of higherorder anisotropic interactions for gravitational, gauge, spinor, Dirac spinorand Proca fields. Motion equations in higher order generalizations of Finslerspaces, of the mentioned type of fields, are defined by using bundles of linearand affine frames locally adapted to the nonlinear connection structure.Comment: 49 pages, latex209, submitted to JHE