Equations of motion for scalar and spinor fields in a four-dimensional non-euclidean momentum space

Equations of motion are obtained for a scalar and a spinor field in a four-dimensional non-Euclidean momentum space. They contain as a parameter a fundamental length $l$ and go over into the ordinary Klein–Gordon and Dirac equations in the limit $l\to0$. In the new formalism, an important part is played by the concept of a “vacuum momentum”, which is due to I. E. Tamm. The obtained equations remain invariant under spatial reflection only when the vacuum momentum is simultaneously transformed.