Finslerian approach to quantized field theory: positivity of scalar field energy and generalization of Pauli-Jordan functions

On the basis of Finslerian Hamiltonian function, the real scalar field is considered. It is shown that the use of the special-relativistic Finslerian metric function leads to positivity of field energy. The Finslerian extension of the Pauli-J"ordan function is proposed to derive the required commutators and the relationship between the amplitudes $u^\pm(\textbf{k})$ and $u^\pm(k)$.