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Generalized Relativistic Hamiltonian in an Alpha Field

An alpha field is a potential field that can be presented by two dimensionless field parameters α and α′. To this category belong, among the others, electromagnetic and gravitational potential fields. The field parameters α and α′ should satisfy the field equations of the related potential field in each concrete case. The problem is to derive the generalized relativistic Hamiltonian that can be applied to an alpha field. Starting with variation principle and with the generalized line element ds2, a linear Dirac's like relativistic Hamiltonian has been derived as the function of the field parameters α and α′. The comparison of the coefficients of that Hamiltonian with the coefficients of the well known Dirac’s Hamiltonian helps to understand their physical sense. The derived linear Dirac's like relativistic Hamiltonian has been applied to an electromagnetic and to a gravitational field. The application to a gravitational field leads to the gravitomagnetic phenomena on the natural way, without any a priory assumption. The nonlinear relativistic Hamiltonian for an alpha field has also been derived starting with the linear one and using quadratic operation. Both Hamiltonians can be applied to the Special and General Relativity, as well as, to the multipotential alpha fields.

Dimensionless Field Parameters; Relativistic Hamiltonian; Linear Dirac's like Hamiltonian; Nonlinear Hamiltonian; Comparison of Hamiltonians.

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