In this paper, the generic part of the gauge theory of gravity is derived,
    based merely on the action principle and on the general principle of
    relativity. We apply the canonical transformation framework to formulate
    geometrodynamics as a gauge theory. The starting point of our paper is
    constituted by the general De~Donder-Weyl Hamiltonian of a system of scalar and
    vector fields, which is supposed to be form-invariant under (global) Lorentz
    transformations. Following the reasoning of gauge theories, the corresponding
    locally form-invariant system is worked out by means of canonical
    transformations. The canonical transformation approach ensures by construction
    that the form of the action functional is maintained. We thus encounter amended
    Hamiltonian systems which are form-invariant under arbitrary spacetime
    transformations. This amended system complies with the general principle of
    relativity and describes both, the dynamics of the given physical system’s
    fields and their coupling to those quantities which describe the dynamics of
    the spacetime geometry. In this way, it is unambiguously determined how spin-0
    and spin-1 fields couple to the dynamics of spacetime.

    A term that describes the dynamics of the free gauge fields must finally be
    added to the amended Hamiltonian, as common to all gauge theories, to allow for
    a dynamic spacetime geometry. The choice of this “dynamics Hamiltonian” is
    outside of the scope of gauge theory as presented in this paper. It accounts
    for the remaining indefiniteness of any gauge theory of gravity and must be
    chosen “by hand” on the basis of physical reasoning. The final Hamiltonian of
    the gauge theory of gravity is shown to be at least quadratic in the conjugate
    momenta of the gauge fields — this is beyond the Einstein-Hilbert theory of
    General Relativity.

    Source link


    Leave A Reply