GEOMETRODYNAMIC SOLITONS

Abstract

A formally renormalizable extended conformal gauge field action is proposed to take the place of the Rainich conditions in geometrodynamics. The moduli parameters of the Lorentzian complex structure of space–time are the dynamical variables of the present action. It admits two kinds of solitons: the pure geometric ("leptonic") solitons with vanishing gauge field and the "hadronic" ones with gauge field contributions. The gauge field modes are perturbatively confined, because the present gauge field action asymptotically generates a linear potential. The pure geometric solitons are topologically separated into three classes. One static massive soliton is found in the first class and one massless stationary soliton in the degenerate sector of every class. The corresponding (complex) conjugate Hermitian structures are the antisolitons. In the static soliton sector the electromagnetic field is explicitly defined via the Lorentzian complex structure tensor. The mass and the charge variables of the static soliton take unique values. This soliton has spin and a fermionic gyromagnetic ratio. The model has no other simple pure geometric static soliton. The energy is properly defined as a function of the moduli parameters of the complex structure. This permits the definition of the corresponding excitation modes. One must be the photonic vector mode, which appears in the static soliton sector, and the other must be massive. There can be one scalar and three vector modes. Based on this soliton (particle) spectrum, an effective Lagrangian is derived with a spontaneously broken SU (2)× U (1) symmetry, implied by the unitarity condition. A general description of asymptotically flat Lorentzian complex structures, using ordinary (not local) twistors, is also found.