Phenomenological Approach to a Unified Field Theory

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Abstract
An attempt is made to give a phenomenological approach to a unified field theory by imposing four restrictions based on known experimental and theoretical considerations. The first two criteria, namely, that for weak electromagnetic fields the unified equations obey the flat space principle of conservation of energy and that the first-order corrections to Maxwell's equations not violate known experiments concerning the electron, lead to the requirement that a microscopic length appear in the Lagrangian. The remaining two conditions are a correspondence principle constraint for determining the form of the affinity and a gauge invariance condition. These four restrictions lead to a Lagrangian. The gauge invariance requirement forces the existence of a cosmological term. The field equations have been investigated for the spherically symmetric static solutions around a point electron. They lead to finite Coulomb energies, the microscopic length acting as the cut-off parameter.

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