Polarization Tensors and the Photon Field

Abstract

A direct calculation of the elements of the photon polarization vector for arbitrary momentum in the helicity basis shows that it is not a vector but a complex bivector. The bivector real and imaginary parts can be directly equated with electromagnetic field amplitudes and the associated field equations are the Maxwell equations in time-imaginary space. The bivector field exhibits a phase freedom (Berry, or geometric phase) dependent on the rotation history of the field or observer. Phase freedom is not intrinsically present in the longitudinal excitations of the field and a general argument connects quantization of angular momentum with the observation of phase changes associated with frame rotation. Current and translation operators can be defined for bivector fields that are free of defects associated with a quantized vector potential.