Reduction and Second Quantization of Six-DimensionalElectromagnetic Fields

The study of reduction of electromagnetic fields in six-space to theirreducible representaion of proper, orthochronous, inhomogeneous Lorentz grouphas been undertaken. Second quantized expresions for field components havebeen derived by defining appropriate set of creation and annihilationoperators in the theory and the commutation relations between various fieldoperators have been derived. The resulting six-photon states correspondingto different polarizations have also been identified in terms of transverseand longitudinal polarizations in both spatial and temporal planes.The second quantized expressions of the six-angular momentum components havealso been derived. The second quantized expressions of electromagneticfields have been used to study the atomic interactions with these fields.The transition probability has been computed using weak field approximationwhich has been shown to exhibit a unique temporal dependence through theatomic dynamical variables and have important bearings on the nature ofinteraction involved.