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Hilbert space representations of the Poincaré group for the Landau gauge. (English) Zbl 0747.46051
Summary: The theory of the electromagnetic quantum field in the Landau gauge has always lacked a treatment based on a Hilbert space of $$\mathbb{C}^ 4$$-valued functions (the one particle space) on which the Poincaré group acts via a continuous representation realized by bounded operators. In the present paper the gap will be filled and it will be shown, through the mathematical technique of jets on the forward light cone in momentum space, how the theory presented extends the previous treatments of the problem. In order to show that the massless vector field theory in the Landau gauge can be obtained, the equation of motion and the two-point function will be derived in the present model according to the Wightman axioms.

MSC:
 46N50 Applications of functional analysis in quantum physics 81T10 Model quantum field theories 22D12 Other representations of locally compact groups 81V10 Electromagnetic interaction; quantum electrodynamics
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References:
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