Fock space construction of the massless dipole field

Anton Z. Capri, Gebhard Grübl* and Randy Kobes

Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2J1, Canada
*Permanent address: Institut für Theoretische Physik der Universität Innsbruck, A-6020, Austria

Received 4 August 1982. Available online 28 September 2004.

Abstract. We construct the Fock space representation of the free massless scalar dipole field in terms of creation and annihilation operators for the eigenvectors of the momentum operator. The Poincaré group is implemented unitarily only on a subspace of the full (positive metric) Hilbert space. The subspace possesses a hermitean, local, irreducible scalar field constructed out of the (non-hermitean) dipole field. Thus this subspace is a perfect candidate for a physical subspace of observable particles. We show that this possibility is however excluded by the fact that these particles interact with an external c-number source in a manner that violates unitarity. We illustrate our construction by applying it to the linearized Higgs model with external c-number source and examine the (non-trivial) dynamics of the dipole degrees of freedom in this case. An explicit separation of the physical degrees of freedom from the unphysical ones is presented for this interacting model.


Annals of Physics, 147, 140 - 170 (1983).

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