Study of a Model of Quantum Electrodynamics

This paper studies the model of the quantum electrodynamics (QED) of a single nonrelativistic electron due to W. Pauli and M. Fierz and studied further by P. Blanchard. This model exhibits infrared divergence in a very simple context. The infrared divergence is associated with the inequivalence of the Hilbert spaces associated with the free Hamiltonian and with the complete Hamiltonian. Infrared divergences that are visible in the perturbative description disappear in the space of the clothed electrons. In this model when the Hamiltonian is expressed in terms of the ``physical'' fields that create the electron together with its cloud of soft photons the variational principle suggested earlier can be applied. At finite time the Heisenberg field of the model acts in the space of the perturbative electron together with a finite number of perturbative photons, while the ``physical'' field can be chosen to act in the space of the exact (``physical'') electron eigenstates together with a finite number of physical photons. The space of the physical (or clothed) electron states can be chosen to be a Fock space.Comment: 11 pages, no figures, to appear in Found. Phys., Vol. 30, No.3 (March 2000) (first issue in honor of Kurt Haller

Variational Principle in the Algebra of Asymptotic Fields

This paper proposes a variational principle for the solutions of quantum field theories in which the ``trial functions'' are chosen from the algebra of asymptotic fields, and illustrates this variational principle in simple cases.Comment: 15 pages, Latex, no figure

Theories of violation of statistics

I discuss theories of violations of statistics, including intermediate statistics, parastatistics, parons, and quons. I emphasize quons, which allow small violations of statistics. I analyze the quon algebra and its representations, implications of the algebra including the observables allowed by the superselection rule separating inequivalent representations of the symmetric group, the conservation of statistics rules, and the rule for composite systems of quons. I conclude by raising the question of possible origins of violations of statistics and of the level at which violations should be expected if they exist.Comment: 16 pages, talk given at the International Conference on the Spin-Statistics Connection and Commutation Relations: Experimental Tests and Theoretical Implications, Capri, Italy, May 31-June 4, 2000. Dedication added. Minor misprints correcte