15,350 research outputs found
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
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