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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 19:59:07 +0000A Study of Some Two-Dimensional Field Theory Models
https://resolver.caltech.edu/CaltechTHESIS:12052017-090641371
Authors: {'items': [{'id': 'Wang-Robert-Tung-Hsing', 'name': {'family': 'Wang', 'given': 'Robert Tung-Hsing'}}]}
Year: 1976
DOI: 10.7907/XRVY-4Z35
<p>Recently it has been pointed out <sup>(6)</sup> that quantum
electrodynamics with a massless fermion in one-space, one-time
dimension exhibits behavior which can be interpreted as being
analogous to scaling and confinement. To learn more about
the occurrence of such behavior, we study several other
two-dimensional quantum field theories. After reviewing the
Thirring model, we construct operator solutions of scale-invariant
generalizations with internal degrees of freedom.
We find that the physics of these models can be equally
well described in terms of a field theory of fermions or
of bosons. Because the physical excitations are massless in
these models, the physical states can also be described,
in general, as many-fermion or many-boson states.</p>
<p>We also generalize Lowenstein and Swieca's operator
solution of quantum electrodynamics in two-dimensions to a
model with more than one massless, charged fermion. Although
the resulting physical states are all electrically neutral,
we find that the fermions may not be completely confined in
the sense that some of their quantum numbers may be represented
by particles in the spectrum. Once again, we discover that
the physics can be represented by a fermion field theory or
by a boson theory.</p>
<p>The fact that the same physics can be represented by
interacting fermions or interacting bosons can be understood
by considering the polarization fields associated with the
fermion charge and axial charge. This general physical
picture allows us to extend the fermion-boson duality to
theories with non-trivial scattering. Although these models
cannot be solved, we can use formal operator structures
to test, in a semi-classical approximation, for the possible
existence of charged fermion states in the spectrum. Because
the fermion states are equivalent to coherent states of bosons,
their physics is approximated by solutions to the appropriate
classical boson theory. Therefore, in two dimensions, confineĀment
may be a phenomenon associated with the classical behavior
of a theory.</p>
https://thesis.library.caltech.edu/id/eprint/10583