272 research outputs found
Electric-Magnetic duality and the "Loop Representation" in Abelian Gauge Theories
Abelian Gauge Theories are quantized in a geometric representation that
generalizes the Loop Representation and treates electric and magnetic operators
on the same footing. The usual canonical algebra is turned into a topological
algebra of non local operators that resembles the order-disorder dual algebra
of 't Hooft. These dual operators provide a complete description of the
physical phase space of the theories.Comment: 13 pages, LaTex (run twice
The Topological Theory of the Milnor Invariant
We study a topological Abelian gauge theory that generalizes the Abelian
Chern-Simons one, and that leads in a natural way to the Milnor's link
invariant when the classical action on-shell is calculated.Comment: 4 pages; corrected equatio
Magnetic Monopole in the Loop Representation
We quantize the electromagnetic field in the presence of a static magnetic
monopole, within the loop-representation formalism. We find that the
loop-dependent wave functional becomes multivalued, in the sense that it
acquires a dependence on the surfaces bounded by the loop. This generalizes
what occurs in quantum mechanics in multiply connected spaces. When Dirac's
quantization condition holds, this surface-dependence disappears, together with
the effect of the monopole on the electromagnetic field.Comment: reference and comment adde
Electromagnetism and multiple-valued loop-dependent wave functionals
We quantize the Maxwell theory in the presence of a electric charge in a
"dual" Loop Representation, i.e. a geometric representation of magnetic
Faraday's lines. It is found that the theory can be seen as a theory without
sources, except by the fact that the wave functional becomes multivalued. This
can be seen as the dual counterpart of what occurs in Maxwell theory with a
magnetic pole, when it is quantized in the ordinary Loop Representation. The
multivaluedness can be seen as a result of the multiply-connectedness of the
configuration space of the quantum theory.Comment: 5 page
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