320 research outputs found
Computation and Homotopical Applications of Induced Crossed Modules
We explain how the computation of induced crossed modules allows the
computation of certain homotopy 2-types and, in particular, second homotopy
groups. We discuss various issues involved in computing induced crossed modules
and give some examples and applications.Comment: 15 pages, xypic, latex2
String rewriting for Double Coset Systems
In this paper we show how string rewriting methods can be applied to give a
new method of computing double cosets. Previous methods for double cosets were
enumerative and thus restricted to finite examples. Our rewriting methods do
not suffer this restriction and we present some examples of infinite double
coset systems which can now easily be solved using our approach. Even when both
enumerative and rewriting techniques are present, our rewriting methods will be
competitive because they i) do not require the preliminary calculation of
cosets; and ii) as with single coset problems, there are many examples for
which rewriting is more effective than enumeration.
Automata provide the means for identifying expressions for normal forms in
infinite situations and we show how they may be constructed in this setting.
Further, related results on logged string rewriting for monoid presentations
are exploited to show how witnesses for the computations can be provided and
how information about the subgroups and the relations between them can be
extracted. Finally, we discuss how the double coset problem is a special case
of the problem of computing induced actions of categories which demonstrates
that our rewriting methods are applicable to a much wider class of problems
than just the double coset problem.Comment: accepted for publication by the Journal of Symbolic Computatio
Magnetic Monopoles as Agents of Chiral Symmetry Breaking in U(1) Lattice Gauge Theory
We present results suggesting that magnetic monopoles can account for chiral
symmetry breaking in abelian gauge theory. Full U(1) configurations from a
lattice simulation are factorized into magnetic monopole and photon
contributions. The expectation is computed using the monopole
configurations and compared to results for the full U(1) configurations. It is
shown that excellent agreement between the two values of is
obtained if the effect of photons, which "dress" the composite operator
psibarpsi, is included. This can be estimated independently by measurements of
the physical fermion mass in the photon background.Comment: 14 pages REVTeX, including 5 figure
Confinement by Monopoles in the Positive Plaquette Model of SU(2) Lattice Gauge Theory
Confinement via 't Hooft-Mandelstam monopoles is studied for the positive
plaquette model in SU(2) lattice gauge theory. Positive plaquette model
configurations are projected into the maximum abelian gauge and the magnetic
current extracted. The resulting magnetic current is used to compute monopole
contributions to Wilson loops and extract a monopole contribution to the string
tension. As was previously found for the Wilson action, the monopole
contribution to the string tension agrees with the string tension calculated
directly from the SU(2) links. The fact that the positive plaquette model
suppresses Z2 monopoles and vortices is discussed.Comment: 8 pages, one Postscript figure, Latex, uses psfig files:
posplaq.tex,posplaq.aux,pp_1_3.ps packaged with uufile
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