281 research outputs found
A Polymer Expansion for the Quantum Heisenberg Ferromagnet Wave Function
A polymer expansion is given for the Quantum Heisenberg Ferromagnet wave
function. Working on a finite lattice, one is dealing entirely with algebraic
identities; there is no question of convergence. The conjecture to be pursued
in further work is that effects of large polymers are small. This is relevant
to the question of the utility of the expansion and its possible extension to
the infinite volume. In themselves the constructions of the present paper are
neat and elegant and have surprising simplicity.Comment: 9 pages, expanded explanatio
A New Formulation and Regularization of Gauge Theories Using a Non-Linear Wavelet Expansion
The Euclidean version of the Yang-Mills theory is studied in four dimensions.
The field is expressed non-linearly in terms of the basic variables. The field
is developed inductively, adding one excitation at a time. A given excitation
is added into the ``background field'' of the excitations already added, the
background field expressed in a radially axial gauge about the point where the
excitation is centered. The linearization of the resultant expression for the
field is an expansion where is a divergence-free wavelet
and is the associated basic variable, a Lie Algebra element of the
gauge group. One is working in a particular gauge, regularization is simply
cutoff regularization realized by omitting wavelet excitations below a certain
length scale. We will prove in a later paper that only the usual
gauge-invariant counterterms are required to renormalize perturbation theory.
Using related ideas, but essentially independent of the rest of paper, we
find an expression for the determinant of a gauged boson or fermion field in a
fixed ``small'' external gauge field. This determinant is expressed in terms of
explicitly gauge invariant quantities, and again may be regularized by a cutoff
regularization.
We leave to later work relating these regularizations to the usual
dimensional regularization.Comment: 22 pages lateX. A better form of determinants is given in chapters 4
and
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