22,929 research outputs found
Universal sextic effective interaction at criticality
The renormalization group approach in three dimensions is used to estimate
the universal critical value g_6^* of the dimensionless sextic effective
coupling constant for the Ising model. The four-loop RG expansion for g_6 is
calculated and resummed by means of the Pade-Borel and Pade-Borel-Leroy
procedures resulting in g_6^* = 1.596, while the most accurate estimate for
g_6^* is argued to be equal to 1.61.Comment: 6 pages, TeX, no figure
Clifford algebra and the projective model of homogeneous metric spaces: Foundations
This paper is to serve as a key to the projective (homogeneous) model
developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain
the underlying concepts in a simple language and give plenty of examples. It is
targeted to physicists and engineers and the emphasis is on explanation rather
than rigorous proof. The projective model is based on projective geometry and
Clifford algebra. It supplements and enhances vector and matrix algebras. It
also subsumes complex numbers and quaternions. Projective geometry augmented
with Clifford algebra provides a unified algebraic framework for describing
points, lines, planes, etc, and their transformations, such as rotations,
reflections, projections, and translations. The model is relevant not only to
Euclidean space but to a variety of homogeneous metric spaces.Comment: 89 pages, 140 figures (many include 3D PRC vector graphics
Algebraic quantum Hamiltonians on the plane
We consider second order differential operators with polynomial
coefficients that preserve the vector space of polynomials of degrees not
greater then . We assume that the metric associated with the symbol of
is flat and that the operator is potential. In the case of two independent
variables we obtain some classification results and find polynomial forms for
the elliptic and Calogero-Moser Hamiltonians and for the elliptic
Inosemtsev model.Comment: 14 page
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