14,583 research outputs found
Lattice Landau gauge via Stereographic Projection
The complete cancellation of Gribov copies and the Neuberger 0/0 problem of
lattice BRST can be avoided in modified lattice Landau gauge. In compact U(1),
where the problem is a lattice artifact, there remain to be Gribov copies but
their number is exponentially reduced. Moreover, there is no cancellation of
copies there as the sign of the Faddeev-Popov determinant is positive. Applied
to the maximal Abelian subgroup this avoids the perfect cancellation amongst
the remaining Gribov copies for SU(N) also. In addition, based on a definition
of gauge fields on the lattice as stereographically-projected link variables,
it provides a framework for gauge fixed Monte-Carlo simulations. This will
include all Gribov copies in the spirit of BRST. Their average is not zero, as
demonstrated explicitly in simple models. This might resolve present
discrepancies between gauge-fixed lattice and continuum studies of QCD Green's
functions.Comment: 5 pages, talk presented at the 8th Conference Quark Confinement and
the Hadron Spectrum, September 1-6, 2008, Mainz, German
Interactive 4-D Visualization of Stereographic Images From the Double Orthogonal Projection
The double orthogonal projection of the 4-space onto two mutually
perpendicular 3-spaces is a method of visualization of four-dimensional objects
in a three-dimensional space. We present an interactive animation of the
stereographic projection of a hyperspherical hexahedron on a 3-sphere embedded
in the 4-space. Described are synthetic constructions of stereographic images
of a point, hyperspherical tetrahedron, and 2-sphere on a 3-sphere from their
double orthogonal projections. Consequently, the double-orthogonal projection
of a freehand curve on a 3-sphere is created inversely from its stereographic
image. Furthermore, we show an application to a synthetic construction of a
spherical inversion and visualizations of double orthogonal projections and
stereographic images of Hopf tori on a 3-sphere generated from Clelia curves on
a 2-sphere.Comment: ICGG 2020 submissio
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