INSPIRE

The Classical geometry from a physical state in canonical quantum gravity

We construct a weave state which approximates a degenerate 3-metric of rank 2 at large scales. It turns out that a non-degenerate metric region can be evolved from this degenerate metric by the ...
INSPIRE

Generalized symplectic geometry as a covering theory for the Hamiltonian theories of classical particles and fields

It is shown that the symplectic potentials which underlie the symplectic geometry of classical particles and the multisymplectic geometry of classical fields are obtained as projections of a ...
Nature

Integral Geometry and Valuation Theory

Integral geometry and valuation theory form a dynamic field at the intersection of geometric analysis and algebraic topology. This discipline addresses the study of measures – known as valuations – ...
Scientific Research Publishing

Hestenes, D., Li, H. and Rockwood, A. (2001) A Unified Algebraic framework for Classical Geometry. In: Sommer, G., Ed., Geometric Computing with Clifford Algebras, Springer ...

ABSTRACT: This paper provides an implementation of a novel signal processing co-processor using a Geometric Algebra technique tailored for fast and complex geometric calculations in multiple ...
Nature

Differential Geometry and Projective Structures

Differential geometry is a pivotal field of mathematics that examines the properties of curves, surfaces and more general manifolds by utilising methods from calculus and linear algebra. Its ...