176 citations · 1.3k across the 156 of their papers we have counts for
189 papers
Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density
David Chester, Xerxes D. Arsiwalla, Louis Kauffman +2
We generalize Koopman-von Neumann classical mechanics to poly-symplectic fields and recover De Donder-Weyl theory. Comparing with Dirac's Hamiltonian density inspires a new Hamilto…
On the Operator Origins of Classical and Quantum Wave Functions
Xerxes D. Arsiwalla, David Chester, Louis H. Kauffman
We investigate operator algebraic origins of the classical Koopman-von Neumann wave function as well as the quantum mechanical one . We introduce a formalism of O…
Graphoids
Neslihan Gügümcü, Louis H. Kauffman, Puttipong Pongtanapaisan
We study invariants of virtual graphoids, which are virtual spatial graph diagrams with two distinguished degree-one vertices modulo graph Reidemeister moves applied away from the…
On Vassiliev Invariants of Virtual Knots
Wout Moltmaker, Louis H. Kauffman
We discuss Vassiliev invariants for virtual knots, expanding upon the theory of quantum virtual knot invariants developed in arXiv:1509.00578. In particular, following the theory o…
Topology of Vortex Reconnection
Louis H. Kauffman
Knotted vortices such as those produced in water by Kleckner and Irvine tend to transform by reconnection to collections of unknotted and unlinked circles. The reconnection number…
New invariants for virtual knots via spanning surfaces
András Juhász, Louis H. Kauffman, Eiji Ogasa
We define three different types of spanning surfaces for knots in thickened surfaces. We use these to introduce new Seifert matrices, Alexander-type polynomials, genera, and a sign…