45 citations · 310 across the 37 of their papers we have counts for
38 papers
Deconjugation of canonical variables and the Koopman-von Neumann theory
Mustafa Amin, Mark A. Walton
The Koopman-von Neumann (KvN) theory is one where the dynamical momentum is not canonically conjugate to position, i.e., position and momentum are deconjugated. From this point of…
Demazure formula for Weyl polytope sums
Jørgen Rasmussen, Mark A. Walton
The weights of finite-dimensional representations of simple Lie algebras are naturally associated with Weyl polytopes. Representation characters decompose into multiplicity-free su…
An illustration of canonical quantum-classical dynamics
Mustafa Amin, Mark A. Walton
Using the example of the harmonic oscillator, we illustrate the use of hybrid dynamical brackets in analyzing quantum-classical interaction. We only assume that a hybrid dynamical…
Demazure Formulas for Weight Polytopes
Mark A. Walton
The characters of simple Lie algebras are naturally decomposed into lattice polytope sums. The Brion formula for those polytope sums is remarkably similar to the Weyl character for…
Quantum-Classical Dynamical Brackets
Mustafa Amin, Mark A. Walton
We study the problem of constructing a general hybrid quantum-classical bracket from a partial classical limit of a full quantum bracket. Introducing a hybrid composition product,…
Can Star Products be Augmented by Classical Physics?
Matthew P. G. Robbins, Mark A. Walton
It has been suggested that star products in phase-space quantization may be augmented to describe additional, classical effects. That proposal is examined critically here. Two know…