7 citations · 18 across the 6 of their papers we have counts for
6 papers
A generic Hopf algebra for quantum statistical mechanics
Allan I. Solomon, Gerard E. H. Duchamp, Pawel Blasiak +2
In this paper, we present a Hopf algebra description of a bosonic quantum model, using the elementary combinatorial elements of Bell and Stirling numbers. Our objective in doing th…
From Quantum Mechanics to Quantum Field Theory: The Hopf route
Allan I. Solomon, Gérard Henry Edmond Duchamp, Pawel Blasiak +2
We show that the combinatorial numbers known as {\em Bell numbers} are generic in quantum physics. This is because they arise in the procedure known as {\em Normal ordering} of bos…
Combinatorial Algebra for second-quantized Quantum Theory
P. Blasiak, G. H. E. Duchamp, A. I. Solomon +2
We describe an algebra G of diagrams which faithfully gives a diagrammatic representation of the structures of both the Heisenberg-Weyl algebra H - the associative algebra of the c…
Hopf algebras: motivations and examples
G. H. E. Duchamp, P. Blasiak, A. Horzela +2
This paper provides motivation as well as a method of construction for Hopf algebras, starting from an associative algebra. The dualization technique involved relies heavily on the…
Monomiality principle, Sheffer-type polynomials and the normal ordering problem
K A Penson, P Blasiak, G Dattoli +3
We solve the boson normal ordering problem for with arbitrary functions and and integer , where and are boson annihilation and creat…
Coherent State Measures and the Extended Dobinski relations
Karol A. Penson, Allan I. Solomon
Conventional Bell and Stirling numbers arise naturally in the normal ordering of simple monomials in boson operators. By extending this process we obtain generalizations of these c…