On urn models, non-commutativity and operator normal forms. (English) Zbl 1238.82003
Summary: Non-commutativity is ubiquitous in mathematical modeling of reality and in many cases same algebraic structures are implemented in different situations. Here we consider the canonical commutation relation of quantum theory and discuss a simple urn model of the latter. It is shown that enumeration of urn histories provides a faithful realization of the Heisenberg-Weyl algebra. Drawing on this analogy we demonstrate how the operator normal forms facilitate counting of histories via generating functions, which in turn yields an intuitive combinatorial picture of the ordering procedure itself.
MSC:
| 82B10 | Quantum equilibrium statistical mechanics (general) |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
Keywords:
urn models; enumeration of histories; Heisenberg-Weyl algebra; generating functions; normal orderingReferences:
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