Polynomial Sequences of Binomial Type and Path Integrals
Vladimir V. Kisil

TL;DR
This paper connects polynomial sequences of binomial type with path integrals in phase space, establishing a link between combinatorics and quantum field theory, and proposing an algorithm for quantum computations.
Contribution
It expresses polynomial sequences as path integrals, bridging combinatorics and quantum physics, and introduces a quantum computation algorithm based on this formulation.
Findings
Path integral representation of polynomial sequences of binomial type
Connection between umbral calculus and quantum field theory
Algorithm for parallel quantum computations
Abstract
Polynomial sequences of binomial type are a principal tool in the umbral calculus of enumerative combinatorics. We express as a \emph{path integral} in the ``phase space'' . The Hamiltonian is and it produces a Schr\"odinger type equation for . This establishes a bridge between enumerative combinatorics and quantum field theory. It also provides an algorithm for parallel quantum computations. Keywords: Feynman path integral, umbral calculus, polynomial sequence of binomial type, token, Schr\"odinger equation, propagator, wave function, cumulants, quantum computation.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Polynomial and algebraic computation · Nonlinear Waves and Solitons
