Polynomial Sequences of Binomial Type and Path Integrals
Kisil, Vladimir V.
arXiv, 9808040 / Harvested from arXiv
Text on arXiv
Polynomial sequences $p_n(x)$ of binomial type are a principal tool in the umbral calculus of enumerative combinatorics. We express $p_n(x)$ as a \emph{path integral} in the ``phase space'' $\Space{N}{} \times {[-\pi,\pi]}$. The Hamiltonian is $h(\phi)=\sum_{n=0}^\infty p_n'(0)/n! e^{in\phi}$ and it produces a Schr\"odinger type equation for $p_n(x)$. 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.
Publié le : 1998-08-09
Classification:  Mathematics - Combinatorics,  Mathematical Physics,  Mathematics - Functional Analysis,  Quantum Physics,  05A40 (Primary), 05A15, 58D30, 81Q30, 81R30, 81S40 (Secondary) 
@article{9808040,
     author = {Kisil, Vladimir V.},
     title = {Polynomial Sequences of Binomial Type and Path Integrals},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9808040}
}

Kisil, Vladimir V. Polynomial Sequences of Binomial Type and Path Integrals. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9808040/