Abstract:
The solution of the problem to generalize, to the multi-dimensional case,
the Favard Lemma, which lies at the foundations of the theory of orthogonal
polynomials in one real variable, was recently obtained in the joint paper [1].
This suggests a new approach to the theory of orthogonal
polynomials, that emphasizes the fact that it generalizes in several, unexpected
and non-trivial ways the usual mathematical structure of quantum mechanics
and (in its infinite dimensional version) quantum field theory.
These generalizations will be briefly described and it will explained in what sense
they extend the program of "non-linear quantization" whose first achievement
was obtained in the paper [2].
Language: English
References
Accardi L., Barhoumi A., Dhahri A., “Identification of the theory of orthogonal polynomials in $d$–indeterminates with the theory of $3$–diagonal symmetric interacting Fock spaces on $\mathbb{C}_d$”, submitted to IDA-QP
Accardi L., Lu Y.G., Volovich I.V.:, “White noise approach to classical and quantum stochastic calculi”, Lecture Notes of the Volterra–CIRM International School with the same title, Trento, Italy, 1999, Volterra Preprint N. 375, July (1999)
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