Abstract
The boson calculus is based on the action of the operators of multiplication by x i and differentiation, D i , acting on polynomials. With x = (x 1 ,…,x N ), D = (D 1 ,…,D N ), define the basis \(\left[\kern-0.15em\left[ n \right]\kern-0.15em\right] = x^n\), then, X j denoting the operator of multiplication by x j ,
And we have the commutator
i.e., the commutation relations [D J , X i ] = δ ij I where I denotes the identity operator.
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© 1996 Kluwer Academic Publishers
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Feinsilver, P., Schott, R. (1996). Operator calculus and Appell systems. In: Algebraic Structures and Operator Calculus. Mathematics and Its Applications, vol 347. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0157-5_2
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DOI: https://doi.org/10.1007/978-94-009-0157-5_2
Publisher Name: Springer, Dordrecht
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