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A FORTRAN Program for Commutators of Polynomials in Annihilation and Creation Operators

Heinrich Böhm, P. Kolář, Wolfgang Lassner, Pavel Exner, Miloslav Havlíček

Published Jan 1, 1977• 0 citations
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Quantum matrix algebras s u q (2) are realized in terms of single-state boson operators and their conjugates, ( a + , a ), ( b + , b ), etc., specified as quantum analogs of symplectons. The boson operators obey the linear transformation of S U q (2) such as a ′ + = a + x + a v and a ′ = a + u + a y . Here, x , u , v , y are non-commutative elements which commute with a + and a . Commutation relations for creation and annihilation operators are determined so as to be invariant under the linear transformation. Exchange algebras with the universal R j ′ j ′′ matrix are realized in terms of P ( j ′ , m ′ ; b ), P ( j ′′ , m ′′ ; a ), etc., where P ( j ′ , m ′ ; b ) is the j z ′ = m ′ component of rank- j ′ tensor written as an order-2 j ′ polynomial in b + and b .

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Creation and Annihilation Operators

WORLD SCIENTIFIC eBooks•Dec 1, 2002•10 citations
Quantum matrix algebras s u q (2) are realized in terms of single-state boson operators and their conjugates, ( a + , a ), ( b + , b ), etc., specified as quantum analogs of symplectons. The boson operators obey the linear transformation of S U q (2) such as a ′ + = a + x + a v and a ′ = a + u + a y . Here, x , u , v , y are non-commutative elements which commute with a + and a . Commutation relations for creation and annihilation operators are determined so as to be invariant under the linear transformation. Exchange algebras with the universal R j ′ j ′′ matrix are realized in terms of P ( j ′ , m ′ ; b ), P ( j ′′ , m ′′ ; a ), etc., where P ( j ′ , m ′ ; b ) is the j z ′ = m ′ component of rank- j ′ tensor written as an order-2 j ′ polynomial in b + and b .