A new mathematical concept, theq-deformation of the determinant is proposed. By using theq-deformed Slater determinant, a unified realization of boson, fermion and quon algebras is presented. The quon algebra is characterized by the qumutation relationajak° -qakδaj = δjk, which interpolates between Fermi anticommutation and Bose commutation relations. It turns out that for allq∈(−1, 1), the Fock-like spaces are the same, that is the direct sum of all tensor product powers of the single particle spaceh,Open image in new window. This state vector space describes systems of identical particles obeying Boltzmann statistics.
04.40 Continuous media electromagnetic and other mixed gravitational systems
02.10.Sp Linear and multilinear algebra matrix theory (finite and infinite)
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