a Kanazawa University, Department of Mathematics, Kanazawa 920-1192, Japan b Setsunan University, Department of Mathematics and Physics, Neyagawa, Osaka 572-8508, Japan
Abstract:
The random point fields which describe the position distributions of the systems of ideal boson gas in states of Bose-Einstein condensations are obtained through the thermodynamic limits. The resulting point fields are given by convolutions of two kinds of independent point fields: the so-called boson processes whose generating functionals are represented by the inverses of the Fredholm determinants for operators related to the heat operator and the point fields whose generating functionals are represented by the resolvents of the operators. The construction of the latter point fields in an abstract formulation is also given.