Mathematical basis of computational statistical physics and quantum analysis Original Research Article

A mathematical basis of quantum Mote Carlo methods is discussed using the exponential product formulas (Suzuki, 1966; Trotter, 1959) which have been generalized by the present author to infinite order (Suzuki, 1990). The investigation of this scheme has inspired the author to construct a new mathematical framework of quantum analysis (Suzuki, 1990; 1991; 1992), namely a noncommutative derivative of f(A) for an operator with respect to the operator A itself. Applications of this quantum analysis to statistical mechanics are discussed briefly (Suzuki, 1991; 1992).