CALCULUS FOR FUNCTIONS OF NONCOMMUTING OPERATORS AND GENERAL PHASE-SPACE METHODS IN QUANTUM MECHANICS. I. MAPPING THEOREMS AND ORDERING OF FUNCTIONS OF NONCOMMUTING OPERATORS.

@article{Agarwal1970CALCULUSFF,
  title={CALCULUS FOR FUNCTIONS OF NONCOMMUTING OPERATORS AND GENERAL PHASE-SPACE METHODS IN QUANTUM MECHANICS. I. MAPPING THEOREMS AND ORDERING OF FUNCTIONS OF NONCOMMUTING OPERATORS.},
  author={G. Agarwal and E. Wolf},
  journal={Physical Review D},
  year={1970},
  volume={2},
  pages={2161-2186}
}
A new calculus for functions of noncommuting operators is developed, based on the notion of mapping of functions of operators onto $c$-number functions. The class of linear mappings, each member of which is characterized by an entire analytic function of two complex variables, is studied in detail. Closed-form solutions for such mappings and for the inverse mappings are obtained and various properties of these mappings are studied. It is shown that the most commonly occurring rules of… Expand
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