Toeplitz operators and quantum mechanics (Q5893772)

Toeplitz operators on the Segal-Bargmann spaces of Gaussian measure square-integrable entire functions on complex n-space \({\mathbb{C}}^ n\) are studied. The \(C^*\)-algebra generated by the Weyl form of the canonical commutation relations consists precisely of the uniform limits of almost- periodic Toeplitz operators. The question of ``which Toeplitz operators admit a symbol calculus modulo the compact operators'' is raised and sufficient conditions are given for such a calculus. These conditions involve a notion of ``slow oscillation at infinity''.