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The Feynman path integral representation for the weak solution of the Schrödinger equation with an inverse quartic oscillator potential is given in terms of a well defined infinite dimensional oscillatory integral. An analytically continued Wiener integral representation for the solution is provided and an explicit description of the quantum dynamics associated with a nonessentially self-adjoint Hamiltonian is given. [ABSTRACT FROM AUTHOR]

A rigorous mathematical formulation of the "phase space Feynman path integral" is given in a general setting. This is then applied to yield a representation of solutions of the Schrödinger equation with potential depending both on the position and momentum variables. [ABSTRACT FROM AUTHOR]

A reference frame F is described by the element g of the Poincaré group P which connects F with a given fixed frame F[sub 0]. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have to be considered as quantum observables. However, these observables are not compatible and some of them, namely the coordinates of the origin of F, cannot be represented by self-adjoint operators. Both these difficulties can be overcome by considering a positive-operator-valued measure on P, covariant with respect to the left translations of the group, namely a covariance system. We develop a construction procedure for this kind of mathematical structure. The formalism is also used to discuss the quantum observables measured with respect to a quantum reference frame. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]