Quantum mechanics of measurements distributed in time. A pathintegral formulation
Abstract
Consider measurements that provide information about the position of a nonrelativistic, onedimensional, quantummechanical system. An outstanding question in quantum mechanics asks how to analyze measurements distributed in timei.e., measurements that provide information about the position at more than one time. I develop a formulation in terms of a path integral and show that it applies to a large class of measurements distributed in time. For measurements in this class, the pathintegral formulation provides the joint statistics of a sequence of measurements. Specialized to the case of instantaneous position measurements, the pathintegral formulation breaks down into the conventional machinery of nonrelativistic quantum mechanics: a system quantum state evolving in time according to two rulesbetween measurements, unitary evolution, and at each measurement, ``collapse of the wave function'' (``reduction of the state vector''). For measurements distributed in time, the pathintegral formulation has no similar decomposition; the notion of a system quantum state evolving in time has no place.
 Publication:

Physical Review D
 Pub Date:
 March 1986
 DOI:
 10.1103/PhysRevD.33.1643
 Bibcode:
 1986PhRvD..33.1643C
 Keywords:

 03.65.Bz