ua nt - p h / 97 10 02 9 v 1 8 O ct 1 99 7 Coherent States in Action ∗

Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the variables involved that is manifestly inconsistent. On the other hand, a phase space path integral based on coherent states entails variables that exhibit a self-consistent physical meaning. 1 Conventional phase space path integrals There is considerable appeal in the formal phase space path integral 〈q| e |q〉 = N ∫ e ∫ [pq̇ − h(p, q)] dtDpDq (1) which yields the propagator in the q-representation [1]. In this relation the integration is over all q-paths q(t), t ≤ t ≤ t ≡ t+T , T > 0, subject to the boundary conditions that q(t) = q and q(t) = q, as well as all p-paths p(t) for t ≤ t ≤ t. It follows from this formula that the meaning of q(t) is the same as the meaning of q(t), namely, as the sharp eigenvalue of the position operator Q, where Q|q〉 = q|q〉. ∗Based on a contribution to the International Conference on Frontiers in Quantum Physics, Kuala Lumpur, Malaysia, July, 1997.