Principles of Quantum General Relativity

Abstract

finishing his Ph.D. there in 1964. After spending an additional year in Princeton as research associate, he became Postdoctoral Fellow at the Theoretical Physics Institute in Edmonton, Canada. In 1967 he joined the University of Toronto, where he became Professor in 1975. He has written numerous articles on the mathematical foundations and methods in quantum mechanics, quantum field theory in flat and curved spacetime, and quantum gravity. He has published three monographs dealing with various aspects of this research:

Stochastically and Intrinsically Extended Non-relativistic Quantum Particles

“…The advantage of the above construction appears in the relativistic and general relativistic regimes where the stochastic extension cures many of their fundamental inconsistencies [15] and [16]. In fact, our conception of the intrinsic extension enables the consideration of confined quantum modes which cannot be observed without the extended particle and may be applicable to hadrons composed of quarks which may play the role of internal quantum modes.…”

“…The measuring apparatus, which is described byχ ξ q (x), acquires a quantum character by interpreting the functionξ as a proper wave function of a stochastically extended test particle playing the role of a (real or imperfect) microdetector which is at stochastic rest at the origin of a classical system of reference. The state |ξ q,p is then interpreted as proper state vector of such a microdetector localized at mean stochastic position q with mean momentum p. The family {|ξ q,p ; (q, p) ∈ R 6 } corresponds to an array of microdetectors and constitutes a quantum frame [14][15][16]. The above POV measures are then associated to these microdetectors and describe this type of measurement.…”

“…We shall not go into these technical details but mention the physical interpretation of the Dirac "bra" space as that of measuring apparatuses states [4] and that ξ q,p;y | is an operator acting [16] on and not on H ξ . Since this latter remark concerns only the internal part of the present work, it is meaningful to interpret |ξ q,p;y as the proper state vector of a microdetector with internal pointlike degrees of freedom.…”

“…The external mode evolves in the external physical space-time and the internal mode is localized in an internal space-time, the points of which are arguments of the physical wave u. Let us call these particles intrinsically or functionally extended as opposed to those which are stochastically extended and introduced in a recent (geometro)-stochastic quantum theory [14][15][16]. The stochastic theory [14] stemmed from group theoretic considerations [2,3] linked with measurement theoretic ones [13], and is based on an operational principle asserting that a physical theory should take into account the experimental circumstances surrounding the observation process.…”

“…The element ξ q,p corresponds to a state of the same particle with stochastic position (q,χ q ) and momentum (p,χ p ). The whole family constitutes a quantum frame lifting the status of space-time to a quantum level in a fiber bundle geometric structure capable of bearing a consistent formulation of quantum gravity [15,16].…”