Showing papers on "Quantum geometry published in 1982"

The unpredictability of quantum gravity

Abstract: Quantum gravity seems to introduce a new level of unpredictability into physics over and above that normally associated with the uncertainty principle. This is because the metric of spacetime can fluctuate from being globally hyperbolic. In other words, the evolution is not completely determined by Cauchy data at past or future infinity. I present a number of axioms that the asymptotic Green functions should obey in any reasonable theory of quantum gravity. These axioms are the same as for ordinary quantum field theory in flat spacetime, except that one axiom, that of asymptotic completeness, is omitted. This allows pure quantum states to decay into mixed states. Calculations with simple models of topologically non-trivial spacetime indicate that such loss of quantum coherence will occur but that the effect will be very small except for fundamental scalar particles, if any such exist.

Quantum theory of polarization in liquids: Exact solution of the mean spherical and related approximations

Abstract: The mean spherical approximation and related integral equations theories (such as the linearized hypernetted chain equation) are studied for a fluid composed of atoms or spherical molecules with quantum mechanical fluctuating internal dipoles. We derive the solutions of these equations for the case in which the intramolecular restoring force for a fluctuating dipole is harmonic (i.e., a quantum Drude model). In the limit of low oscillator frequencies, the solutions reduce to those deduced by Pratt on the basis of classical theory. We discuss the frequency dependence of the fluid renormalizations of atomic polarizabilities, and show that for the zero frequency applications discussed by Pratt, the classical theory is correct. We find, however, that the finite frequency quantum effects play a dominant role for many experimentally relevant properties. Generalizations of the quantum theory to include features such as charge overlap and hyperpolarizabilities are also discussed. The relationship between low orde...

Relativity and quantum mechanics

Abstract: Conditions under which quantum mechanics can be made compatible with the curved space-time of gravitation theories is investigated. A postulate is imposed in the formv=vg wherev is the kinematical Hamilton-Jacobi (geometric optic limit) velocity andvg is the group velocity of the waves. This imposes a severe condition on the possible coordinates in which the Schrodinger form (the coordinate realization) of quantum mechanics can be set up for purposes of calculating observable effects. Some such effects are calculated for a class of theories and are compared with experiments.

Modification of quantum mechanics at short distances

Abstract: To make quantum mechanics a suitable description of short-distance (≲10−13 cm) physics, we introduce a spatial variation of Planck’s constanth. In the new system, the dynamics of a test particle is developed and discussed. As one of the consequences it is shown that the new theory can lead to asymptotic freedom and quark confinement in a simple way.

Geodesics of free particles in QM phase space: Free mass as a quantum effect, reciprocity

Abstract: I t is na tu r a l to inqu i re , h a v i n g set up a mode l of Q ~ in m e t r i z e d p h a s e space, w h a t is t h e role of geodes ics in th i s mode l . Def in i t ion a n d n o t a t i o n s a re as in ref. ( ' ) . T~ is no t s y m m e t r i c in i t s lower indices ; t h e s t a n d a r d def in i t ion , r e l a t ed to para l le l t r a n s p o r t , can st i l l , and wil l be used , as i t is t h e s imples t :

Semiclassical Expanding Discrete Space-Times

Abstract: Given the close ties between general relativity and geometry one might reasonably expect that quantum effects associated with gravitation might also be tied to the geometry of space-time, namely, to some sort of discreteness in space-time itself. In particular we suppose space-time to consist of a discrete lattice of points rather than the usual continuum. Since astronomical evidence seems to suggest that the universe is expanding, we also demand that the lattice is expanding. Some of the implications of such a model are that the proton should presently be stable, and the universe should be closed although the mechanism for closure is quantum mechanical.

Quantum corrections to the thermodynamic properties of a two-dimensional fluid with hard-core potential

Abstract: A simple theory, based on the physical interpretation of the reciprocal of activity, is developed to evaluate the thermodynamic properties of a two-dimensional fluid in the semi-classical limit. The theory is applied to calculate the quantum corrections to the equation of state and excess free energy of two-dimensional fluids, whose molecules interactvia hard-disc and square-well potential. It is found that the quantum effect increases with the increase of density and decrease of temperature.

Some remarks on the small-distance behaviour of quantum gravity

Abstract: We discuss the important role played by dilatation invariance in the study of the small-distance behaviour of quantum gravity. We show that a treatment of inverse operators leads to a simple ultraviolet behaviour of the two- and three-point Green’s functions in substantial agreement with the scale-invariant estimates.