Showing papers on "Quantum geometry published in 1977"
TL;DR: In this paper, it was proved that for two-particle phenomena the P(ϕ)2 quantum field theories with speed of lightc converge to non-relativistic quantum mechanics with a δ function potential in the limitc→∞.
Abstract: It is proved that for two-particle phenomena theP(ϕ)2 quantum field theories with speed of lightc converge to non-relativistic quantum mechanics with a δ function potential in the limitc→∞.
25 citations
TL;DR: In this article, the authors carried out the spectral analysis of the n-band Hill equation by examining the external problem for a class of entire functions with least derivation from zero, and characterized the spectrum in terms of hyperellyctic integrals and the geometry of admissible points (band edges).
Abstract: We carry out the spectral analysis of the n‐band Hill equation by examining the external problem for a class of entire functions with least derivation from zero. The spectrum is characterized in terms of hyperellyctic integrals and the geometry of admissible points (band edges).
24 citations
TL;DR: In this article, the authors derived the functional measure for quantum gravity by reducing to independent degrees of freedom in the light-cone gauge, where all eight dependent components of the metric may be explicitly functionally eliminated, leaving only two unconstrained variables.
Abstract: We derive the functional measure for quantum gravity by reducing to independent degrees of freedom in the light-cone gauge. We use the recently developed functional techniques devised to handle field theories with second-class constraints in order to analyze quantum gravity quantized along null planes, where it has been shown that all eight dependent components of the metric may be explicitly functionally eliminated, leaving only two unconstrained variables. Using our result, we confirm the result of Fradkin and Vilkovisky for the functional measure for quantum gravity, though we disagree with several other authors who have different measures.
12 citations
9 citations
TL;DR: In this paper, the authors consider a specific example of this, the gravitational collapse of a spherical dust ball, and discuss the behaviour of a physical system which is initially in the classical domain (S ≫ ħ) but whose later development may well take it into the region of quantum uncertainty.
Abstract: THE ratio of the action S to ħ (Planck's constant/2π) determines whether the physical system in question is to be treated classically or quantum mechanically. In the area of classical physics the ratio S/ħ is large compared with unity, and the governing equations are given by δS = 0. Quantum mechanics begins to be important when S ≲ ħ, and the definitive approach of classical physics is replaced by quantum uncertainty. We discuss here the behaviour of a physical system which is initially in the classical domain (S ≫ ħ) but whose later development may well take it into the region of quantum uncertainty. We consider a specific example of this—the gravitational collapse of a spherical dust ball. While classically such a dust ball ends up in a space–time singularity, the corresponding quantum mechanical result suggests a range of final states some of which are non-singular.
8 citations
7 citations
TL;DR: In this paper, a causal explanation of the quantum effect at a known potential energy is provided, based on the topology of flows on a cusp catastrophe obtained by the minimization of a potential function.
Abstract: The dynamics underlying quantum theory for macroscopic physics is based on the topology of flows on a cusp catastrophe obtained by the minimization of a potential function. By this relation at a known potential energy, a causal explanation of the quantum effect is provided.
5 citations
TL;DR: In this paper, the authors show to what extent observable differences exist also betwecn these models and QM for the singlet state of QM, J = M = 0, for a system composed of two spin89 particles.
Abstract: Interest in the foundations of quantum mechanics (QM) has considerably grown in recent years, mainly in the direction of finding clear experimental tests of the states of QM for composite systems. This aspect of the problem started essentially with the results of Bell (1) and had a further development with the recent introduction of new (~ sensitivc)> observables (2,3). A rccent paper (4) has more clearly pointed out that the different (~local ~) models, that have been proposed as possible alternative to the quantum mechanical states (the name of second-kind states has become usual), lead to observable different results and has proposed a still more proper experimental test in the case corresponding to the singlet state of QM. On the same line, we have tried to complete the state of the art by an examination of the <(nonlocal ~) theoretical descriptions or models which have been proposed up to now. In the present paper we show to what extent observable differences exist also betwecn these models and QM. We shall always limit ourselves in the following to the singlet state of QM, J = M = 0, for a system composed of two spin89 particles
2 citations
TL;DR: In this article, the transition from classical observables to quantum (operator) observables in quantum mechanics is discussed, and it is shown that even in simple cases, the method of self-adjoint extensions of formal differential expressions for defining physical observables as operators is not equivalent to the procedure of forming operator functions corresponding to these observables.
Abstract: The procedure of transition from classical observables to quantum (operator) observables in quantum mechanics is discussed. By an example it is shown that, even in simple cases, the method of self-adjoint extensions of formal differential expressions for defining physical observables as operators is not equivalent to the procedure of forming operator functions corresponding to these observables. This inequivalence is not a formal one but has physical consequences connected with the compatibility of observables.
1 citations