Geometric quantization of the five-dimensional Kepler problemMladenov, Ivailo
doi: 10.1007/BF00733213pmid: N/A
An extension of the Hurwitz transformation to a canonical transformation between phase spaces allows conversion of the five-dimensional Kepler problem into that of a constrained harmonic oscillator problem in eight dimensions. Thus a new regularization of the Kepler problem is established. Then, following Dirac, we quantize the extended phase space, imposing constraint conditions as superselection rules. In that way the interchangeability of the reduction and the quantization procedures is proved.
“Special” states in quantum measurement apparatus: Structural requirements for the recovery of standard probabilitiesSchulman, L.
doi: 10.1007/BF00733216pmid: N/A
In a recently proposed quantum measurement theory the definiteness of quantum measurements is achieved by means of “special” states. The recovery of the usual quantum probabilities is related to the relative abundance of particular classes of “special” states. In the present article we consider two-state discrimination, and model the apparatus modes that could provide the “special” states. We find that there are structural features which, if generally present in apparatus, will provide universal recovery of standard probabilities. These structural features relate to the distribution of certain Hamiltonian matrix elements or interaction times. In particular, those quantities must be asymptotically (x → ∞) distributed according to the Cauchy law, Ca(x)=a/π(x
2
+a
2
).
A quantum time machineVaidman, Lev
doi: 10.1007/BF00733217pmid: N/A
A novel description of quantum systems is employed for constructing a “time machine” capable of shifting in time the wave function of a quantum system. This device uses gravitational time dilations and a peculiar quantum interference effect due to preselection and postselection. In most trials this time machine fails to operate but when it does succeed it accomplishes tasks which no other machine can.
The asymmetry of radiation: Reinterpreting the Wheeler-Feynman argumentPrice, Huw
doi: 10.1007/BF00733218pmid: N/A
This paper suggests a novel reinterpretation of the mathematical core of Wheeler-Feynman absorber theory, and hence a new route to the conclusion that the temporal asymmetry of classical electromagnetic radiation has the same origin as that of thermodynamics. The argument begins (Sec. 2) with a careful analysis of what the apparent asymmetry of radiation actually involves. Two major flaws in the standard version of the Wheeler-Feynman treatment of radiative asymmetry are then identified (Secs. 4–5), and the proposed reinterpretation is described (Sec. 6). This avoids the two flaws previously mentioned, and also the problematic dependence of radiation on cosmological structure.
Self-generating Universe and many worldsRosen, Joe
doi: 10.1007/BF00733219pmid: N/A
A novel, compact conceptual framework for the origin of the Universe is proposed, whereby the Universe is identified with a baby universe born ofitself. This picture indicates an intimate meshing of gravitation, space-time, and the quantum and offers a framework for the many-worlds interpretation of quantum theory.
Linear and nonlinear Schrödinger equationsAdomian, G.; Rach, R.
doi: 10.1007/BF00733220pmid: N/A
The Schrödinger equation for a point particle in a quartic potential and a nonlinear Schrödinger equation are solved by the decomposition method yielding convergent series for the solutions which converge quite rapidly in physical problems involving bounded inputs and analytic functions. Several examples are given to demonstrate use of the method.