Dirac versus Reduced Quantization of the Poincar\'{e} Symmetry in Scalar Electrodynamics

The generators of the Poincar\'{e} symmetry of scalar electrodynamics are quantized in the functional Schr\"{o}dinger representation. We show that the factor ordering which corresponds to (minimal) Dirac quantization preserves the Poincar\'{e} algebra, but (minimal) reduced quantization does not. In the latter, there is a van Hove anomaly in the boost-boost commutator, which we evaluate explicitly to lowest order in a heat kernel expansion using zeta function regularization. We illuminate the crucial role played by the gauge orbit volume element in the analysis. Our results demonstrate that preservation of extra symmetries at the quantum level is sometimes a useful criterion to select between inequivalent, but nevertheless self-consistent, quantization schemes.Comment: 24 page

Determination of Sulfur and Iron Valence by Microprobe

SKα, SKβ and FeKβ valence related wavelength changes are large enough to be measured with microprobe spectrometers. The relative difference between S2- and S6+ is measured as 1.27 eV for the SKα line and 1.66 eV for the SKβ line. This SKα and SKβ peak shift is function of the valence. Accurate microprobe measurement of the peak shift allows the determination of the sulfur valence in a microarea. The relative difference between Fe2+ and Fe3+ for the FeKβ line is 0.94 eV. Considering the achieved accuracy of measurements, this peak can only be used for an approximate determination of the iron valence in a microarea

Nonlinear quantum gravity on the constant mean curvature foliation

A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum constraints in canonical general relativity. It is, however, argued that the Hamiltonian constraint may be advantageously retained in the reduced classical system to be quantized. This permits the Hamiltonian constraint equation to be consistently turned into an expectation value equation on quantization that describes the scale factor on each spatial hypersurface characterized by a constant mean exterior curvature. This expectation value equation augments the dynamical quantum evolution of the unconstrained conformal three-geometry with a transverse traceless momentum tensor density. The resulting quantum theory is inherently nonlinear. Nonetheless, it is unitary and free from a nonlocal and implicit description of the Hamiltonian operator. Finally, by imposing additional homogeneity symmetries, a broad class of Bianchi cosmological models are analyzed as nonlinear quantum minisuperspaces in the context of the proposed theory.Comment: 14 pages. Classical and Quantum Gravity (To appear

Semiclassical States in Quantum Cosmology: Bianchi I Coherent States

We study coherent states for Bianchi type I cosmological models, as examples of semiclassical states for time-reparametrization invariant systems. This simple model allows us to study explicitly the relationship between exact semiclassical states in the kinematical Hilbert space and corresponding ones in the physical Hilbert space, which we construct here using the group averaging technique. We find that it is possible to construct good semiclassical physical states by such a procedure in this model; we also discuss the sense in which the original kinematical states may be a good approximation to the physical ones, and the situations in which this is the case. In addition, these models can be deparametrized in a natural way, and we study the effect of time evolution on an "intrinsic" coherent state in the reduced phase space, in order to estimate the time for this state to spread significantly.Comment: 21 pages, 1 figure; Version to be published in CQG; The discussion has been slightly reorganized, two references added, and some typos correcte

An action principle for the quantization of parametric theories and nonlinear quantum cosmology

By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to nonlinear quantum mechanics. This generalization enables a unitary description of the quantum evolution for a broad class of constrained Hamiltonian systems with a nonlinear kinematic structure. In particular, the new theory is applicable to the quantization of cosmological models where a chosen gravitational degree of freedom acts as geometric time. This is demonstrated explicitly using three cosmological models: the Friedmann universe with a massless scalar field and Bianchi type I and IX models. Based on these investigations, the prospect of further developing the proposed quantization scheme in the context of quantum gravity is discussed.Comment: 14 page

Призначення та проведення експертиз: проблеми законодавства і практики

It has been noted that the problems of procedural guaranteeing of the rights of victims, suspects (accused) in terms of reforming the criminal procedural legislation are relevant during the appointment and holding of the examination and require further research. The aim of this study is to analyze the current criminal procedural legislation on the appointment and conduction of examination and to develop propositions for its improvement. The authors of the article have analyzed the existing procedural legislation on the appointment and conduction of examination; have defined the problematic issues of procedural guaranteeing of the rights of victims, suspects (accused) in the appointment and conduction of examination; and have offered the ways to solve them; have substantiated the need for legislative regulation of additional and re-examination of explosive and technical examination and have provided forensic recommendations to eliminate these problems. Based on the conducted research, the authors have provided the following suggestions and recommendations: 1) to enshrine the right of the prosecution and defense parties in the Art. 243 of the Criminal Procedural Code of Ukraine (CPC) to independently appoint an examination; 2) to declare it appropriate to supplement Section 3 of the CPC with the Art. 56-1 “Rights of the victim in the appointment and conduction of examination”, which should enshrine the relevant rights; 3) to declare it expedient to supplement Section 20 of the CPC of Ukraine with the Art. 242-1, which should determine the rights of the suspect (accused) in the appointment and conduction of examination; 4) to standardize the procedure for the appointment of additional expertise in paragraph 11 of the Art. 101 of the CPC; 5) to standardize the procedure for the appointment of re-examination in paragraph 12 of the Art. 101 of the CPC; 6) to recommend investigators and judges to determine the expert’s questions depending on the objects of expert examination; 7) to improve the stage of experimental testing of objects in carrying out explosive examination.Розглянуто проблемні питання призначення та проведення експертизи, обґрунтовано необхідність унормування процесуальної процедури призначення повторної та додаткової експертиз. Проаналізовано практику призначення та проведення вибухотехнічних експертиз, надано рекомендації щодо підготовки експертних об’єктів

Unification of the conditional probability and semiclassical interpretations for the problem of time in quantum theory

We show that the time-dependent Schr\"odinger equation (TDSE) is the phenomenological dynamical law of evolution unraveled in the classical limit from a timeless formulation in terms of probability amplitudes conditioned by the values of suitably chosen internal clock variables, thereby unifying the conditional probability interpretation (CPI) and the semiclassical approach for the problem of time in quantum theory. Our formalism stems from an exact factorization of the Hamiltonian eigenfunction of the clock plus system composite, where the clock and system factors play the role of marginal and conditional probability amplitudes, respectively. Application of the Variation Principle leads to a pair of exact coupled pseudoeigenvalue equations for these amplitudes, whose solution requires an iterative self-consistent procedure. The equation for the conditional amplitude constitutes an effective "equation of motion" for the quantum state of the system with respect to the clock variables. These coupled equations also provide a convenient framework for treating the back-reaction of the system on the clock at various levels of approximation. At the lowest level, when the WKB approximation for the marginal amplitude is appropriate, in the classical limit of the clock variables the TDSE for the system emerges as a matter of course from the conditional equation. In this connection, we provide a discussion of the characteristics required by physical systems to serve as good clocks. This development is seen to be advantageous over the original CPI and semiclassical approach since it maintains the essence of the conventional formalism of quantum mechanics, admits a transparent interpretation, avoids the use of the Born-Oppenheimer approximation, and resolves various objections raised about them.Comment: 10 pages. Typographical errors correcte

Time in quantum gravity

Quantum gravity--the marriage of quantum physics with general relativity--is bound to contain deep and important lessons for the nature of physical time. Some of these lessons shall be canvassed here, particularly as they arise from quantum general relativity and string theory and related approaches. Of particular interest is the question of which of the intuitive aspects of time will turn out to be fundamental, and which 'emergent' in some sense.Comment: 18 pages, 1 figur