Scalar-tensor theory and propagating torsion theory

We prove that scalar conformal transformations can convert the variational principle of the propagating torsion theory into the variational principle of general scalar-tensor theory, and show that scalar-tensor theory is conformally equivalent to propagating torsion theory.     

Direct measurement theory, Ito-Stratonovich theory, and weakly dissipative Kolmogorov-Arnold-Moser theory

The direct measurement theory studies linear functionals as applied to the problems of quantum mechanics in addition to considering quadratic functionals on the space of wave functions, well established since the beginning of the 20th century. The theory is based on the time invariance principle of an appropriate space for linear functionals. In this case, it turns out that the second-order Schr?dinger equation is factorized: factors “respect” the effect of one of two groups, i.e., the group of inertial gas motion or the nonlinear group. In the weakly dissipative Kolmogorov-Arnold-Moser (KAM) theory, the former group is of extraordinary interest in connection with the formation of caustic curves which, in turn, cause the appearance of advanced and delayed potentials, which makes it possible to estimate anew the ideas of Ito-Stratonovich in the theory of stochastic processes.     

Quantum theory as a universal physical theory

The problem of setting up quantum theory as a universal physical theory is investigated. It is shown that the existing formalism, in either the conventional or the Everett interpretation, must be supplemented by an additional structure, the interpretation basis. This is a preferred ordered orthonormal basis in the space of states. Quantum measurement theory is developed as a tool for determining the interpretation basis. The augmented quantum theory is discussed.     

Simplicial gauge theory and quantum gauge theory simulation

We propose a general formulation of simplicial lattice gauge theory inspired by the finite element method. Numerical tests of convergence towards continuum results are performed for several SU(2) gauge fields. Additionally, we perform simplicial Monte Carlo quantum gauge field simulations involving measurements of the action as well as differently sized Wilson loops as functions of β.     

Introduction to string theory and conformal field theory

A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.     

Hilbertian quantum theory as the theory of complementarity

It is demonstrated that the notion of complementary physical quantities assumes the possibility of performing ideal first-kind measurements of such quantities. This then leads to an axiomatic reconstruction of the Hilbertian quantum theory based on the complementarity principle and on its connection with the measurement theoretical idealization known as the projection postulate. As the notion of complementary physical quantities does not presuppose the notion of probability, the given axiomatic reconstruction reveals complementarity as an essential reason for the irreducibly probabilistic nature of the quantum theory.     

Quantum decision theory as quantum theory of measurement

We present a general theory of quantum information processing devices, that can be applied to human decision makers, to atomic multimode registers, or to molecular high-spin registers. Our quantum decision theory is a generalization of the quantum theory of measurement, endowed with an action ring, a prospect lattice and a probability operator measure. The algebra of probability operators plays the role of the algebra of local observables. Because of the composite nature of prospects and of the entangling properties of the probability operators, quantum interference terms appear, which make actions noncommutative and the prospect probabilities nonadditive. The theory provides the basis for explaining a variety of paradoxes typical of the application of classical utility theory to real human decision making. The principal advantage of our approach is that it is formulated as a self-consistent mathematical theory, which allows us to explain not just one effect but actually all known paradoxes in human decision making. Being general, the approach can serve as a tool for characterizing quantum information processing by means of atomic, molecular, and condensed-matter systems.     

Quark-gluon transport theory I. The classical theory

A classical relativistic kinetic theory for a plasma with non-Abelian gauge interactions is formulated. After the local equilibrium solutions for the quark distribution function are found, the associated moment equations and their near-equilibrium expansion, leading to a set of relativistic chromohydrodynamical equations for viscous colored fluids, are studied.     

q-transformation theory

We obtain the complete set of states of theq-oscillator in both configuration space and momentum space as well as the transformation between these spaces. The states as well as the matrix elements lie in the SU _q (2) algebra. To obtain transition probabilities, one must take the Woronowicz square.     

Lepton theory

Within the framework of the elementary-particle theory proposed in [1], the electron, muon, and τ-lepton masses are calculated. Khar’kov Physicotechnical Institute, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 29–37, July, 1997.     

Chemisorption theory

The aim of chemisorption theory is to achieve for any adsorbateladsorbent system complete quantum predictions of the equilibrium positions of all the nuclei, the ground-state (electronically adiabatic) potential energy surface, the electronic excitation spectrum, and the response of the system to external probes. We are still a very long way from this goal, but some simplified models can now be explored in depth. Serious quantitative work begins with Toya,^1,2 and my review ends with the work of Appelbaum and Hamann³ These works provide examples of two of the three approaches to chemisorption theory. Toya's is a configuration interaction (CI) approach, using the states of the noninteracting adsorbate/solid system as basis states; Appelbaum and Hamann try to integrate Schrodinger's equation directly. The third approach is the linear combination of atomic orbitals molecular orbital (LCAO-MO) theory, and I begin with it because it is generally familiar in its simpler forms through its widespread use in molecular quantum mechanics. However, I remark at this stage that the direct integration of Schrodinger's equation may be more economical in computer time than the traditional quantum chemistry approach; it is certainly more economical if the nonlocal Hartree-Fock exchange potential is replaced by a local approximation to it.     

Superluminescent-laser theory

A theoretical study is made of the pulse shape of superluminescent lasers based on dye solutions excited by supershort pumping pulses. A relation is obtained between the shape of the luminescence-pulse envelope and the shape of the pumping pulse. The effect of diffraction phenomena due to inhomogeneity of inversion over the amplification-tube cross section is analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 118–125, August, 1978.