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.     

Quantum theory of Ur-objects as a theory of information

The quantum theory of ur-objects proposed by C. F. von Weizsäcker has to be interpreted as a quantum theory of information. Ur-objects, or urs, are thought to be the simplest objects in quantum theory. Thus an ur is represented by a two-dimensional Hilbert space with the universal symmetry groupSU(2), and can only be characterized asone bit of potential information. In this sense it is not a spatial but aninformation atom. The physical structure of the ur theory is reviewed, and the philosophical consequences of its interpretation as an information theory are demonstrated by means of some important concepts of physics such as time, space, entropy, energy, and matter, which in ur theory appear to be directly connected with information as the fundamental substance. This hopefully will help to provide a new understanding of the concept of information.     

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.     

Quantum theory: The classical theory of nonlinear electromagnetics

This paper combines a classical electrodynamic base, adaptive electrons, and reactive radiation reaction energy effects and obtaines atomic stability, the Schrödinger equation, and quantized radiation. Electrons are assigned intrinsic parameter values and modeled as dynamic distributions of charge and current densities, bound together in a soliton-like way, with a form that alters in response to local force fields: not as waves or rigid spheres. The result is a deterministic view of quantum theory. Its postulatory base is replaced with derived results. The statistical interpretation of the wave function is that of standard quantum mechanics. When combined with classical electrodynamics, the theory completely describes quantum radiation.     

Quantum theory of light propagation I. General theory

We present a particular approach to quantum theory of light propagation in nonlinear medium using space and time dependent modal operators. Spatial and temporal evolutions of this space and time dependent modal operators are given by the Heisenberg-like equation involving the momentum operator and Heisenberg equation, respectively, which can be justified from point of view of quantum electrodynamics. This useful concept can be applied to an arbitrary nonlinear interaction.The author would like to express his sincere thanks to Professor J. Peina for advice, comments and stimulating discussions.This work was partially supported by the grant PV202/1994 of Czech Ministry of Education and by an internal grant of the Palacký University.     

A nonperturbative stability theory of quantum field theory models

A nonperturbative method of analysis of the stability problem of quantum field theory models is proposed. The method consists in the systematic analysis of the functional dependence on boson field B of the effective boson Lagrangian S^eff(B) consisting of the fermion term S_l^F(B), constraint term S_l^FP(B) and the boson self-interaction term S_l(B). A new heat kernel representation for S_l^F(B) is derived in which counterterms are calculated in the explicit functional form by means of the analytic renormalization method. Using these results the instabillity of Yukawa₄, four-Fermi₄, and the massive Gürsey models is demonstrated.     

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.     

Kaluza-Klein theory from the viewpoint of gauge theory of gravity

We consider Kaluza-Klein theory based on the fiber bundle. We obtain the modified Kaluza-Klein metric as an invariant line element of a bundle. Its reduced action includes a higher derivative action in gravitation as well as a term linear inR.     

Conformal field theory and the symmetries of string field theory

The two-dimensional conformal field theory representation of Witten's bosonic string field theory is discussed. The basic overlap equations, K_n symmetry and BRST invariance are proved directly, without the usual expansion in oscillators. The conformal field theory approach naturally provides local overlap identities which (when integrated over half the string) can be used to verify properties of the cubic action. In particular, a recently proposed diffeomorphism invariance is shown to be free of anomalies. Finally, a new class of symmetries, including generalizations of the K_n symmetries which are local in spacetime, are presented.     

Kinetic theory of classical liquids. I. Basic theory

A somewhat new approach to a kinetic theory of classical liquids is presented, and it is used to calculate the dynamical structure factor S(qω). It gives correctly the zeroth, second, and fourth frequency moments of S(qω), and it goes correctly over to the free particle value for large q. For small q and ω it goes over to proper hydrodynamics, including the coupling to heat diffusion. Results of numerical calculations on liquid argon are presented and they show very good agreement with available neutron scattering and molecular dynamics data.     

Scattering theory in the presence of a soliton asymptotic theory

We present evidence for the following conjecture: when quantized, the magnetic monopole soliton solutions constructed by 't Hooft and Polyakov, as modified by Prasad, Sommerfield and Bogomolny, form a gauge triplet with the photon, corresponding to a Lagrangian similar to the original Georgi-Glashow one, but with magnetic replacing electric charge.     

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.