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Information-theoretic derivations of the formalism of quantum theory have recently attracted much attention. We analyze the axioms underlying a few such derivations and propose a conceptual framework in which, by combining several approaches, one can retrieve more of the conventional quantum formalism.

The study provided research and experimental verification of the hypothetic-deductive scheme for teaching the theory of quantum physics to secondary school students. The study highlighted the technologies and didactic tools, which help to boost the effectiveness of teaching physics to students and develop their critical thinking. It was found that the hypothetic-deductive scheme is based on the concept of critical rationalism and it has such stages: problem-hypotheses-rational criticism-choice of hypothesis-rational criticism of the new theory-new problem. The study described the stages of its implementation for teaching students the basics of quantum physics. To prove the effectiveness of the suggested scheme, the study carried out a comparative experiment in which 479 students took part (there were 241 students in experimental classes and 238 students in control classes). The statistical procession and interpretation of the experiment results were carried out with Pearson’s Chi-squared test. After the experiment, the quality of learning achievements that corresponds to the sufficient and high levels is 62.87% in the experimental classes, whereas in the control classes this figure is 52.48%. In further prospect, researchers plan to check the effectiveness of the suggested scheme to study other theories, which are studied in secondary school.

Recently A. Zamolodchikov obtained a series of identities for the expectation values of the composite operator T\bar{T} constructed from the components of the energy-momentum tensor in two-dimensional quantum field theory. We show that if the theory is integrable the addition of a requirement of factorization at high energies can lead to the exact determination of the generic matrix element of this operator on the asymptotic states. The construction is performed explicitly in the Lee-Yang model.

We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe Ansatz model can be regarded as a suitable non-relativistic limit of the S-matrix of a field theory, and when there is a well-defined mapping between the Hilbert spaces and operators of the two theories. This correspondence provides an efficient method to compute matrix elements of Bethe Ansatz integrable models, overpassing the technical difficulties of their direct determination. We analyze this correspondence for the simplest example in which it occurs, i.e. the Quantum Non-Linear Schrodinger and the Sinh-Gordon models.

The subject of the first section-lecture is concerned with the strength and the weakness of the perturbation theory (PT) approach, that is expansion in powers of a small parameter $\alpha$, in Quantum Theory. We start with outlining a general troublesome feature of the main quantum theory instrument, the perturbation expansion method. The striking issue is that perturbation series in powers of $\alpha \ll 1$ is not a convergent series. The formal reason is an essential singularity of quantum amplitude (matrix element) $C(\alpha)$ at the origin $\alpha=0$. In many physically important cases one needs some alternative means of theoretical analysis. In particular, this refers to perturbative QCD (pQCD) in the low-energy domain. In the second section-lecture, we discuss the approach of Analytic Perturbation Theory (APT). We start with a short historic preamble and then discuss how combining the Dispersion Relation with the Renormalization Group (RG) techniques yields the APT with \myMath{\displaystyle e^{-1/\alpha}} nonanalyticity. Next we consider the results of APT applications to low-energy QCD processes and show that in this approach the fourth-loop contributions, which appear to be on the asymptotic border in the pQCD approach, are of the order of a few per mil. Then we note that using the RG in QCD dictates the need to use the Fractional APT (FAPT) and describe its basic ingredients. As an example of the FAPT application in QCD we consider the pion form factor $F_\pi(Q^2)$ calculation. At the end, we discuss the resummation of nonpower series in {(F)APT} with application to the estimation of the Higgs-boson-decay width $\Gamma_{H\to\bar{b}b}(m_H^2)$.

Quantum theory is one of the most successful theories in physics. Because of its abstract, mathematical, and counter-intuitive nature, many students have problems learning the theory, just as teachers experience difficulty in teaching it. Pedagogical research on quantum theory has mainly focused on cognitive issues. However, affective issues about student learning are just as important as cognitive issues. The purpose of this study was to investigate pre-service physics teachers' motivation towards learning quantum theory by examining motivational constructs such as expectancies, values, ability beliefs, and goals. The participants (n = 6) of this case study were fourth-year pre-service physics teachers at a state university in Turkey. Through semi-structured interviews, the participants were asked seventeen questions that focused on motivational constructs. Analysis of the qualitative data indicated that the instructor, nature of the content, and previous performance were three motivational elements that originated in the context of the quantum mechanics course. Furthermore, these context-dependent elements interacted with the other elements of motivational constructs in both direct and indirect ways. Because unsuccessful learning situations are explained by low motivation, context-dependent affective elements and their interactions should be considered in the teaching and learning of quantum theory.

Quantum theory is one of the most successful theories in physics. Because of its abstract, mathematical, and counter-intuitive nature, many students have problems learning the theory, just as teachers experience difficulty in teaching it. Pedagogical research on quantum theory has mainly focused on cognitive issues. However, affective issues about student learning are just as important as cognitive issues. The purpose of this study was to investigate pre-service physics teachers' motivation towards learning quantum theory by examining motivational constructs such as expectancies, values, ability beliefs, and goals. The participants (n = 6) of this case study were fourth-year pre-service physics teachers at a state university in Turkey. Through semi-structured interviews, the participants were asked seventeen questions that focused on motivational constructs. Analysis of the qualitative data indicated that the instructor, nature of the content, and previous performance were three motivational elements that originated in the context of the quantum mechanics course. Furthermore, these context-dependent elements interacted with the other elements of motivational constructs in both direct and indirect ways. Because unsuccessful learning situations are explained by low motivation, context-dependent affective elements and their interactions should be considered in the teaching and learning of quantum theory.

The descripition of in a Hermitian setting seemingly nonlocal and nonperturbative phenomena like confinement or superconductivity is most conveniently performed by generalizing quantum theory to a non-Hermitian regime where these phenomena appear perturbative and local. The short presentation provides a clue how this can be done on the basis of Lorentz covariance while preserving the analyticity of the theory. After deriving with the help of Lorentz covariance a quantum scalar product without making any use of metric or complex conjugation we sketch how the formalism of scattering theory can be extended analytically to a non-Hermitian regime.

Niels Bohr wrote: "There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we can say about Nature." In an analogous way, von Weizsaecker suggested that the notion of the elementary alternative, the "Ur", should play a pivotal role when constructing physics. Both approaches suggest that the concept of information should play an essential role in the foundations of any scientific description of Nature. We show that if, in our description of Nature, we use one definite proposition per elementary constituent of Nature, some of the essential characteristics of quantum physics, such as the irreducible randomness of individual events, quantum complementary and quantum entanglement, arise in a natural way. Then quantum physics is an elementary theory of information.

Niels Bohr wrote: "There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we can say about Nature." In an analogous way, von Weizsaecker suggested that the notion of the elementary alternative, the "Ur", should play a pivotal role when constructing physics. Both approaches suggest that the concept of information should play an essential role in the foundations of any scientific description of Nature. We show that if, in our description of Nature, we use one definite proposition per elementary constituent of Nature, some of the essential characteristics of quantum physics, such as the irreducible randomness of individual events, quantum complementary and quantum entanglement, arise in a natural way. Then quantum physics is an elementary theory of information.

FORTRAN 4 subroutines for coupling coefficients and matrix elements in quantum mechanical theory of angular momentum

xii, 269 p. 24 cm

xii, 269 p. 24 cm