The Higgs field as an inflaton

The Higgs field of the pure Standard Model can lead to the inflationary expansion of the early Universe if it is non-minimally coupled to gravity. The model predicts Cosmic Microwave Background (CMB) parameters in perfect agreement with the current observations and has implications for the Higgs boson mass. We review the model, its predictions, problems arising with its quantization and some closely related models.Comment: 21 pages, 4 figures. Journal version -- several clarifications and improved list of reference

Can We Believe in a Purely Unitary Quantum Dynamics?

It is pointed out that the question of a purely unitary quantum dynamics amounts to the question if von Neumann entropy of a dynamically closed quantum system is preserved in evolution.Comment: 2 page

Polynomial Approach to Explicit Formulae for Generalized Binomial Coefficients

We extend the polynomial approach to hook length formula proposed in a recent joint paper with K\'arolyi, Nagy and Volkov to several other problems of the same type, including number of paths formula in the Young graph of strict partitions

Indeterminate Probabilities and the Weak Quantum Law of Large Numbers

The quantum probabilistic convergence in measurement, distinct from mathematical convergence, is derived for indeterminate probabilities from the weak quantum law of large numbers. This is presented in three theorems. The first establishes the necessary bridge between ensemble theory and experiment. The second analyzes the most important theoretical ensemble entity: the eigen-projector of the relative frequency operator. Its physical meaning is the experimental relative frequency. The third theorem formulates the quantum probabilistic convergence, which is the final result of this investigation.Comment: 19 pages, no figure

On Elementary Theories of GLP-Algebras

There is a polymodal provability logic $GLP$. We consider generalizations of this logic: the logics $GLP_{\alpha}$, where $\alpha$ ranges over linear ordered sets and play the role of the set of indexes of modalities. We consider the varieties of modal algebras that corresponds to the polymodal logics. We prove that the elementary theories of the free $\emptyset$-generated $GLP_{n}$ -algebras are decidable for all finite ordinals $n$.Comment: 39 page

Derivation of quantum probability from measurement

To begin with, it is pointed out that the form of the quantum probabil- ity formula originates in the very initial state of the object system as seen when the state is expanded with the eigen-projectors of the measured ob- servable. Making use of the probability reproducibility condition, which is a key concept in unitary measurement theory, one obtains the relevant coher- ent distribution of the complete-measurement results in the final unitary- measurement state in agreement with the mentioned probability formula. Treating the transition from the final unitary, or premeasurement, state, where all possible results are present, to one complete-measurement result sketchily in the usual way, the well-known probability formula is derived. In conclusion it is pointed out that the entire argument is only formal unless one makes it physical assuming that the quantum probability law is valid in the extreme case of probability-one (certain) events (projectors).Comment: 10 fage

Vanishing theorems and universal coverings of projective varieties

This article contains a new argument which proves vanishing of the first cohomology for negative vector bundles over a complex projective variety if the rank of the bundle is smaller than the dimension of the base. Similar argument is applied to the construction of holomorphic functions on the universal covering of the complex projective variety .Comment: 6 pages, AMSTe

Distinguishing quantum measurements of observables in terms of state transformers

The modern framework of state transformers, i. e., the first Kraus representation of quantum measurement, is introduced and related both to the known textbook concepts and to measurement-interaction evolution (the second Kraus representation). In this framework the known kinds of measurements of ordinary (as distinct from generalized) observables are distinguished by necessary and sufficient conditions. Thus, repeatable,nonrepeatable, and ideal measurements are characterized both algebraically and geometrically in terms of polar factors of state transformers.Comment: 13 pages, Latex2e. Written for the Am. J. Phys.; after three resubmissions, when both referees were satisfied,it was rejected. It is put on the web to do justice to the great efforts of the referees and the autho

Critical Assessment of Wave-Particle Complementarity via Derivation from Quantum Mechanics

After introducing sketchily Bohr's wave-particle complementarity principle in his own words, a derivation of an extended form of the principle from standard quantum mechanics is performed. Reality-evaluation of each step is given. The derived theory is applied to simple examples and the extended entities are illustrated in a thought experiment. Assessment of the approach of Bohr and of this article is taken up again with a rather negative conclusion as far as reflecting reality is concerned. The paper ends with selected incisive opinions on Bohr's dogmatic attitude and with some comments by the present author.Comment: 44 pages, one figur

Bipartite Entanglement Review of Subsystem-Basis Expansions and Correlation Operators in It

The present review presents the authors previous results on the topic from the title in a new light. Most of the previous results were obtained using the techniques of antilinear Hilbert-Schmidt mappings of one Hilbert pace into another, which is unknown and unused in the literature. This, naturally, diminished the impact of the results. In this article the results are derived anew with standard techniques. The topics listed at the end of the Introduction, are expounded in 9 theorems, 5 propositions etc. Partial scalar product and partial trace methods are used throughout. Further relevant research articles that are not reproduced in this review, are sketched in the Concluding remarks.Comment: 37 pages, no figues or table