The physical meaning of weak values and measurements can be completely understood with Born rule and the general probability theory. It is known that the weak value of an observable \(\hat {A}\) with post-selection 〈F| may be out of the eigenvalue range of \(\hat {A}\). This is because the weak value of \(\hat {A}\) with the post-selection is, in general, not the expectation...

The original version of this article unfortunately contained a mistake. The second author B. D. Indu is not connected to affiliation 2. Instead, B. D. Indu is connected to affiliation 1. The correct information is shown in this erratum.

The aim of this paper is to investigate Cournot-type competition in the quantum domain with the use of the Li-Du-Massar scheme for continuous-variable quantum games. We derive a formula which, in a simple way, determines a unique Nash equilibrium. The result concerns a large class of Cournot duopoly problems including the competition, where the demand and cost functions are not...

The authors want to add two references in the original version of this article.

The original version of this article unfortunately contained a mistake.

This paper focuses on estimating real and quantum potentials from financial commodities. The log returns of six common commodities are considered. We find that some phenomena, such as the vertical potential walls and the time scale issue of the variation on returns, also exists in commodity markets. By comparing the quantum and classical potentials, we attempt to demonstrate that...

The aim of the paper is to draw attention to a special class of two parameter unitary strategies in the Eisert-Wilkens-Lewenstein scheme for quantum games. We identify the players’ strategies with basis change matrices. Then we prove that the resulting quantum game is invariant with respect to isomorphic transformations of the input game. Moreover, it is shown that the game so...

The problem of the codirectional Kerr coupler has been considered several times from different point of view. In the present paper we introduce the interaction between a two-level atom and the codirectional Kerr nonlinear coupler in terms of su\(\left (2\right ) \) Lie algebra. Under certain conditions we have adjusted the Kerr coupler and consequently we have managed to handle...

The long-lasting problem of proper mathematical representation of conjunctions and disjunctions in quantum logics is reviewed and three recent proposals of solutions are described.

On spacetimes that are not time orientable we construct a U(1) bundle to measure the twisting of the time axis. This single assumption, and simple construction, gives rise to Maxwell’s equations of electromagnetism, the Lorentz force law and the Einstein-Maxwell equations for electromagnetism coupled to General relativity. The derivations follow the Kaluza Klein theory, but with...

Recently the method based on irreducible representations of finite groups has been proposed as a tool for investigating the more sophisticated versions of Bell inequalities (V. Ugǔr Gűney, M. Hillery, Phys. Rev. A90, 062121 ([2014]) and Phys. Rev. A91, 052110 ([2015])). In the present paper an example based on the symmetry group S 4 is considered. The Bell inequality violation...

Properties of Segal’s entropy for semifinite and finite von Neumann algebras are investigated. In particular, its invariance with respect to a trace-preserving normal *-homomorphism is studied, as well as norm-continuity in the trace norm on the set of bounded in the operator norm density matrices.

Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, \(\mathbb {R}_{+}^{4}\) and (−L/2,L/2)4, are considered where different types of arithmetic and calculus coexist simultaneously. In all the examples there exists a non-Diophantine arithmetic that makes the space...

David Finkelstein was a co-pioneer of the use of topology and solitons in theoretical physics. The author reflects on the great impact Finkelstein had on his research throughout his career. The author provides an application of one of Finkelsteins idea pertaining to the fusion of quantum theory with relativity by utilizing techniques from Loop Quantum Gravity.

Time, positions and spacetimes are modelled by groups and subgroup classes. Their Hilbert space representations define particles and interactions. Electroweak spacetime, proposed as nature-realized manifold, represents the homogeneous groups of the electroweak standard model. The leptonic and hadronic (quark) sectors, characteristic for particles and interactions, are related to...

Using the Damour-Ruffini method, Hawking radiation of charged particles from squashed charged rotating five-dimensional Kaluza-Klein black holes is investigated extensively. Under the generalized tortoise coordinate transformation, Hawking temperature of the black holes is calculated by using charged scalar particles and Dirac fermions respectively. We find that the obtained...

Since every lattice effect algebra decomposes into blocks which are MV-algebras and since every MV-algebra can be represented by a certain semiring with an antitone involution as shown by Belluce, Di Nola and Ferraioli, the natural question arises if a lattice effect algebra can also be represented by means of a semiring-like structure. This question is answered in the present...

Aim of this paper is to provide a scheme for the construction of a conceptual, virtual machine (the term has here a significance analogous to that of the Turing machine, i.e., a formal device which manipulates and evolves ‘states’), able to perform all that living matter – as distinguished from inert matter – can do and inanimate matter cannot, in a setting consistent exclusively...

Let S be a set of states of a physical system. The probabilities p(s) of the occurrence of an event when the system is in different states s ∈ S define a function from S to [0, 1] called a numerical event or, more precisely, an S-probability. If one orders a set P of S-probabilities in respect to the order of functions, further includes the constant functions 0 and 1 and defines...

Wavepackets in quantum mechanics spread and the Universe in cosmology expands. We discuss a formalism where the two effects can be unified. The basic assumption is that the Universe is determined by a unitarily evolving wavepacket defined on space-time. Space-time is static but the Universe is dynamic. Spreading analogous to expansion known from observational cosmology is...

We consider the functor \({\mathcal {C}}\) that to a unital C*-algebra A assigns the partial order set \({\mathcal {C}}(A)\) of its commutative C*-subalgebras ordered by inclusion. We investigate how some C*-algebraic properties translate under the action of \(\mathcal {C}\) to order-theoretical properties. In particular, we show that A is finite dimensional if and only...