False constraints. A toy model for studying dynamical systems with degenerate Hessian form

This paper studies various aspects of the motion of relativistic rotators, both in the presence and absence of external fields, using a toy model which, in a sense, can be regarded as a non-relativistic limit of the rotators. In a simpler setup, this enables one to gain an insight into the principal difference between mechanical systems with singular and non-singular Hessian, whilst avoiding the complications resulting from the more intricate form of the equations of motion in the fully relativistic regime. In particular, one can comprehend the apparent contradiction between Hessian singularity and simultaneous occurrence of unique solutions for the motion of the fundamental relativistic rotator minimally coupled to the electromagnetic field. With the aid of the toy model the author supports and illustrates his thesis put forward elsewhere that the Hessian singularity is a defect that makes physically unviable some geometric models of spinning particles considered in the literature.Comment: v2: 16 pages (in v2 language corrections + minor changes

Fundamental Relativistic Rotator. Hessian singularity and the issue of the minimal interaction with electromagnetic field

There are two relativistic rotators with Casimir invariants of the Poincar\'{e} group being fixed parameters. The particular models of spinning particles were studied in the past both at the classical and quantum level. Recently, a minimal interaction with electromagnetic field has been considered. We show that the dynamical systems can be uniquely singled out from among other relativistic rotators by the unphysical requirement that the Hessian referring to the physical degrees of freedom should be singular. Closely related is the fact that the equations of free motion are not independent, making the evolution indeterminate. We show that the Hessian singularity cannot be removed by the minimal interaction with the electromagnetic field. By making use of a nontrivial Hessian null space, we show that a single constraint appears in the external field for consistency of the equations of motion with the Hessian singularity. The constraint imposes unphysical limitation on the initial conditions and admissible motions. We discuss the mechanism of appearance of unique solutions in external fields on an example of motion in the uniform magnetic field. We give a simple model to illustrate that similarly constrained evolution cannot be determinate in arbitrary fields.Comment: 16 pages, in v2: shortened, improved presentation, proofs moved to Appendices, in v3: further text permutations and a comment added concerning hamiltonization, in v4: language corrections, final for

Direct vs. final state tensor meson photoproduction - amplitude analysis

Tensor meson photoproduction is described as either a direct production process or a consequence of the final state \pi\pi interactions. We calculate the mass distributions for selected partial waves and confront our predictions with the measurements of the CLAS experiment. We also point out the structures in the photoproduction amplitudes which may result in observable effects able to indicate the dominant tensor meson photoporduction mechanism

Quantum Prisoner's Dilemma game on hypergraph networks

We study the possible advantages of adopting of quantum strategies in multi-player evolutionary games. We base our study on the three-player Prisoner's Dilemma (PD) game. In order to model the simultaneous interaction between three agents we use hypergraphs and hypergraph networks. In particular, we study two types of networks: a random network and a SF-like network. The obtained results show that in the case of a three player game on a hypergraph network, quantum strategies are not necessarily stochastically stable strategies. In some cases, the defection strategy can be as good as a quantum one.Comment: 6 pages, 5 figures. arXiv admin note: text overlap with arXiv:quant-ph/0004076 by other author

a0(980)a_0(980) photoproduction in the coupled channel model

We calculated the coupled channel photoproduction amplitudes of the scalar isovector resononace $a_0(980)$, which include the $\pi\eta$, $K^+K^-$ and $K^0\overline{K^0}$ intermediate states. Based on them we obtained the mass distribution in the $\pi\eta$ channel at photon energy $E_\gamma$=7 GeV, corresponding to energy accissible in new JLab experiments CLAS12 and GlueX. We also analyzed the shape of mass distribution as a function of the phase of the background amplitude.Comment: 5 pages, 3 figure