International Journal of Modern Physics A

In this paper, we review some aspects of relativistic particles' mechanics in the case of a nontrivial geometry of momentum space. We start by showing how the curved momentum space arises in the theory of gravity in 2+1 dimensions coupled to particles, when (topological) degrees of freedom of gravity are solved for. We argue that there might exist a similar topological phase of quantum gravity in 3+1 dimensions. Then, we characterize the main properties of the theory of interacting particles with curved momentum space and the symmetries of the action. We discuss the space–time picture and the emergence of the principle of relative locality, according to which locality of events is not absolute but becomes observer dependent, in the controllable, relativistic way. We conclude with the detailed review of the most studied κ-Poincaré framework, which corresponds to the de Sitter momentum space.

We present several theories of four-dimensional gravity in the Plebanski formulation, in which the tetrads and the connections are the independent dynamical variables. We consider the relation between different versions of gravitational theories: Einsteinian, "topological," "mirror" gravities and gravity with torsion. We assume that our world, in which we live, is described by the self-dual left-handed gravity, and propose that if the Mirror World exists in Nature, then the "mirror gravity" is the right-handed antiself-dual gravity. In this connection, we give a brief review of gravi-weak unification models. In accordance with cosmological measurements, we consider the Universe with broken mirror parity. We also discuss the problems of cosmological constant and communication between visible and mirror worlds. Investigating a special version of the Riemann–Cartan space–time, which has torsion as an additional geometric property, we have shown that in the Plebanski formulation the ordinary and dual "topological" sectors of gravity, as well as the gravity with torsion, are equivalent. Equations of motion are obtained. In this context, we have also discussed a "pure connection gravity" — a diffeomorphism-invariant gauge theory of gravity. Loop Quantum Gravity is also briefly reviewed.

We study the implications of a criterion of naturalness for a simple two Higgs doublet model in the context of the discovery of a Higgs-like particle with a mass at 125 GeV. This condition which measures the amount of fine-tuning further limits the parameter space of this particular model and together with other phenomenological constraints lead to an allowed range of masses for the other neutral or charged Higgs bosons: H, a^±, a⁰.

The process of two-pion production in the electron-polarized proton scattering is investigated. In the Weizsäcker–Williams approximation the differential spectral distributions and the spin-momentum correlations are considered. The spin correlation effects caused by ρ-meson widths are estimated to be of an order of several per cent. Both channels of the π⁺π^- and π⁺π⁰ creation are considered. The effects of intermediate excited baryons are not considered. The spectral distributions on pion energy fractions in polarized and unpolarized cases are presented analytically and numerically.

A spectral action for a generalized bosonic sector corresponding to the Dirac operator of Euclidean supergravity is proposed. We calculate, up to a₄, the Seeley–DeWitt coefficients in the expansion of the spectral action. It is in general not known how to construct a "matter fermionic" supersymmetric partner to the spectral action. The action we propose provides the effective action to be completed to get, at any order of the expansion, the corresponding supersymmetric action.

We analyze the charge-exchange (CX) measurements π^-p→π⁰n below pion laboratory kinetic energy of 100 MeV. After the removal of five degrees of freedom from the initial database, we combine it with the truncated π⁺p database [E. Matsinos and G. Rasche, J. Mod. Phys.3, 1369 (2012)] and fit the ETH model [P. F. A. Goudsmit, H. J. Leisi, E. Matsinos, B. L. Birbrair and A. B. Gridnev, Nucl. Phys. A575, 673 (1994)] to the resulting data. The set of the parameter values of the ETH model, as well as the predictions derived on their basis for the hadronic phase shifts and for the low-energy πN constants, are significantly different from the results obtained in the analysis of the truncated π^±p elastic-scattering databases. The main difference in the hadronic phase shifts occurs in . We discuss the implications of these findings in terms of the violation of the isospin invariance in the hadronic part of the πN interaction. The effect observed amounts to the level of 7–8% in the CX scattering amplitude below 70 MeV. The results and conclusions of this study agree well with those obtained in the mid 1990s, when the isospin invariance was first tested by using πN experimental data, and disagree with the predictions obtained within the framework of the heavy-baryon Chiral-Perturbation Theory.

The Daya Bay and RENO reactor neutrino experiments have revealed that the smallest neutrino mixing angle is in fact relatively large, i.e. θ₁₃ ≈9°. Motivated by this exciting progress, we perform a systematic study of the neutrino mass matrix M_ν with one or two texture zeros, in the assumption that neutrinos are Dirac particles. Among 15 possible patterns with two texture zeros, only three turn out to be favored by current neutrino oscillation data at the 3σ level. Although all the six patterns with one texture zero are compatible with the experimental data at the 3σ level, the parameter space of each pattern is strictly constrained. Phenomenological implications of M_ν on the leptonic CP violation and neutrino mass spectrum are explored, and the stability of texture zeros against the radiative corrections is also discussed.

We first revisit the nonrelativistic minimal length quantum mechanics and reveal an interesting symmetry of the problem. In fact, we will show that the cumbersome problem can be cast into the ordinary Schrödinger equation with a new effective potential. Next, as a typical example, we show the minimal length Schrödinger equation in the presence of a nonminimal Hulthén vector interaction. The transmission and reflection coefficients are reported as well.

We show how to map gravitational theories formulated in the Jordan frame to the Einstein frame at the quantum field theoretical level considering quantum fields in curved space–time. As an example, we consider gravitational theories in the Jordan frame of the type F(ϕ, R) = f(ϕ)R-V(ϕ) and perform the map to the Einstein frame. Our results can easily be extended to any gravitational theory. We consider the Higgs inflation model as an application of our results.

In this paper, we study the action of the nonplanar two-loop dilatation operator in an SU(2)×SU(2) subsector of the ABJ Chern–Simons-matter theory. The gauge invariant operators we consider are the restricted Schur polynomials. As in ABJM theory, there is a limit in which the spectrum reduces to a set of decoupled harmonic oscillators, indicating integrability in the large M and N double limit of the theory. We then consider parity transformations on the gauge invariant operators. In this case the nonplanar anomalous dimensions break parity invariance. Our analysis shows that (M-N) is related to the holonomy in the string theory, confirming one of the main features of the theory and its string dual. Furthermore, in the limit where ABJ theory reduces to ABJM theory, parity invariance is restored.