International Journal of Modern Physics A

The index theorems relate the gauge field and metric on a manifold to the solution of the Dirac equation on it. In the standard approach, the Dirac operator must be massless to make the chirality operator well defined. In physics, however, the index theorem appears as a consequence of chiral anomaly, which is an explicit breaking of the symmetry. It is then natural to ask if we can understand the index theorems in a massive fermion system which does not have chiral symmetry. In this review, we discuss how to reformulate the chiral anomaly and index theorems with massive Dirac operators, where we find nontrivial mathematical relations between massless and massive fermions. A special focus is placed on the Atiyah–Patodi–Singer index, whose original formulation requires a physicist-unfriendly boundary condition, while the corresponding massive domain-wall fermion reformulation does not. The massive formulation provides a natural understanding of the anomaly inflow between the bulk and edge in particle and condensed matter physics.

In the system of a pair of quantum-entangled neutral kaons from meson decays, when one kaon collapses into the $K_S$ state, the other will collapse instantaneously into the $K_L$ state, due to entanglement and nonlocality. However, if the alternative hypothesis is correct and there is a time window during which one kaon is unaware that the other has decayed, some quantum mechanically prohibited $K_S{K}_S$ decays may occur. We calculate the branching ratios of $K_S{K}_S$ in vector meson decays under locality hypothesis and compare them with experimental results. We show that the branching ratio of $J/\psi \to K_S{K}_S$ under locality assumption is already excluded by the BESIII experimental upper limit. Additional experimental results are proposed to perform this test in the future.

We evaluate the stellar energy-loss rates ${𝒬}$ due to the production of neutrino pair in 3-3-1 models. The energy loss rate ${𝒬}$ is evaluated for different values of $\beta =\pm \frac{1}{\sqrt{3}},\pm \frac{2}{\sqrt{3}},\pm \sqrt{3}$ in which $\beta$ is a parameter used to define the charge operator in the 331 models. We show that the contribution of dipole moment to the energy loss rate is small compared to the contribution of new natural gauge boson $Z^{\prime }$. The correction ${𝒬}$ compared with that of Standard Model is evaluated and do not exceed 14% and is highest with $\beta =-\sqrt{3}$. Of all the evaluated models, model with $\beta =-\sqrt{3}$ give a relative large ${𝒬}$ correction for the mass of $Z^{\prime }$$m_{Z^{\prime }}\le 4000$ GeV. This mass range is within the searching range for $Z^{\prime }$ boson at LHC.

This paper analyses the algebraic and physical properties of the spin and orbital angular momenta of light in the quantum mechanical framework. The consequences of the fact that these are not angular momenta in the quantum mechanical sense are worked out in mathematical detail. It turns out that the spin part of the angular momentum has continuous eigenvalues. Particular attention is given to the paraxial limit, and to the definition of Laguerre–Gaussian modes for photons as well as classical light fields taking full account of the polarization degree of freedom.

In this study, we use the concept of Bohmian trajectories to present a dynamical and deterministic interpretation for the gravity-induced wave function reduction. We shall classify all possible regimes for the motion of a particle, based on the behavior of trajectories in the ensemble and under the influence of quantum and gravitational forces. In the usual approaches all the information is obtained from the wave function evolution. But, on the basis of Bohm’s deterministic quantum theory, we can investigate the motion of the particle during the reduction processes. This leads to analytical and numerical results for the reduction time and equation of motion of the particle. In this regard, a new visualization will be provided for the reduction time.

This work studies the theoretical construction of charged quintessence thin-shell wormholes using Israel thin-shell approach. The stability of these wormhole solutions is investigated by taking linear, logarithmic and Chaplygin gas models as a constituent of exotic matter at thin-shell. The presence of wormhole stability regions particularly relies on the physically justifiable values of charge and quintessence parameter. It is noted that the increasing value of charge seems as an effective component for stable regions while the rise in negativity of the quintessence parameter gives more stable wormhole configurations.

In this work we construct metrics corresponding to radiating black holes whose near horizon regions cannot be approximated by Rindler space–time. We first construct infinite parameter coordinate transformations from Minkowski coordinates, such that an observer using these coordinates to describe space–time events measures the Minkowski vacuum to be Planckian. Utilizing these results, we construct a family of black holes that radiate at spatial infinity. As an illustration, we study a subset of the black hole solutions and show that they satisfy the null energy condition.

We address the bound-state dynamics of a neutron with anomalous magnetic dipole moment in the presence of electromagnetic (EM) fields described by a generalized Dirac–Pauli equation. This generalization consists of including appropriate couplings between Lorentz scalar and pseudoscalar fields with EM fields in the Lagrangian of the system. We exactly solve two single-particle problems: first, a Hydrogen-like system; second, a relativistic Schrödinger-like equation for a linear confining potential. We comment on the relevance of this approach to explore fermion (e.g. neutron) self-interactions as solitonic models of the neutron.

In this paper, we study the Duffin–Kemmer–Petiau (DKP) equation in the presence of a smooth barrier in dimensions space–time (1+1) dimensions. The eigenfunctions are determined in terms of the confluent hypergeometric function $M(\alpha ;\beta ;y)$. The transmission and reflection coefficients are calculated, special cases as a rectangular barrier and step potential are analyzed. A numerical study is presented for the transmission and reflection coefficients graphs for some values of the parameters $(V_0,E)$ are plotted.

Experimental collaborations for the large hadron collider conducted various searches for supersymmetry. In the absence of signals, lower limits were put on sparticle masses but usually within frameworks with (over-)simplifications relative to the entire indications by supersymmetry models. For complementing current interpretations of experimental bounds, we introduce a 30-parameter version of the R-parity conserving Minimal Supersymmetric Standard Model (MSSM-30). Using a sample of the MSSM-30 which are in harmony with cold dark matter, flavor and precision electroweak constraints, we explicitly show the prospects for assessing neutralino candidate dark matter in contrast to future searches for supersymmetry. The MSSM-30-parameter regions that are beyond reach to dark matter direct detection experiments could be probed by future hadron–hadron colliders.

Starting from noncommutative Fermi theory in two dimensions, we construct a deformed Kac–Moody algebra between its vector and chiral currents. The higher-order corrections to the deformed Kac–Moody algebra are explicitly calculated. We observe that the ordinary Schwinger terms are not affected by noncommutativity. Finally we conclude that the deformed Kac–Moody algebra can be given in term of ordinary Kac–Moody algebra plus infinitely many Lie algebraic structures at each nonzero power of the antisymmetric coefficient $𝜃$.

We consider the orbits of test particles moving in the gravitational field of a noncommutative-inspired Einstein–Euler–Heisenberg black hole. Using the geometric metric, we determine the circular orbits followed by massless particles, comparing them with the circular photon orbits coming from the Plebanski pseudo-metric that takes into account the nonlinear nature of the Euler–Heisenberg electrodynamics. Using the impact parameter of the photon orbits, we define the shadow of the noncommutative-inspired black hole and discuss the constraints on the model by comparing its shadow with the prediction from General Relativity.