International Journal of Modern Physics A

This note aims to provide an entrée to two developments in two-dimensional topological gravity — that is, intersection theory on the moduli space of Riemann surfaces — that have not yet become well known among physicists. A little over a decade ago, Mirzakhani discovered${}^{1,2}$ an elegant new proof of the formulas that result from the relationship between topological gravity and matrix models of two-dimensional gravity. Here we will give a very partial introduction to that work, which hopefully will also serve as a modest tribute to the memory of a brilliant mathematical pioneer. More recently, Pandharipande, Solomon, and Tessler³ (with further developments in Refs. 4–6) generalized intersection theory on moduli space to the case of Riemann surfaces with boundary, leading to generalizations of the familiar KdV and Virasoro formulas. Though the existence of such a generalization appears natural from the matrix model viewpoint — it corresponds to adding vector degrees of freedom to the matrix model — constructing this generalization is not straightforward. We will give some idea of the unexpected way that the difficulties were resolved.

A fair knowledge of the atmospheric muon distributions at Earth is a prerequisite for the simulations of cosmic ray setups and rare event search detectors. A modified power law is proposed for atmospheric muon energy distribution which gives a good description of the cosmic muon data in low as well as high energy regime. Using this distribution, analytical forms for zenith angle $(𝜃)$ distribution are obtained. Assuming a flat Earth, it leads to the ${cos}^{n-1}𝜃$ form where it is shown that the parameter $n$ is nothing but the power of the energy distribution. Exact analytical function is obtained for inclined trajectory of muon. A new closed form for zenith angle distribution is obtained without assuming a flat Earth and which gives an improved description of the data at all angles even above $70^{\circ }$. These distributions are tested with the available atmospheric muon data of energy and angular distributions. The parameters of these distributions can be used to characterize the cosmic muon data as a function of energy, angle and altitude.

In this paper, incorporating the effect of the deformed commutation relation on de Sitter background, we studied the deformed Schwinger mechanism in (1+1) dimensions for scalars particle of spin-0 in a constant electric field. The Klein–Gordon equation is solved exactly and the wave function is given in term of hypergeometric functions. The canonical method based on a Bogoliubov transformation is applied. The pair creation probability and the density number of created particles are calculated.

In this paper we briefly review the main idea of the localization technique and its extension suitable in supersymmetric gauge field theory. We analyze the partition function of the vector multiplets with supercharges and its blocks on the even- and odd-dimensional spheres and squashed spheres. We exploit the so-called Faà di Bruno’s formula and show that multipartite partition functions can be written in the form of expansion series of the Bell polynomials. Applying the restricted specialization argument we show that q-infinite-product representation of partition functions admits presentation in terms of the Patterson–Selberg (or the Ruelle-type) spectral functions.

In this work we formulate the Galilei-covariant version of an effective theory containing nonrelativistic heavy mesons and pions as degrees of freedom. This manifestly Galilean covariant framework is based on a five-dimensional space–time that has been used in the description of covariant nonrelativistic physics. In this context, effective Lagrangian is introduced without ambiguities, containing kinetic and interaction terms that are naturally Galilean invariant. The leading-order scattering amplitudes and the properties of possible heavy-meson bound states are calculated and discussed.

An attempt to extend simple Parton Distribution Functions based on the quantum statistical model to consider more active flavors is presented here. Considering partons as clusters, inspiring from the static picture of proton composed of three valence quarks, such a reasonable extension is surveyed to improve the results. Analytic expressions for the longitudinal Quantum Statistical Parton Distribution Functions are obtained by applying the maximum entropy principle beside theoretical proton sum rules. Furthermore, the main purpose of this study is to predict a minimum energy scale to probe the proton with a defined condition, theoretically. An interesting approach to determine the statistical variables exactly without fitting and fixing is employed and the consistency of computed distributions with the experimental observations gives a robust confirm of presented simple statistical model.

The Hamiltonian of a nonrelativistic particle coupled to non-Abelian gauge fields is defined to construct a non-Abelian gauge theory. The Hamiltonian which includes isospin as a dynamical variable dictates the dynamics of the particle and isospin according to the Poisson bracket that incorporates the Lie algebraic structure of isospin. The generalized Poisson bracket allows us to derive Wong’s equations, which describe the dynamics of isospin, and the homogeneous (sourceless) equations for non-Abelian gauge fields by following Feynman’s proof of the homogeneous Maxwell equations.

It is shown that the derivation of the homogeneous equations for non-Abelian gauge fields using the generalized Poisson bracket does not require that Wong’s equations be defined in the time-axial gauge, which was used with the commutation relation. The homogeneous equations derived by using the commutation relation are not Galilean and Lorentz invariant. However, by using the generalized Poisson bracket, it can be shown that the homogeneous equations are not only Galilean and Lorentz invariant but also gauge independent. In addition, the quantum ordering ambiguity that arises from using the commutation relation can be avoided when using the Poisson bracket.

From the homogeneous equations, which define the “electric field” and “magnetic field” in terms of non-Abelian gauge fields, we construct the gauge and Lorentz invariant Lagrangian density and derive the inhomogeneous equations that describe the interaction of non-Abelian gauge fields with a particle.

In this paper, we investigate the possibility of superluminal velocities and the appertaining underlying geometry. We consider three different approaches and arrive at the same status quo.

Using the Einstein, Bergmann–Thomson (BT) and Landau–Lifshitz (LL) energy and momentum formulations in teleparallel gravity (TG), we obtain the total energy and momentum distributions for phantom black hole metric. We get different energy distributions similar to the earlier study and the momentum distributions vanish for phantom black hole metric in TG. These momentum solutions agree with the study of Sahoo et al. in general relativity. However, using Einstein, Bergmann–Thomson and Landau–Lifshitz energy and momentum complexes, we investigate regular black hole, asymptotically flat wormhole, anti-de Sitter wormhole and Ellis wormhole solutions in TG. We obtain (i) same BT and LL energy density solutions for regular black hole metric, (ii) same and zero energy distribution for asymptotically flat wormhole, (iii) proportion with Einstein and BT energy density solutions for anti-de Sitter wormhole, (iv) same and negative Einstein and BT energy density solutions for Ellis wormhole in TG.