arXiv subjects

M. A. A. Ahmed

Publications and source records attributed to M. A. A. Ahmed.

8 recordsLinked to original sources

arXiv2026

Finite-Volume Non-extensive statistical in QCD phase

Recently, some research has emerged that used the Tsallis statistics in Quantum Chromodynamics (QCD). In Tsallis statistics, the Tsallis parameter $\mathfrak{q}$ reflects long-range interactions, non-Markovian memory, and multifractal boundary effects, linking directly to temperature variance in fluctuating systems, which vanish in the Boltzmann-Gibbs limit. This is our motivation to investigate the thermodynamical variables of a hot and dense system. Within a non-extensive color QCD MIT-Bag Model and using the Tsallis distributions to describe the thermal response functions related to the equation of state. The study focuses on the deconfinement phase transition from a hadronic gas to a quark-gluon plasma in order to analyze the behavior of thermodynamical quantities of the system, such as the energy density, the pressure and the interaction measure at finite volume under Tsallis statistics. Furthermore, the effect of the $\mathfrak{q}$-parameter on the phase transition point is investigated. We find that the transition point is significantly affected by the $\mathfrak{q}$-parameter in the framework of non-extensive statistics.

hep-ph↗

arXiv2026

Real-time thermal self-energies: In the variational bases and spaces

In this work, we introduce a systematic study for studying the scalar propagator and tadpole self-energy by considering an arbitrary parameter $σ$ that allows for a path integral description in real-time formalism (RTF). The closed time path formalism (CTP) and Thermofield Dynamics (TFD) are two popular choices for the parameter $σ$ in the Feynman rules. We have constructed a scalar propagator and a tadpole self-energy in two different bases in the momentum space as well as the mixed space. The results show that the diagonal components of self-energy in both spaces for the 1/2 basis are the same in both approaches within RTF, whereas the other off-diagonal components of self-energy are different because they depend on the path parameter. On the other hand, the diagonal components of self-energy in both spaces for the new basis are not the same in both approaches within RTF, whereas the off-diagonal components of self-energy are vanishing. That means the new basis allows one to reduce the components for the quantities studied, like self-energy or other.

hep-th↗

arXiv2026

Real-time thermal photon-photon interactions in the mixed space

Using the effective Lagrangian for the low-energy/temperature of photon-photon interaction and the lowest-order photon self-energy is calculated in the Real Time Formalism (RTF) for an arbitrary path specified by the $σ$-parameter within the new basis. The causal Green's functions (without chemical potential) for the scalar field are evaluated to derive the usual thermal propagators in the mixed space. It is shown that the symmetric propagator does not depend on $σ-$ parameter. Furthermore, the photon self-energy is used to calculate some electromagnetic properties, such as dielectric tensor and velocity of light from photon self-energy in the mixed space that greatly simplifies calculations in RTF. Their time dependence is investigated, and a comparison between our results and those obtained by other models is discussed.

hep-th↗

arXiv2026

Thermal propagator of the bosons and fermions fields

In a thermodynamic environment, thermal field theory (TFT) describes a large ensemble of interacting particles. This may appear to be the same as in classical statistical mechanics. Therefore, we study the scalar propagator and fermion propagator by considering an arbitrary parameter $σ$ that allows for a path integral description in real-time formalism (RTF). We constructed those propagators which allowed us to know how particles moved from one point to another point in momentum space as well as in mixed space, at finite temperature without a chemical potential.

hep-th↗

arXiv2021

On certain three algebras generated by binary algebras

This paper's central theme is to prove the existence of an n-algebra whose multiplication cannot be expressed employing any binary operation. Furthermore, to prove if two algebras are not isomorphic, this property does not hold for $3$-algebras corresponding to these two algebras. The proof drives applying some results gotten early applying a new approach for the classification algebras problem, introduced recently, which showed great success in solving many classification algebras problems.

math.RA↗

arXiv2020

Finite Size Scaling in Time Evolution During the Colorless-QCD Confining Phase Transition

The time evolution of the expanding Colorless Partonic Matter, created in Ultra-Relativistic Heavy Ion Collisions and undergoing the confining phase transition towards a Hadronic Gas, is discussed in the context of a unified model combining our Colorless QCD-MIT Bag Model with the boost invariant Bjorken expansion. The Bjorken Equation in the case of a longitudinal expansion scenario of a non-ideal relativistic medium in finite volume is solved using certain initial conditions $(τ_i,T(τ_i))$ and their effect is studied in detail. The evolution of the temperature as a function of the proper time $T(τ,V)$ is then obtained at different volumes. Different times characterising different scales of the whole time evolution, like the time of the finite volume transition point $τ_0(V)$, the hadronic time $τ_H(V)$ at which the hadronization is completed, the lifetime of the Colorless Partonic Plasma $Δτ_{CPP}(V)$ and the lifetime of the confining phase transition $Δτ_{PT}(V)$ are calculated and their finite size scaling properties are studied in detail. New finite size scaling laws are derived. Also, the time evolution of some Thermal Response Functions as the order parameter $\mathcal{H}(τ,V)$, energy density $ε(τ,V)$, pressure $\mathscr{P}(τ,V)$ and the sound velocity $\mathscr{C}_{s}(τ,V)$ are investigated and studied in detail. We find that the time evolution of our system is really affected by the colorlessness requirement and the initial conditions of the partonic matter: the closer the volume is to the thermodynamic limit, the longer are the times and the lifetimes of the system. A detailed analysis of the temporal decreasing, in negative power, of the energy density $ε(τ,V) \propto τ^{-θ}$ in each of the three stages of the Bjorken expansion is carried out.

hep-ph↗

arXiv2016

Higher Order Cumulants in Colorless Partonic Plasma

Any physical system considered to study the QCD deconfinement phase transition certainly has a finite volume, so the finite size effects are inevitably present. This renders the location of the phase transition and the determination of its order as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement transition point in finite volume $T_{0}(V)$, a new approach based on the finite-size cumulant expansion of the order parameter and the $\mathscr{L}_{m,n}$-Method is used.We have shown that both cumulants of higher order and their ratios, associated to the thermodynamical fluctuations of the order parameter, in QCD deconfinement phase transition behave in a particular enough way revealing pronounced oscillations in the transition region. The sign structure and the oscillatory behavior of these in the vicinity of the deconfinement phase transition point might be a sensitive probe and may allow one to elucidate their relation to the QCD phase transition point. In the context of our model, we have shown that the finite volume transition point is always associated to the appearance of a particular point in whole higher order cumulants under consideration.

hep-th↗

arXiv2015

Finite Volume Cumulant Expansion in QCD-Colorless Plasma

Due to the finite size effects, the localisation of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite volume transition point $T_{0}(V)$ of the QCD deconfinement phase transition to a Colorless QGP, we have developed a new approach using the finite size cumulant expansion of the order parameter and the $L_{mn}$-method. The first six cumulants $C_{1,2,3,4,5,6}$ with the corresponding under-normalized ratios(skewness $Σ$, kurtosis $κ$ ,pentosis $Π_{\pm}$ and hexosis $\mathcal{H}_{1,2,3}$) and three unnormalized combinations of them ($\mathcal{O}={\mathcal{σ}^{2} \mathcal{κ} }{\mathbf{Σ}^{-1} }$, $\mathcal{U} ={\mathcal{σ}^{-2} \mathbf{Σ}^{-1} }$, $\mathcal{N} = \mathcal{σ}^{2} \mathcal{κ}$) are calculated and studied as functions of $(T,V)$. A new approach, unifying in a clear and consistent way the definitions of cumulant ratios, is proposed. A numerical FSS analysis of the obtained results has allowed us to locate accurately the finite volume transition point. The extracted transition temperature value $T_{0}(V)$ agrees with that expected $T_{0}^{N}(V)$ from the order parameter and the thermal susceptibility $χ_{T}\left( T,V\right)$, according to the standard procedure of localization to within about $2\%$. In addition to this, a very good correlation factor is obtained proving the validity of our cumulants method. The agreement of our results with those obtained by means of other models is remarkable.

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