Análise termoestatística dos potenciais de Yukawa e Lee–Wick em espaços de fase não comutativos

Abstract

In recent years, physical models based on noncommutative algebras have attracted considerable interest, since they provide a framework for investigating theories involving a fundamental parameter at the Planck scale, often associated with semiclassical aspects of quantum gravity. Noncommutative geometry modifies the underlying phase-space structure, potentially leading to new insights into unresolved problems in theoretical physics. In this thesis, we adopt a classical approach to perform a thermostatistical analysis of the well-established Yukawa and Lee – Wick interaction potentials in a noncommutative phase space. Using the noncommutative algebra, we derive the equations of motion associated with these potentials and investigate the corresponding thermodynamic quantities, including the density of states, partition function, mean energy, and heat capacity. Both the microcanonical and canonical ensemble formalisms are considered within the framework of Boltzmann – Gibbs statistical mechanics. Our results show that the introduction of the noncommutative parameter Θ induces nontrivial modifications in thermodynamic quantities, including qualitative changes in the heat capacity. In particular, regions with negative heat capacity may emerge, which we interpret as signatures of the limitations of the semiclassical and perturbative treatment rather than definitive physical effects. The analysis is carried out under the assumptions of weak noncommutativity and |βV (r)| ≪ 1, which constrain the regime of validity of the results. Within this domain, our findings highlight the role of phase-space geometry in shaping thermodynamic behavior. In recent years, physical models based on noncommutative algebras have attracted considerable interest, since they provide a framework for investigating theories involving a fundamental parameter at the Planck scale, often associated with semiclassical aspects of quantum gravity. Noncommutative geometry modifies the underlying phase-space structure, potentially leading to new insights into unresolved problems in theoretical physics. In this thesis, we adopt a classical approach to perform a thermostatistical analysis of the well-established Yukawa and Lee – Wick interaction potentials in a noncommutative phase space. Using the noncommutative algebra, we derive the equations of motion associated with these potentials and investigate the corresponding thermodynamic quantities, including the density of states, partition function, mean energy, and heat capacity. Both the microcanonical and canonical ensemble formalisms are considered within the framework of Boltzmann – Gibbs statistical mechanics. Our results show that the introduction of the noncommutative parameter Θ induces nontrivial modifications in thermodynamic quantities, including qualitative changes in the heat capacity. In particular, regions with negative heat capacity may emerge, which we interpret as signatures of the limitations of the semiclassical and perturbative treatment rather than definitive physical effects. The analysis is carried out under the assumptions of weak noncommutativity and |βV (r)| ≪ 1, which constrain the regime of validity of the results. Within this domain, our findings highlight the role of phase-space geometry in shaping thermodynamic behavior.