We construct a fractional Laplacian spinning particle model in an external electromagnetic field that generalizes a standard relativistic spinning particle model without anti-commuting spin variables. The one-dimensional fractional Laplacian in world-line variable $\lambda$ governs the kinetic energy that is non-local in $\lambda$. The interaction between the particle’s charge and the electromagnetic four-potential is non-local in $\lambda$, while the interaction between the particle’s spin tensor and the electromagnetic field is standard. By applying the variational principle, we obtain the equations of motion for particle coordinates. We solve analytically the equations of motion in two particular cases: the constant electric and magnetic field. For more complex field configurations, the equations are, in general, non-local and non-linear. By making the assumption of a much weaker interaction term between the charge and four-potential compared with the interaction between spinning degrees of freedom and the electromagnetic field, we obtain approximate analytical solutions in the case of a quadratic electromagnetic potential.

We construct the conformable actuated pendulum model in the conformable Lagrangian formalism. We solve the equations of motion in the absence of force and in the case of a specific force resulting from torques which generalizes a well known mechanical model. Our study shows that the conformable model captures essential information about the physical system encoded in the parameters which depend on the conformability factor α. This dependence can describe internal variations such as viscous friction, transmission or environmental effects. We solve the equations of motion analytically for α=1/2 and by Frobenius’ method for α≠1/2.

In this paper we present a study of the production and decay of exotic heavy quarks in the fermion–mirror-fermion, vector singlet, and vector doublet models. A Monte Carlo final-state reconstruction of events is given for kinematical distributions. At energies reached at DESY HERA we show that exotic quarks in the mass range 100–150 GeV, and with mixing angles of the order of ${\sin }^2$θ=0.05, can be clearly dominant over the standard ‘‘top’’ quark production. We discuss experimental cuts that can eliminate the ‘‘bottom’’ background. We compare the theoretical predictions of the three models above in order to indicate a way to establish the origin of a possible experimental signal of an exotic quark. Even if no such signal is found, HERA can still improve the experimental bounds on exotic objects, although there is some model dependence on the estimates of total cross sections.

In this paper, we construct the conformable actuated pendulum model in the conformable Lagrangian formalism. We solve the equations of motion in the absence of force and in the case of a specific force resulting from torques, which generalizes a well known mechanical model. Our study shows that the conformable model captures essential information about the physical system encoded in the parameters which depend on the conformability factor $\alpha$. This dependence can describe internal variations such as viscous friction, transmission, or environmental effects. We solve the equations of motion analytically for $\alpha =1/2$ and using Frobenius’ method for $\alpha \ne 1/2$.

The recently proposed conformable deformation of quantum mechanics by a fractional parameter $\alpha \in (0,1]$ has been used to construct a conformable quantum harmonic oscillator, which coincides with the standard quantum oscillator at $\alpha =1$. We argue that there is a conformable generalization of the uncertainty principle and use it to define the conformable coherent states of the conformable quantum oscillator along the general line of quantum mechanics. We investigate the fundamental physical and mathematical properties of these states in the $x^{\alpha }$-representation. In particular, we determine these states from the minimum uncertainty, compute their energy, find their conformable time-dependent form, determine the conformable translation operator, and show that conformable coherent states are eigenstates of the conformable annihilation operator. These states reproduce in the $\alpha =1$ limit of the correspondence principle the coherent states of the standard quantum harmonic oscillator.

Resumo Neste trabalho fazemos uma apresentação didática da chamada Revolução Copernicana, destacando alguns aspectos históricos e epistemológicos a ela associados. Procuramos, em especial, mostrar como a história da ciência astronômica, na qual está inserida o modelo heliocêntrico de Copérnico, esteve sempre sujeita a uma disputa entre duas concepções científicas, que poderíamos chamar de realismo e de instrumentalismo, sobretudo no que se refere ao emprego por Ptolomeu de dispositivos como o equanto e o excêntrico na descrição dos movimentos planetários. Fazemos uma breve exposição do pensamento cosmológico de Aristóteles e dos modelos astronômicos geocêntricos de Ptolomeu e seus sucessores árabes e, então, uma exposição mais detalhada, ainda que qualitativa, da nova proposta de Copérnico, bem como de seus fundamentos epistemológicos. Por último, procuramos mostrar também como essa proposta, em princípio restrita a um campo de saber específico, abalou completamente a concepção científica e filosófica aristotélica então amplamente prevalecente, constituindo mais um elemento de confronto entre uma nova visão de mundo emergente e outra, já em seus derradeiros momentos, conflito que se refletiu de maneira acentuada no domínio religioso.