We consider the quantization of a scalar κ-deformed field up to the point of obtaining an expression for its vacuum energy. The expression is given by the half sum of the field frequencies, as in the nondeformed case, but with the frequencies obeying the κ-deformed dispersion relation. We consider a set of κ-deformed Maxwell equations and show that for the purpose of calculating the Casimir energy the Maxwell field, as in the non-deformed case, behaves as a pair of scalar fields. Those results provide a foundation for computing the Casimir energy starting from the the half sum of field frequencies. A method of calculation starting from this expression is briefly described.
, we use the non-relativistic one, omega(p) = p²/2m. It turns out that the Casimir energy is zero. We include the relativistic corrections perturbatively and show that at all orders the Casimir energy remains zero, since each term in the power series in 1/c² is proportional to the Riemann zeta function of a negative even integer. This puzzling result shows that, at least for the free massive scalar field, the Casimir effect is non-perturbative in the relativistic sense.]]>
Este relato traz uma reflexão sobre a indissociabilidade entre extensão, pesquisa e ensino a partir da experiência dos autores no curso de extensão “CAPDança: capacitação de professores de dança através do Sistema Laban”. Com carga horária total de 45 horas, o curso de extensão surgiu em uma parceria entre o Bacharelado em Dança da Universidade Federal de Uberlândia e o SESC-Uberlândia, tendo sido ofertado presencialmente para 30 professores de dança de Uberlândia e região, de forma gratuita, no segundo semestre de 2019. O texto se apresenta em forma de diálogo informal entre os autores, disparado por quatro perguntas, e toca em pontos importantes para a extensão em dança, como: a aproximação entre saberes produzidos ou pesquisados dentro e fora da universidade; a importância de experiências formativas continuadas para professores de dança; os impactos da promoção de encontros formativos e troca de saberes entre profissionais da dança de diferentes perfis e modos de atuação; o potencial do trabalho por uma compreensão mais expandida e embasada do movimento humano a partir da sistematização proposta por Rudolf Laban. Além disso, aborda desdobramentos e influências do curso de extensão e da lógica extensionista – conexão entre universidade e sociedade – em atividades de ensino e de pesquisa.
Field theories whose space-time symmetries are governed by the κ-deformed Poincaré algebra exhibit peculiar properties which can be used to study physics at very short scales. Those properties also rise interesting questions about how to quantize such theories. We present some results on the quantization of κ-deformed field theories which can shed some light on those questions.
We present the one-loop effective action of a quantum scalar field with DSR1 space-time symmetry as a sum over field modes. The effective action has real and imaginary parts and manifest charge conjugation asymmetry, which provides an alternative theoretical setting to the study of the particle-antiparticle asymmetry in nature. *
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