In this work, we study the chiral symmetry breaking in pseudo-quantum electrodynamics in (2 þ 1) dimensions, which is designed to reproduce a Coulomb potential for charged particles on a plane interacting via photons propagating in (3 þ 1) space-time dimensions and would be relevant for applications to condensed-matter systems. Using an ultraviolet cutoff in the momentum integrals, we show that there is a critical dimensionless coupling c ¼ =4 above which there is chiral symmetry breaking. In the case of the theory with N massless fermions, we obtain a critical value of the number of fermion flavors, N c , below which the chiral symmetry breaking occurs. Finally, we discuss the relevance of our results to graphene in the ultimate deep infrared regime where the Fermi velocity of the Dirac fermions approaches the velocity of light.

Photon spheres, surfaces where massless particles are confined in closed orbits, are expected to be common astrophysical structures surrounding ultracompact objects. In this paper a semiclassical treatment of a photon sphere is proposed. We consider the quantum Maxwell field and derive its energy spectra. A thermodynamic approach for the quantum photon sphere is developed and explored. Within this treatment, an expression for the spectral energy density of the emitted radiation is presented. Our results suggest that photon spheres, when thermalized with their environment, have nonusual thermodynamic properties, which could lead to distinct observational signatures.

We analyze the thermodynamics of massless bosonic systems in D-dimensional anti-de Sitter spacetime, considering scalar, electromagnetic, and gravitational fields. Their dynamics are described by Pöschl-Teller effective potentials and quantized in a unified framework, with the determination of the associated energy spectra. From the microscopic description developed, a macroscopic thermodynamic treatment is proposed, where an effective volume in anti-de Sitter geometry is defined and a suitable thermodynamic limit is considered. Partition functions are constructed for the bosonic gases, allowing the determination of several thermodynamic quantities of interest. With the obtained results, general aspects of the thermodynamics are explored.