Quantum electrodynamics (QED) of electrons confined in a plane and that yet can undergo interactions mediated by an unconstrained photon has been described by the so-called pseudo-QED (PQED), the (2+1)-dimensional version of the equivalent dimensionally reduced original QED. In this work, we show that PQED with a nonlocal Chern-Simons term is dual to the Chern-Simons Higgs model at the quantum level. We apply the path-integral formalism in the dualization of the Chern-Simons Higgs model to first describe the interaction between quantum vortex particle excitations in the dual model. This interaction is explicitly shown to be in the form of a Bessel-like type of potential in the static limit. This result per se opens exciting possibilities for investigating topological states of matter generated by interactions, since the main difference between our new model and the PQED is the presence of a nonlocal Chern-Simons action. Indeed, the dual transformation yields an unexpected square root of the d'Alembertian operator, namely, ( √ − ) −1 multiplied by the well-known Chern-Simons action. Despite the nonlocality, the resulting model is still gauge invariant and preserves the unitarity, as we explicitly prove. Finally, when coupling the resulting model to Dirac fermions, we then show that pairs of bounded electrons are expected to appear, with a typical distance between the particles being inversely proportional to the topologically generated mass for the gauge field in the dual model.
Out-of-equilibrium states in glasses and crystals have been a major topic of research in condensed-matter physics for many years, and the idea of time crystals has triggered a flurry of new research. Here, we provide a description for the recently conjectured time glasses using fractional calculus methods. An exactly solvable effective theory is introduced with a continuous parameter describing the transition from liquid through normal glass and time glass into the Gardner phase. The phenomenological description with a fractional Langevin equation is connected to a microscopic model of a particle in a sub-Ohmic bath in the framework of a generalized Caldeira-Leggett model.
The Casimir force for a planar gauge model is studied considering perfect conducting and perfect magnetically permeable boundaries. By using an effective model describing planar vortex excitations, we determine the effect these can have on the Casimir force between parallel lines. Two different mappings between models are considered for the system under study, where generic boundary conditions can be more easily applied and the Casimir force be derived in a more straightforward way. It is shown that vortex excitations can be an efficient suppressor of vacuum fluctuations. In particular, for the model studied here, a planar Chern-Simons type of model that allows for the presence of vortex matter, the Casimir force is found to be independent of the choice of boundary conditions, at least for the more common types, like Neumann, perfect conducting and magnetically permeable boundary conditions. We give an interpretation for these results and some possible applications for them are also discussed.Comment: 20 pages, 1 eps figur
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