Received 7 August 2021DOI:https://doi.org/10.1103/PhysRevA.104.029903©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectronic structure of atoms & moleculesElectronic transitionsRelativistic quantum electrodynamic effects in atoms, molecules,& ionsAtomic, Molecular Optical

Electromagnetic coupling between plasmonic resonances in metallic nanoparticles allows for engineering of the optical response and generation of strong localized near-fields. Classical electrodynamics fails to describe this coupling across sub-nanometer gaps, where quantum effects become important owing to non-local screening and t...

Attention is focused on quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. There are algebra isomorphisms that allow to identify quantum spaces with commutative coordinate algebras. This observation enables the realization of braiding mappings on commutative algebras. The aim of the article is to...

Category theory provides a more abstract and thus more general setting for considering the structure of mathematical objects. 2-dimensional quantum field theories arise in physics as objects that assign vector spaces to 1-manifolds and linear maps to 2-cobordisms. From a categorical perspective, we find that they are the same as commutative Frobenius algebras. Our main goal is to explain this e...

Four-dimensional quantum field theory suffers from infrared and ultraviolet divergences as well as from the divergence of the renormalised perturbation expansion. Despite early suggestions as to modify the space-time structure [1], quantum field theory on non-commutative spaces was studied in details only after Alain Connes developed noncommutative geometry [2]. The first steps were connected t...

A quantum deformation of the conformal algebra of the Minkowskian spacetime in (3 + 1) dimensions is identified with a deformation of the (4 + 1)-dimensional AdS algebra. Both Minkowskian and AdS first-order non-commutative spaces are explicitly obtained, and the former coincides with the well known κ-Minkowski space. Next, by working in the conformal basis, a new non-commutative Minkowskian sp...

A relativistic Navier-Stokes equation is constructed as the equation of motion of a gauge-invariant bosonic lagrangian. It is shown that the quantum-electrodynamic-like lagrangian is suitable for this purpose with a particular form of gauge field, A µ = φ, A ≡ −c 2 1 − | v| 2 /c 2 , − v. The equation of motion coincides with the classical Navier-Stokes equation at non-relativistic limit | v| ≪ c.

We show that the Drinfel’d double associated to the standard quantum deformation slη(2,R) is isomorphic to the (2+1)-dimensional AdS algebra with the initial deformation parameter η related to the cosmological constant Λ = −η. This gives rise to a generalisation of a non-commutative Minkowski spacetime that arises as a consequence of the quantum double symmetry of (2+1) gravity to non-vanishing...

The space-time symmetry of noncommutative quantum field theories with a deformed quantization is described by the twisted Poincaré algebra, while that of standard commutative quantum field theories is described by the Poincaré algebra. Based on the equivalence of the deformed theory with a commutative field theory, the correspondence between the twisted Poincaré symmetry of the deformed theory ...