Related papers: UV/IR mixing in noncommutative QED defined by Seib…
We formulate a mathematical setup for computational neural networks using noncommutative algebras and near-rings, in motivation of quantum automata. We study the moduli space of the corresponding framed quiver representations, and find…
We discuss the problem of gauge fixing for strongly correlated electrons coupled to quantum light, described by projected low-energy models such as those obtained within tight-binding methods. Drawing from recent results in the field of…
We address the problem of UV/IR mixing in noncommutative quantum field theories from the perspective of braided $L_\infty$-structures and the Batalin-Vilkovisky formalism. We describe the example of braided noncommutative scalar field…
The paper considers quantum electrodynamics (QED) and weak interaction of elementary particles in the lower orders of the perturbation theory using nonlocal Hamiltonian in the Foldy-Wouthuysen (FW) representation. Feynman rules in the FW…
We consider noncommutative analogs of scalar electrodynamics and N=2 D=4 SUSY Yang-Mills theory. We show that one-loop renormalizability of noncommutative scalar electrodynamics requires the scalar potential to be an anticommutator squared.…
Neutral triple gauge couplings (nTGCs) are manifestation of new physics beyond the Standard Model (SM), as they are absent in the SM and are first generated by dimension-8 operators in the SM Effective Field Theory (SMEFT). We study the UV…
The results of our research on noncommutative perturbative quantum field theory and its relation to string theory are exposed with details. 1) We give an introduction to noncommutative quantum field theory and its derivation from open…
The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed…
Noncommutative quantum field theory of a complex scalar field is considered. There is a two-coupling noncommutative analogue of U(1)-invariant quartic interaction $(\phi^*\phi)^2$, namely $A\phi^*\star\phi\star\phi^*\star\phi+…
The many open questions concerning the existence of IR and UV fixed points in gauge theories as a function of the number of fermion flavors and bare coupling are briefly reviewed and discussed. It is pointed out that only a small subset of…
We discuss the equivalence between light-front time-ordered-perturbation theory and covariant quantum field theory in light-front quantization, in the case of quantum electrodynamics at one-loop level. In particular, we review the one-loop…
The semiclassical limit of full non-commutative gauge theory is known as Poisson gauge theory. In this work we revise the construction of Poisson gauge theory paying attention to the geometric meaning of the structures involved and advance…
The instability of a Fermi surface against Ising nematic order destroys the quasiparticle character of the low-energy degrees of freedom. Therefore, observables exhibit deviations from Fermi liquid behavior which gives rise to the term…
It is shown that non-commutative spaces, which are quotients of associative algebras by ideals generated by non-linear relations of a particular type, admit extremely simple formulae for deformed or star products. Explicit construction of…
An enveloping algebra valued gauge field is constructed, its components are functions of the Lie algebra valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of…
We elaborate on the dynamics of noncommutative two-dimensional gauge field theories. We consider U(N) gauge theories with fermions in either the fundamental or the adjoint representation. Noncommutativity leads to a rather non-trivial…
We present a detailed study of the topological Schwinger model [Phys. Rev. D 99, 014503 (2019)], which describes (1+1) quantum electrodynamics of an Abelian $U(1)$ gauge field coupled to a symmetry-protected topological matter sector, by…
Using noncommutative deformed canonical commutation relations, a model describing a noncommutative complex scalar field theory is considered. Using the path integral formalism, the noncommutative free and exact propagators are calculated to…
In an alternative interpretation, the Seiberg-Witten map is shown to be induced by a field dependent co-ordinate transformation connecting noncommutative and ordinary space-times. Furthermore, following our previous ideas, it has been…
We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order to construct a quantum mechanics over noncommutative Heisenberg algebras. The…