Braided quantum electrodynamics

Abstract

The homotopy algebraic formalism of braided noncommutative field theory is used to define the explicit example of braided electrodynamics, that is, U(1) gauge theory minimally coupled to a Dirac fermion. We construct the braided L∞-algebra of this field theory and obtain the braided equations of motion, action functional and conserved matter current. The modifications of the electric charge conservation law due to the braided noncommutative deformation are described. We develop a braided generalization of Wick’s theorem, and use it to compute correlation functions of the braided quantum field theory using homological perturbation theory. Our putative calculations indicate that the braided theory does not contain the non-planar Feynman diagrams of conventional noncommutative quantum field theory, and that correlators do not exhibit UV/IR mixing.

BV quantization of braided scalar field theory

“…BV quantization of braided scalar field theory M. Dimitrijević Ćirić In this contribution we address the problem of quantization of noncommutative scalar field theory initiated in [12] using the underlying braided 𝐿 ∞ -algebra and its associated BV formalism; for simplicity, here we will work with the Moyal-Weyl deformation, but more general deformations can be studied analogously, see Appendix A. In Section 2 we briefly review the connection between 𝐿 ∞algebras and the BV formalism in field theory.…”

“…Braided noncommutative field theories [9] are constructed using the twist formalism briefly reviewed in Appendix A; here we consider the Moyal-Weyl twist (A.5). Following [12,16], we define the braided 𝐿 ∞ -algebra for 𝜙 4 -theory. The underlying graded vector space 𝑉 = 𝑉 1 ⊕ 𝑉 2 and the kinetic bracket (5) are unchanged, ℓ ★ 1 = ℓ 1 , while the interaction bracket (6) changes to…”

“…Let us now explain how to compute correlation functions of the interacting braided scalar field theory using the braided BV formalism developed in [11]. More details can be found in [12].…”

“…We consider first the braided 𝜙 4 -theory on R 1,3 from Section 3, which was studied in [12] in position space representation. Let us compute the one-loop correction to the free two-point function from Section 3.2 in momentum space.…”

“…[10], was generalized to braided 𝐿 ∞ -algebras in [11], giving another route to braided quantum field theory that is now capable of treating gauge theories. The BV quantization of braided fuzzy scalar field theories was discussed in [11], while the BV quantization of braided scalar field theory as well as braided quantum electrodynamics was discussed in [12].…”