UV/IR mixing in noncommutative scalar field theories is shown to be an artifact of a non-covariant quantization choice rather than an intrinsic feature of noncommutativity.
Braided Commutative Geometry and Drinfel'd Twist Deformations
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abstract
In this thesis we give obstructions for Drinfel'd twist deformation quantization on several classes of symplectic manifolds. Motivated from this quantization procedure, we further construct a noncommutative Cartan calculus on any braided commutative algebra, as well as an equivariant Levi-Civita covariant derivative for any non-degenerate equivariant metric. This generalizes and unifies the Cartan calculus on a smooth manifold and the Cartan calculus on twist star product algebras. We prove that the Drinfel'd functor leads to equivalence classes in braided commutative geometry and commutes with submanifold algebra projection.
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2026 2representative citing papers
First order vector field calculi are shown to be categorically adjoint to first order differential calculi, with bicovariant versions in bijection with quantum tangent spaces and a sheaf-theoretic Atiyah sequence on quantum principal bundles.
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UV/IR mixing as an artifact of non-covariant quantisation
UV/IR mixing in noncommutative scalar field theories is shown to be an artifact of a non-covariant quantization choice rather than an intrinsic feature of noncommutativity.
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Noncommutative vector field calculi
First order vector field calculi are shown to be categorically adjoint to first order differential calculi, with bicovariant versions in bijection with quantum tangent spaces and a sheaf-theoretic Atiyah sequence on quantum principal bundles.