Related papers: Dimensional regularization and renormalization of …
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation…
In this paper the massive neutrinos model arising due to the Snyder noncommutative geometry, proposed recently by the author is partially developed. By straightforward calculation it is shown that the masses of the chiral left- and…
Dimensional regularization is incompatible with the standard covariant projection methods that are used to calculate the short-distance coefficients in inclusive heavy quarkonium production and annihilation rates. A new method is developed…
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+…
It has been suggested that higher-derivative gravity theories coupled to a scalar field with shift symmetry may be an important candidate for a quantum gravity. We show that this class of gravity theories are renormalizable in D = 3 and 4…
The general features of renormalization and the renormalization group in QED and in general quantum field theories in curved spacetime with additional Lorentz- and CPT-violating background fields are reviewed.
In a minimalistic view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind: 1-particle solutions (wavefunctions) of the equation of motion in the presence of an…
We demonstrate the renormalisability of quantum field theories in four dimensions with elementary self-interacting Dirac fermions and to leading order in the limit of many fermion flavours $N_{\rm f}$. Starting from the underlying…
Studying the gauge-invariant renormalizability of four-dimensional Yang-Mills theory using the background field method and the BV-formalism, we derive a classical master-equation homogeneous with respect to the antibracket by introducing…
We calculate quantum corrections to the mass of noncommutative phi^4 kink in (1+1) dimensions for intermediate and large values of the noncommutativity parameter theta. All one-loop divergences are removed by a mass renormalization (which…
We study the IR/UV connection of the four-dimensional non-commutative phi^4 theory by using the Wilsonian Renormalization Group equation. Extending the usual formulation to the non-commutative case we are able to prove UV renormalizability…
When considering quantum field theories on non-commutative spaces one inevitably encounters the infamous UV/IR mixing problem. So far, only very few renormalizable models exist and all of them describe non-commutative scalar field theories…
We present a perturbative construction of the $\varphi^4$ model on a smooth globally hyperbolic space-time. Our method relies on a adaptation of the Epstein and Glaser method of renormalization to curved space-times using techniques from…
We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In…
The advantage of Pauli-Villars regularization in quantum field theory quantized on the light front is explained. Simple examples of scalar $\lambda\varphi^4$ field theory and Yukawa-type model are used. We give also an example of…
Field theories with combinatorial non-local interactions such as tensor invariants are interesting candidates for describing a phase transition from discrete quantum-gravitational to continuum geometry. In the so-called cyclic-melonic…
The non-perturbative autonomous renormalization of the scalar $\Phi^4$-model is applied in the framework of stochastic quantization. I show that this requires a selective, momentum-dependent renormalization of the Onsager coefficient…
Contrary to the classical methods of quantum mechanics, the deformation quantization can be carried out on phase spaces which are not even topological manifolds. In particular, the Moyal star product gives rise to a canonical functor $F$…
In the practice of physics model building, the process of renormalization, resummation, and anomaly cancellation is to incrementally repair initially ill-defined Lagrangian quantum field theories. Impressive as this is, one would rather…
We propose a renormalization scheme for non-local Quantum Field Theories (QFTs) with infinite derivatives inspired by string theory. Our Non-locality Renormalization Scheme (NRS) is inspired by Dimensional Regularization (DR) in local QFTs…