Related papers: Feynman amplitudes in renormalizable non-commutati…
In this contribution to the proceedings of the Corfu Summer Institute 2015, I give an overview over quantum field theories on non-commutative Moyal space and renormalization. In particular, I review the new features and challenges one faces…
We study quantum electrodynamics on the noncommutative Minkowski space in the Yang-Feldman formalism. Local observables are defined by using covariant coordinates. We compute the two-point function of the interacting field strength to…
We discuss some properties of noncommutative supersymmetric field theories which do not involve gauge fields. We concentrate on the renormalizability issue of these theories.
This paper continues our previous study of Feynman integrals in configuration spaces and their algebro-geometric and motivic aspects. We consider here both massless and massive Feynman amplitudes, from the point of view of potential theory.…
We start by reviewing the formulation of noncommutative quantum mechanics as a constrained system. Then, we address to the problem of field theories defined on a noncommutative space-time manifold. The Moyal product is introduced and the…
Returning to the old problems in ordinary QED, by an appropriate extension of the dimensional regularization method in noncommutative space we try to provide a quite coherent look into NCQED.The renormalisation of theories, the $\beta$…
New approach to computing the amplitudes of multi-particle processes in renormalizable quantum field theories is presented. Its major feature is a separation of the renormalization from the computation. Within the suggested approach new…
An overview of recent developments in the renormalization and in the implementation of spacetime symmetries of noncommutative field theory is presented, and argued to be intimately related.
Amplitudes of ordinary tensor models are dominated at large $N$ by the so-called melonic graph amplitudes. Enhanced tensor models extend tensor models with special scalings of their interactions which allow, in the same limit, that the…
We implement the worldline formalism in phase space to compute scattering amplitudes. First, the Feynman rules exhibit several useful universal features, reflecting elements of the symplectic geometry of the phase space target. Next,…
We extend the parametric representation of renormalizable non commutative quantum field theories to a class of theories which we call "critical", because their power counting is definitely more difficult to obtain. This class of theories is…
We argue that the renormalizability of interacting quantum field theory on the curved-space background with an additional external antisymmetric tensor (two-form) field requires nonminimal interaction of the antisymmetric field with quantum…
Recently, a topological field theory of membrane-matter coupled to BF theory in arbitrary spacetime dimensions was proposed [1]. In this paper, we discuss various aspects of the four-dimensional theory. Firstly, we study classical solutions…
Feynman's formulation of quantum theory is remarkable in its combination of formal simplicity and computational power. However, as a formulation of the abstract structure of quantum theory, it is incomplete as it does not account for most…
The main difficulty of quantum field theory is the problem of divergences and renormalization. However, realistic models of quantum field theory are renormalized within the perturbative framework only. It is important to investigate…
The previously developed renormalizable perturbative 1/N-expansion in higher dimensional scalar field theories is extended to gauge theories with fermions. It is based on the $1/N_f$-expansion and results in a logarithmically divergent…
We generalize the Mellin representation for a generic co-dimension flat defect CFT. We study the analytic structure of the Mellin amplitudes. We also compute Witten diagrams for a generic co-dimension flat defect CFT.
We present a non-perturbative regularization scheme for Quantum Field Theories which amounts to an embedding of the originally unregularized theory into a spacetime with an extra compactified dimensions of length L ~ Lambda^{-1} (with…
We propose to include gravity in quantum field theory non-perturbatively, by modifying the propagators so that each virtual particle in a Feynman graph move in the space-time determined by the four-momenta of the other particles in the same…
We present an amplitude-generating formula in renormalizable quantum field theory. It reflects the self-similarity of loop amplitudes, in which an amplitude can also be a subamplitude of another. Amplitudes are generated by a small number…