Related papers: Convergence Theorem for Non-commutative Feynman Gr…
Non(anti)commutative gauge theories are supersymmetric Yang-Mills and matter system defined on a deformed superspace whose coordinates obey non(anti)commutative algebra. We prove that these theories in four dimensions with N=1/2…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
The current article considers Mayer cluster integrals of n-dimensional hard particles in the n>1 dimensional flat Euclidean space. Extending results from Wertheim and Rosenfeld, we proof that the graphs are completely reducible into 1- and…
To any graph with external half-edges and internal masses, we associate canonical integrals which depend non-trivially on particle masses and momenta, and are always finite. They are generalised Feynman integrals which satisfy graphical…
We present significant evidence that the powerful property of Yangian invariance extends to a new large class of conformally invariant Feynman integrals. Our results apply to planar Feynman diagrams in any spacetime dimension dual to an…
I describe a mathematical framework for the efficient processing of the very large sets of Feynman diagrams contributing to the scattering of many particles. I reexpress the established numerical methods for the recursive construction of…
A construction of master field describing multicolour QCD is presented. The master fields for large N matrix theories satisfy to standard equations of relativistic field theory but fields are quantized according $q$-deformed commutation…
We review some aspects of non commutative quantum field theory and group field theory, in particular recent progress on the systematic study of the scaling and renormalization properties of group field theory. We thank G. Zoupanos and the…
Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. However, the validity of relativistic quon theories is still in doubt. In this paper we prove that there exists a…
Quantum field theory has been shown recently renormalizable on flat Moyal space and better behaved than on ordinary space-time. Some models at least should be completely finite, even beyond perturbation theory. In this paper a first step is…
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
We study the quantum mechanical consistency of noncommutative gauge theories by perturbatively analyzing the Wilsonian quantum effective action in the matrix formulation. In the process of integrating out UV states, we find new divergences…
A correlational dialect is introduced within the quantum theory language to give a unified treatment of finite-dimensional informational/operational quantum theories, infinite-dimensional relativistic quantum theories, and quantum gravity.…
Manifestly invariant renormalization scheme for supersymmetric gauge theories is proposed. This scheme is applied to supersymmetric quantum electrodynamics.
We present the current status of the a new approach to quantum general relativity based on the exact resummation of its perturbative series as that series was formulated by Feynman. We show that the resummed theory is UV finite and we…
In this paper, we use a topological quantum field theory (TQFT) to define families of new homology theories of a $2$-dimensional CW complex of a smooth closed surface. The dimensions of these homology groups can be used to count the number…
In this paper, we show how the finite formulation of QFT based on Callan-Symanzik equations can be generalised to the case of non-renormalizable theories. We derive an equation for effective action for an arbitrary single scalar field…
A simple integral that illustrates the concepts of regularization, subtraction, renormalization and renormalization group employed in perturbative quantum field theory(PQFT) is considered.
The mathematical formalism necessary for the diagramatic evaluation of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The evaluation of…