Related papers: Renormalization and quantum field theory
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…
Symanzik showed that quantum field theory can be formulated on a space with boundaries by including suitable surface interactions in the action to implement boundary conditions. We show that to all orders in perturbation theory all the…
In this work we develop a re-formulation of quantum field theory through the more general weighted Lorentz invariant measures that the definition of quantum fields allows; this approach provides finite answers for the long-live problems of…
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…
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…
As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in…
I review the theory of renormalization, as applied to weak-coupling perturbation theory in quantum field theories.
The main theme of the paper is the detailed discussion of the renormalization of the quantum field theory comprising two interacting scalar fields. The potential of the model is the fourth-order homogeneous polynomial of the fields,…
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect…
In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one…
We consider here the Feynman amplitudes of renormalizable non-commutative quantum field theory models. Different representations (the parametric and the Mellin one) are presented. The latter further allows the proof of meromorphy of a…
We discuss how basic notions of graph theory and associated graph polynomials define questions for algebraic geometry, with an emphasis given to an analysis of the structure of Feynman rules as determined by those graph polynomials as well…
Computing a perturbative S-matrix through Feynman series in quantum field theory, the regularization used does not affect the final result. We propose a new approach to construction of the perturbative S-matrices, so that they will depend…
We extend the general framework of perturbative quantum field theory developped for the pure Yang-Mills model to gravity. First we present a variant of the elimination procedure of the anomalies in the second order of perturbation theory.…
In this paper I argue that infinities in the classical computation theory such as the unsolvability of the Halting Problem can be addressed in the same way as Feynman divergences in Quantum Field Theory, and that meaningful versions of…
These are introductory lecture notes aimed at beginning graduate students covering fundamental concepts and ideas behind the renormalisation group. Our main goal is to motivate it and then explore its consequences, in the context of quantum…
Feynman perturbation theory for nonabelian gauge theory in light-like gauge is investigated. A lattice along two space-like directions is used as a gauge invariant ultraviolet regularization. For preservation of the polinomiality of action…
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…
A simple integral that illustrates the concepts of regularization, subtraction, renormalization and renormalization group employed in perturbative quantum field theory(PQFT) is considered.