Related papers: Asymptotic regularization method. A constructive a…
The problem of ultraviolet divergences is analysed in the quantum field theory. It was found that it has common roots with the problem of cosmological singularity. In the context of fibre bundles the second quantization method is…
Based on the Taylor expansion, we propose a renormalization method for asymptotic analysis. The standard renormalization group (RG) method for asymptotic analysis can be derived out from this new method, and hence the mathematical essence…
A perturbative renormalization group method is used to obtain steady-state density profiles of a particle non-conserving asymmetric simple exclusion process. This method allows us to obtain a globally valid solution for the density profile…
A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g.,…
A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.
A geometric formulation of Wilson's exact renormalisation group is presented based on a gauge invariant ultraviolet regularisation scheme without the introduction of a background field. This allows for a manifestly background independent…
Conventional renormalization methods in statistical physics and lattice quantum field theory assume a flat metric background. We outline here a generalization of such methods to models on discretized spaces without metric background.…
A divergence-free approach to relativistic quantum electrodynamics based on regularisation of equations of quantum mechanics is discussed. This approach is shown to be exactly equivalent to the conventional Feynman-Dyson renormalisation…
Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which…
We study the renormalization group flow of non-local form factors in four-dimensional quantum gravity within the proper-time formalism at quadratic order in the curvature expansion. We show that the flow equations can be integrated down to…
The methods of the renormalization group and the $\varepsilon$-expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical…
The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…
We consider a possibility to unify the methods of regularization, such as the renormalization group method, stochastic quantization etc., by the extension of the standard field theory of the square-integrable functions $\phi(b)\in…
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the…
We reconsider the renormalization of scalar mass and point out that the quantum correction to the physical observable, as opposed to the bare parameter, of a renormalizable operator, is technically insensitive to ultraviolet physics and…
Asymptotic safety is a powerful mechanism for obtaining a consistent and predictive quantum field theory beyond the realm of perturbation theory. It hinges on an interacting fixed point of the Wilsonian renormalization group flow which…
In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure…
Implicit Regularization is a 4-dimensional regularization initially conceived to treat ultraviolet divergences. It has been successfully tested in several instances in the literature, more specifically in those where Dimensional…
There exist certain intrinsic relations between the ultraviolet divergent graphs and the convergent ones at the same loop order in renormalizable quantum field theories. Whereupon we may establish a new method, the intrinsic regularization…
In this paper we consider introducing careful regularization in the quantization of Maxwell theory in the asymptotic null infinity. This allows systematic discussions of the commutators in various boundary conditions, and application of…