相关论文: Scaling Algebras and Renormalization Group in Alge…

The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species…

We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…

Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…

It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics…

Quantization relates Poisson algebras to $C^*$-algebras. The analysis of local gauge symmetries in algebraic quantum field theory is approached through the quantization of classical gauge theories, regarded as constrained dynamical systems.…

We report on a rigorous operator-algebraic renormalization group scheme and construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the…

The dilation invariance is studied in the framework of Epstein-Glaser approach to renormalization theory. Some analogues of the Callan-Symanzik equations are found and they are applied to the scalar field theory and to Yang-Mills models. We…

Using the machinery of smooth scaling and coarse-graining of observables, developed recently in the context of so-called fluctuation operators (originally developed by Verbeure et al), we extend this approach to a rigorous renormalisation…

$S$-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and…

We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…

We analyse a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R.…

In 2017, G. P. de Brito and co-workers suggested a covariant generalization of the Kempf-Mangano algebra in a $(D+1)$-dimensional Minkowski space-time [A. Kempf and G. Mangano, Phys. Rev. D \textbf{55}, 7909 (1997); G. P. de Brito, P. I. C.…

We address the question of whether the quantum scale-invariant theories introduced in [1] are renormalizable or play the role of effective field theories that are valid below the Planck scale $M_P$. We show that starting from two-loop level…

The second alternative conformal limit of the recently proposed general higher derivative dilaton quantum theory in curved spacetime is explored. In this version of the theory the dilaton is transformed, along with the metric, to provide…

The description of symmetry breaking proposed by K. Symanzik within the framework of renormalizable theories is generalized from the geometrical point of view. For an arbitrary compact Lie group, a soft breaking of arbitrary covariance, and…

The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type Universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the…

We consider scalar field theory in the D-dimensional space with nontrivial metric and local action functional of most general form. It is possible to construct for this model a generalization of renormalization procedure and RG-equations.…

We put forward the idea that in addition to diffeomorphism invariance of general relativity (GR) the gravitational interaction is invariant under arbitrary scale-deformations of the metric field. In addition, we assume that the scaling…

For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework…

Within the algebraic setting of quantum field theory, a condition is given which implies that the intersection of algebras generated by field operators localized in wedge--shaped regions of two--dimensional Minkowski space is non--trivial;…