Related papers: A Perspective on Regularization and Curvature
This is a short guide to some uses of the zeta-function regularization procedure as a a basic mathematical tool for quantum field theory in curved space-time (as is the case of Nambu-Jona-Lasinio models), in quantum gravity models (in…
We study the role of categorical symmetries in constraining the renormalisation of couplings in two-dimensional non-linear sigma models with Wess-Zumino term. A large class of these theories admit self-duality symmetries associated with…
The effects of quantum corrections to a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary are considered in the context of a renormalisation procedure. The renormalisation of the…
We consider how gauge theories can be described by matrix models. Conventional matrix regularization is defined for scalar functions and is not applicable to gauge fields, which are connections of fiber bundles. We clarify how the degrees…
A real space renormalization group technique, based on the hierarchical baby-universe structure of a typical dynamically triangulated manifold, is used to study scaling properties of 2d and 4d lattice quantum gravity. In 4d, the…
The perturbative quantization of gauge theories is shortly reviewed with emphasis of the local operator BRST-formalism.
The decoupling of heavy fields as required by the Appelquist-Carazzone theorem plays a fundamental role in the construction of any effective field theory. However, it is not a trivial task to implement a renormalization prescription that…
We present a perturbative construction of the $\varphi^4$ model on a smooth globally hyperbolic space-time. Our method relies on a adaptation of the Epstein and Glaser method of renormalization to curved space-times using techniques from…
The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
The renormalization-group improved effective potential for an arbitrary renormalizable massless gauge theory in curved spacetime is found,thus generalizing Coleman-Weinberg's approach corresponding to flat space.Some explicit examples are…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
Many authors have considered and investigated generalized fractional differential operators. The main object of this present paper is to define a new generalized fractional differential operator $\mathfrak{T}^{\beta,\tau,\gamma},$ which…
We study the regularization ambiguities in an exact renormalized (1+1)-dimensional field theory. We show a relation between the regularization ambiguities and the coupling parameters of the theory as well as their role in the implementation…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
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…
We investigate $\beta$-functions of quantum gravity using dimensional regularisation. In contrast to minimal subtraction, a non-minimal renormalisation scheme is employed which is sensitive to power-law divergences from mass terms or…
A new method is presented for assigning distributional curvature, in an invariant manner, to a space-time of low differentiability, using the techniques of Colombeau's `new generalised functions'. The method is applied to show that…
Motivated by the study of quantum fields in a Friedman-Robertson-Walker (FRW) spacetime, the one-loop effective action for a scalar field defined in the ultrastatic manifold $R\times H^3/\Gamma$, $H^3/\Gamma$ being the finite volume,…
Renormalization Group Equations (RGEs) are indispensable tool to know the behavior of physical parameters at different energy scales. They are also extremely crucial if we want to extend our known Standard Model gauge group by some extra…