Related papers: Unifying renormalization group and the continuous …
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…
Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the…
Following previous work by one of the authors [M.V.Altaisky, Unifying renormalization group and the continuous wavelet transform, Phys. Rev. D 93, 105043 (2016).], we develop a new approach to the renormalization group, where the effective…
We investigate possible renormalization-group fixed points at nonzero coupling in $\phi^3$ theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three theories of this type, with (a) a…
The renormalization that relates a coupling "a" associated with a distinct renormalization group beta function in a given theory is considered. Dimensional regularization and mass independent renormalization schemes are used in this…
The regularization of quantum electrodynamics in the space of functions $\psi_a(x)$, which depend on both the position $x$ and the scale $a$, is presented. The scale-dependent functions are defined in terms of the continuous wavelet…
The problem considered here is the determination of the hamiltonian of a first quantized nonrelativistic particle by the help of some measurements of the location with a finite resolution. The resulting hamiltonian depends on the resolution…
The effective potential $V$ is considered in massless $\lambda\phi^4_4$ theory. The expansion of $V$ in powers of the coupling $\lambda$ and of the logarithm of the background field $\phi$ is reorganized in two ways; first as a series in…
Effective potential for scalar $\lambda\phi^4$ theory is obtained using the exact renormalization group method which includes both the usual one-loop contribution as well as the dominant higher loop effects. Our numerical calculation…
We define the renormalization group flow for a renormalizable interacting quantum field in curved spacetime via its behavior under scaling of the spacetime metric, $\g \to \lambda^2 \g$. We consider explicitly the case of a scalar field,…
Extending the principle of local gauge invariance $\psi(x)\to \exp\left(\imath \sum_A \omega^A(x)T^A \right) \psi(x), x \in \mathbb{R}^d$, with $T^A$ being the generators of the gauge group $\mathcal{A}$, to the fields $\psi(g)\equiv…
It is shown that exact renormalization group (RG) equations (including rescaling and field-renormalization) for respectively the scale-dependent full action $S[\phi,t]$ and the scale-dependent full effective action $\Gamma[\Phi,t]$ --in…
It has been previously shown that calculation of renormalization group (RG) functions of the scalar \phi^4 theory reduces to the analysis of thermodynamic properties of the Ising model. Using high-temperature expansions for the latter, RG…
The renormalization group is used to improve the effective potential of massive ${\rm O}(N)$ symmetric $\phi^4$ theory. Explicit results are given at the two-loop level.
The motivation and the challenge in applying the renormalization group for systems with several scaling regimes is briefly outlined. The four dimensional $\phi^4$ model serves as an example where a nontrivial low energy scaling regime is…
The renormalization group functions are calculated in $D=4-\epsilon$ dimensions for the $\phi^4$-theory with two coupling constants associated with an ${O}(N)$-symmetric and a cubic interaction. Divergences are removed by minimal…
We explore a geometric perspective on quantum field theory by considering the configuration space, where all field configurations reside. Employing $n$-particle irreducible effective actions constructed via Legendre transforms of the…
Real-Space renormalization group techniques are developed for tackling large curvature fluctuations in quantum gravity. Within cells of invariant volume $a^4$, only certain types of fluctuations are allowed. Normal coordinates are used to…
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…
As a first application of our renormalisation group approach to non-local matrix models [hep-th/0305066], we prove (super-)renormalisability of Euclidean two-dimensional noncommutative \phi^4-theory. It is widely believed that this model is…