Related papers: Scalar Kinetic Mixing and the Renormalization Grou…
Most general renormalizable interaction in the system with a set of scalar fields having identical quantum numbers generates naturally mixed kinetic terms in the Lagrangian. Taking into account these terms leads to modification both the…
We consider the renormalization of theories with many scalar fields. We discuss at the one-loop level some simple, non-gauge models with an arbitrary number of scalars and fermions both in mass-shell and MS schemes. In MS scheme we give a…
Quantum field theories containing fields with the same quantum numbers allow for mixed kinetic terms in the Lagrangian, leading to off-diagonal elements in the tree-level two-point function. After removing the mixing by a field rotation,…
Multi-scale renormalization group (RG) methods are reviewed and applied to the analysis of the effective potential for radiative symmetry breaking with multiple scalar fields, allowing an extension of the Gildener & Weinberg (GW) method…
We show that for any effective field theory of colorless meson fields, the mixing schemes of particle states and decay constants are not only related but also determined exclusively by the kinetic and mass Lagrangian densities. In the…
The stability of tree-level relations among the parameters of a quantum field theory with respect to renormalization group (RG) running is typically explained by the existence of a symmetry. We examine a toy model of a quantum field theory…
We obtain the renormalization group(RG) functions for the massless scalar field theory where symmetry breaking occurs radiatively. After obtaining the effective potential for the radiative symmetry breaking scheme from that of the minimal…
In the context of the Renormalization Group (RG) for gravity I discuss the role of field rescalings and their relation to choices of units. I concentrate on a simple Higgs model coupled to gravity, where natural choices of units can be…
$S$-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 revisit the renormalisation of models with two U(1) gauge symmetries, in a formulation with non-canonical gauge kinetic terms which is covariant under field reparametrisations among the two gauge bosons. This approach is convenient to…
Renormalization group methods are applied to a scalar field within a finite, nonlocal quantum field theory formulated perturbatively in Euclidean momentum space. It is demonstrated that the triviality problem in scalar field theory, the…
The standard demand for the quantum partition function to be invariant under the renormalization group transformation results in a general class of exact renormalization group equations, different in the form of the kernel. Physical…
The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x << 1. Particular emphasis is paid to theories with interactions…
Starting from a well defined local Lagrangian, we analyze the renormalization group equations in terms of the two different arbitrary scales associated with the regularization procedure and with the physical renormalization of the bare…
We revisit the renormalisation group equations (RGE) for general renormalisable gauge theories at one- and two-loop accuracy. We identify and correct various mistakes in the literature for the $\beta$-functions of the dimensionful…
We show how the synergy of scaling and non-overlapping global symmetries can lead to Renormalisation Group Invariants (RGIs) among the parameters of potentials with multiple scalars. The instrumental role of scale-invariant field directions…
For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $\overline{\text{MS}}$ scheme.…
We present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective…
Recently, the connections between gradient flow and renormalization group have been explored analytically and numerically. Gradient flow (when modified by a field rescaling) can be characterized as a continuous blocking transformation. In…
Two-loop renormalization group equations in gauge theories with multiple U(1) groups are presented. Instead of normalizing the abelian gauge fields in canonical forms, we retain kinetic-mixing terms and treat the mixing coefficients as free…