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For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic…
In linearized quantum gravity, a shift of the average energy-momentum can be compensated by a shift of the average gravitational field. This allows a renormalization scheme that naturally removes the contribution of quantum vacuum…
We review the effective field theories (EFTs) developed for few-nucleon systems. These EFTs are controlled expansions in momenta, where certain (leading-order) interactions are summed to all orders. At low energies, an EFT with only contact…
Renormalization group ideas and effective operators are used to efficiently determine localized unitaries for preparing the ground states of non-interacting scalar field theories on digital quantum devices. With these methods, classically…
We study Monte Carlo calculations of the effective potential for a scalar field theory using three techniques. One of these is a new method proposed and tested for the first time. In each case we extract the renormalised quantities of the…
Following the previously developed approach to the calculation of quantum corrections to the effective potential in arbitrary scalar field theories in the leading logarithmic approximation, we extended it to the next-to-leading order. Based…
We have addressed the issue of field redefinition in connection with renormalisability. Our study is restricted to theories of interacting scalar fields. We have, in particular, shown that if a theory is renormalisable in the usual…
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…
Quantum cosmology is traditionally formulated in a minisuperspace setting, implicitly averaging fields over space to obtain homogeneous models. For universal reasons related to the uncertainty principle, quantum corrections then depend on…
Nonrenormalizable quantum field theories require counterterms; and based on the hard-core interpretation of such interactions, it is initially argued, contrary to the standard view, that counterterms suggested by renormalized perturbation…
An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what…
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…
We review recent developments in tensor network approaches, focusing on renormalization group methods. Since they are free from the negative sign and complex action problems, there is growing interest in their application to lattice field…
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space).…
We relate renormalization in perturbative quantum field theory to the theory of limiting mixed Hodge structures using parametric representations of Feynman graphs.
We provide an elementary pedagogical introduction to some basic concepts and techniques of soft (or Sudakov) resummation, specifically in QCD, paying particular attention to simple but useful tricks of the trade. We briefly review collinear…
We derive a universal formula for the one-loop renormalization of the effective K\"ahler potential that applies to general supersymmetric effective field theories of chiral multiplets, with arbitrary interactions respecting N=1…
Techniques based on $n$-particle irreducible effective actions can be used to study systems where perturbation theory does not apply. The main advantage, relative to other non-perturbative continuum methods, is that the hierarchy of…
We briefly review the Hopf algebra structure arising in the renormalization of quantum field theories. We construct the Hopf algebra explicitly for a simple toy model and show how renormalization is achieved for this particular model.
The long standing problem of a non-perturbative renormalization of a gauge field theoretical Hamiltonian is addressed and explicitly carried out within an (effective) light-cone Hamiltonian approach to QCD. The procedure is in line with the…