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We extend the OPE-based renormalization algorithm to composite operators with operator mixing, focusing on scalar operators in $\phi^4$ and $\phi^3$ models. Using the OPE of operators with a fundamental field, we show that the $Z$-factors…
We discuss the action of the configuration operators of loop quantum gravity. In particular, we derive the generalised eigenbasis for the Wilson loop operator and show that the transformation between this basis and the spin-network basis is…
The presence of an infinite number of marginal four-fermion operators is a key characteristic of the two-dimensional Gross-Neveu model. In this study, we investigate the structure of UV divergences in this model, and by symmetry argument we…
Using the tool of unitary transformations of the extended receiver we perform simple operations with the non-diagonal elements of the initial sender's density matrix after their transferring to the receiver. These operations are following:…
We renormalize massless scalar effective field theories (EFTs) to higher loop orders and higher orders in the EFT expansion. To facilitate EFT calculations with the R* renormalization method, we construct suitable operator bases using…
It may be possible to use operator regularization with Feynman diagrams, which would greatly simplify its use as it has so far been limited to the more complicated Schwinger approach. Operator regularization, unlike $\zeta$-function…
We provide the renormalization constants of the axial current operators, both singlet and non-singlet, in dimensional regularization up to four-loop order in QCD, determined using the off-shell Ward-Takahashi identity for an axial current…
We derive a basis for the vector space of bounded operators acting on a $d$-dimensional system Hilbert space $C^d$. In the context of quantum computation the basis elements are identified as the generalised Pauli matrices - the error…
It has been shown that the negative norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter space [1,2]. In this process ultraviolet and infrared divergences have been automatically…
Six-loop massive scheme renormalization group functions of a d=3-dimensional cubic model (J.M. Carmona, A. Pelissetto, and E. Vicari, Phys. Rev. B vol. 61, 15136 (2000)) are reconsidered by means of the pseudo-epsilon expansion. The…
Four-fermion operators have been utilized in the past to link the quark-exchange processes in the interaction of hadrons with the effective meson-exchange amplitudes. In this paper, we apply the similar idea of a Fierz rearrangement to the…
We derive bases of improved operators for all bilinear quark currents up to spin two (including the operators measuring the first moment of DIS Structure Functions), and compute their one-loop renormalization constants for arbitrary…
In this paper we describe a novel, graphical method, allowing the fast computation of field operator transformations for linear lossless optical devices in Quantum Optics (QO). The advantage of this method grows with the complexity of the…
We calculate one loop $y_t$ and $\lambda$ dependent corrections to $\bar{\Gamma}_Z,\bar{R}_f^0$ and the partial $Z$ widths due to dimension six operators in the Standard Model Effective Field Theory (SMEFT), including finite terms. We…
The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel…
Understanding the scale dependence of parton distribution functions is vital for precision physics at hadron colliders. The well-known DGLAP evolution equation relates this scale dependence to the QCD splitting functions, which can be…
We review the techniques necessary for the calculation of virtual electroweak and soft photonic corrections at the one-loop level. In particular we describe renormalization, calculation of one-loop integrals and evaluation of one-loop…
Many state-of-the-art QCD calculations for multileg processes use helicity amplitudes as their fundamental ingredients. We construct a simple and easy-to-use helicity operator basis in soft-collinear effective theory (SCET), for which the…
We study the phenomenology of the simplest renormalisable model that, at low energy, leads to the effective field theory of the Standard Model extended with right-handed neutrinos ($\nu$SMEFT). Our aim is twofold. First, to contextualise…
We discuss an application of the transfer operator approach to the analysis of the different spectral characteristics of 1d random band matrices (correlation functions of characteristic polynomials, density of states, spectral correlation…