Related papers: Higher-derivative operators and effective field th…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
Effective theories are well established theoretical frameworks to describe the effect of energetically widely separated UV models on observables at lower energy scales. Due to the complexity of the effective theory when taking all the…
This article explores an algebraic-recursive approach to construct differential operators that commute with a central operator $\hat{H}$ in quantum mechanics. Starting from the Schr\"odinger equation for a free particle, the work derives…
We study the leading irrelevant operators along the flat directions of certain supersymmetric theories. In particular, we focus on finite N=2 (including N=4) supersymmetric field theories in four dimensions and show that these operators are…
It is known that local operators in quantum field theory transform in representations of ordinary global symmetry groups. The purpose of this paper is to generalise this statement to extended operators such as line and surface defects. We…
Ostrogradsky instability generally appears in nondegenerate higher-order derivative theories and this issue can be resolved by removing any existing degeneracy present in such theories. We consider an action involving terms that are at most…
We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.
We study a free scalar field $\phi$ in a fixed curved background spacetime subject to a higher derivative field equation of the form $F(\Box)\phi =0$, where $F$ is a polynomial of the form $F(\Box)= \prod_i (\Box-m_i^2)$ and all masses…
High derivative terms do not play a major role in field theories because of the associated complexity and inherent difficulty in connecting these terms to physically measurable quantities. A role for higher derivative terms is analyzed for…
We consider the extension of techniques for bounding higher-dimension operators in quantum effective field theories to higher-point operators. Working in the context of theories polynomial in $X=(\partial \phi)^2$, we examine how the…
The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide…
Energy momentum tensors of higher-derivative free scalar conformal field theories in flat spacetime are discussed. Two algorithms for the computation of energy momentum tensors are described, which accomplish different goals: the first is…
We classify higher-order Maxwell-Einstein theories linear in the curvature tensor and quadratic in the derivatives of the electromagnetic field strength whose kinetic matrices are degenerate. This provides a generalisation of quadratic…
In the single-field case, Horndeski provides the most general scalar-tensor theory with second-order field equations. By contrast, systematic multi-field extensions remain incomplete: while the general field equations for the bi-Horndeski…
We discuss the role of a class of higher dimensional operators in 4D N=1 supersymmetric effective theories. The Lagrangian in such theories is an expansion in momenta below the scale of "new physics" ($\Lambda$) and contains the effective…
Darboux Transformation, well known in second order differential operator theory, is applied here to the difference equation satisfied by the discrete hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn).
In this short note we explain how to use the linear equation of motions to simplify the third-order action for the cosmological fluctuations. No field redefinition is needed in this exact procedure which considerably limits the range of…
In effective field theory, the positivity bounds of higher derivative operators are derived from analyticity, causality, and unitarity. We show that the positivity bounds on some operators of the effective field theory, e.g.,…
We consider renormalisable models extended in the scalar sector by a generic scalar field in addition to the standard model Higgs boson field, and work out the effective theory for the latter in the decoupling limit. We match the full…
This article presents a natural extension of the tensor algebra. In addition to "left multiplications" by vectors, we can consider "derivations" by covectors as basic operators on this extended algebra. These two types of operators satisfy…