Related papers: Operator bases, $S$-matrices, and their partition …
We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of $S$-matrix elements, in arbitrary spacetime dimensions and with…
We introduce a systematic framework for counting and finding independent operators in effective field theories, taking into account the redundancies associated with use of the classical equations of motion and integration by parts. By…
We present the first complete non-redundant operator basis for the Standard Model Effective Field Theory (SMEFT) at finite temperature, using the imaginary-time formalism. By employing the Hilbert series method on the space-time manifold…
Effective Field Theory technique is one of the most elegant ways to capture the impact of high scale theory, if any, at some low energy by incorporating higher mass dimensional ($\geq 5$) effective operators ($\mathcal{O}_i$). The low…
We implement modular flavor symmetries within the Standard Model Effective Field Theory (SMEFT) framework, using the flavor group $A_4^{(q)} \times A_4^{(e)}$ with distinct moduli $\tau_q$ and $\tau_e$, and assigning different modular…
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…
Identifying a full basis of operators to a given order is key to the generality of Effective Field Theory (EFT) and is by now a problem of known solution in terms of the Hilbert series. The present work is concerned with hidden symmetry in…
We present DECO ("Discrete and Efficient Counting of Operators"), an implementation of the Hilbert Series to enumerate subleading operator bases for SMEFT-like EFTs with symmetry groups as typically found in flavour and BSM physics. DECO…
Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…
The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…
In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…
In this paper we introduce a Hilbert series approach to build the operator basis for a N = 1 supersymmetry theory with chiral superfields. We give explicitly the form of the corrections that remove redundancies due to the equations of…
This work establishes a systematic framework for operator construction in the non-relativistic effective field theory, incorporating both the three dimensional Euclidean symmetry and the internal symmetries. By employing double cover of the…
S-matrix is one of the fundamental observables of the quantum theory of relativistic particles. There have been attempts to understand the quantum dynamics of relativistic particles abstractly in terms of S-matrix bypassing a Lagrangian…
In this paper it is investigated how to find a matrix representation of operators on a Hilbert space with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs).…
The standard model effective field theory (SMEFT) provides systematic parameterization of all possible new physics above the electroweak scale. According to the amplitude-operator correspondence, an effective operator can be decomposed into…
The main purpose of this paper is to construct convergent series for the approximate calculation of certain integrals over the Gaussian measure with a nuclear covariance operator, nonlocal propagator, in separable Hilbert space. Such series…
We study models that give rise to scalar-tensor effective field theories (EFTs) at low energies. Our framework involves massive particles of spin $S=0, 1/2, 1$ coupled to gravity and to a real massless scalar in the UV. Integrating out the…
In the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of "physical experiment" and assuming "experimental accessibility and simplicity" as specified by…
We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…