相关论文: Systematic Operator Construction for Non-relativis…
We fully solve the long-standing problem of operator basis construction for fields with any masses and spins. Based on the on-shell method, we propose a novel method to systematically construct a complete set of lowest dimensional amplitude…
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…
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…
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…
We describe a general procedure to construct the independent and complete operator bases for generic Lorentz invariant effective field theories, given any kind of gauge symmetry and field content, up to any mass dimension. By considering…
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 focuses on non-compact groups and their applications to quantum gravity, mainly through the use of tensor operators. First, the mathematical theory of tensor operators for a Lie group is recast in a new way which is used to…
Relativistic quantum systems that admit scattering experiments are quantitatively described by effective field theories, where $S$-matrix kinematics and symmetry considerations are encoded in the operator spectrum of the EFT. In this paper…
We present a systematic procedure for determining the Hilbert series that counts the number of independent operators in the Higgs effective field theory. After removing the redundancies from equation-of-motion and integration-by-part, we…
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…
We propose an effective field theory to describe hadrons with two heavy quarks without any assumption on the typical distance between the heavy quarks with respect to the typical hadronic scale. The construction is based on Non-Relativistic…
In this chapter of the book entitled, "Extending the Theory of Composites to Other Areas of Science" [edited by Graeme W. Milton, 2016] we give a rigorous derivation of the field equation recursion method in the abstract theory of…
In this paper we develop a Young diagram approach to constructing higher dimensional operators formed from massless superfields and their superderivatives in $\mathcal{N}=1$ supersymmetry. These operators are in one-to-one correspondence…
We use a Hilbert series to construct an operator basis in the $1/m$ expansion of a theory with a nonrelativistic heavy fermion in an electromagnetic (NRQED) or color gauge field (NRQCD/HQET). We present a list of effective operators with…
We enumerate the complete and independent sets of operators at the next-to-leading order (NLO) in the Higgs effective field theory (HEFT), based on the Young tensor technique on the Lorentz, gauge and flavor structures. The…
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…
We systematically develop the Hilbert series technique for counting independent operators in Effective Field Theories. In the hope of providing more approachable entry point to the subject we include a detailed introduction of all necessary…
An operator basis of an effective theory with a heavy particle, subject to external gauge fields, is spanned by a particular kind of neutral scalar primary of the nonrelativistic conformal group. We calculate the characters that can be used…
Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in…
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…