Related papers: Counting operators in Effective Field Theories
Since Weinberg's proposal two decades ago, chiral effective field theory in the NN sector has been developed and applied up to order $O((Q/M_{hi})^4)$. In principle it could provide a model-independent description of nuclear force from QCD.…
General formulation for the effective field theory with differential operator technique and the decoupling approximation with larger finite clusters (namely EFT-$N$ formulation) has been derived, for S-1/2 bulk systems. The effect of the…
We implement methods from the geometry of numbers to give explicit estimates for the number of integral ideals in a number field. We pay particular attention to minimising the effect of the degree $n$ of the number field on the error term…
Effective Field Theory calculations used in countless phenomenological analyses employ dimensional regularization, and at intermediate stages of computations, the operator bases extend beyond the four-dimensional ones. The extra pieces --…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
We define a notion of formal quantum field theory and associate a formal quantum field theory to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfaces. This enables us to find an effective way to compute…
Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with…
The application of the effective field theory (EFT) method to nuclear systems is reviewed. The roles of degrees of freedom, QCD symmetries, power counting, renormalization, and potentials are discussed. EFTs are constructed for various…
Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low ultraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term…
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…
It is important to obtain effective operators by integrating out high energy degrees of freedom in physics. We suggest a general method of calculating accurate irrelevant operators in a scattering process without use of equation of motions.…
Using effective field theory, we calculate the S-factor for the hep process in a totally parameter-free formulation. The transition operators are organized according to chiral counting, and their matrix elements are evaluated using the…
In resonance to a recent geometric framework proposed by Douglas and Yang, a functional model for certain linear bounded operators with rank-one self-commutator acting on a Hilbert space is developed. By taking advantage of the refined…
We present a clear, step-by-step method for counting degrees of freedom and identifying constraints in general field theories. This approach, grounded in the works of Einstein, Hilbert, Cartan, Kuranishi, and, more recently, Seiler, is…
The analytic aspects of the operator realization of Wick power series of infrared singular free fields are considered. Taking advantage of the holomorphy properties of the two-point correlation function and its Hilbert majorant in x-space,…
The use of effective field theory offers a systematic way to improve calculations of nuclear reactions and the properties of atomic nuclei. Its successes have led to the widespread belief that the predictions of this approach are model…
The methods of integral operators on the cohomology of Hilbert schemes of points on surfaces are developed. They are used to establish integral bases for the cohomology groups of Hilbert schemes of points on a class of surfaces (and…
We discuss the role effective field theory plays in making predictions in nuclear physics in an approach that combines both the high sophistication of the standard nuclear many-body approach and the power of systematic higher chiral-order…
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…