Related papers: Counting operators in Effective Field Theories
Of crucial importance to the development of quantum computing and information has been the construction of a quantum operations formalism that admits a description of quantum noise while simultaneously revealing the behavior of an open…
Strongly correlated electron systems require the development of new theoretical schemes in order to describe their unusual and unexpected properties. The usual perturbation schemes are inadequate and new concepts must be introduced. In our…
Category and multicategory theory provide abstract frameworks for describing structures and their compositions, with multicategories extending traditional categories to handle multi-input operations. These theories enable modular reasoning…
We review the effective field theories (EFTs) developed for few-nucleon systems. These EFTs are controlled expansions in momenta, where certain (leading-order) interactions are summed to all orders. At low energies, an EFT with only contact…
We outline a proposal, based on the Heat-Kernel method, to compute 1PI effective action up to any loop order for quantum field theory with scalar and fermion fields. We algebraically extract the divergences associated with the composite…
In this paper we study expansions of infinite dimensional Hilbert spaces with a unitary representation of a discrete countable group. When the group is finite, we prove the theory of the corresponding expansion, regardless if it is…
We give a function field specific, algebraic proof of the main results of class field theory for abelian extensions of degree coprime to the characteristic. By adapting some methods known for number fields and combining them in a new way,…
The asymptotic strong-coupling behavior as well as the exact critical exponents from scalar field theory even in the simplest case of $1+1$ dimensions have not been obtained yet. Hagen Kleinert has linked both critical exponents and strong…
Let $K$ be a global field of positive characteristic. We give an asymptotic formula for the number of $K$-points of bounded height on the Hilbert scheme $\text{Hilb}^2\mathbb{P}^2$ and show that by eliminating an exceptional thin set, the…
We introduce the notion of fully Hilbertian fields, a strictly stronger notion than that of Hilbertian fields. We show that this class of fields exhibits the same good behavior as Hilbertian fields, but for fields of uncountable…
A system of fermions with short-range interactions at finite density is studied using the framework of effective field theory. The effective action formalism for fermions with auxiliary fields leads to a loop expansion in which…
A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties…
We apply the Hilbert series to extend the gravitational action for a scalar field to a complete, non-redundant basis of higher-dimensional operators that is quadratic in the scalars and the Weyl tensor. Such an extension of the action fully…
The one loop effects of two dimension-six operators on gauge boson self energies are computed within an effective field theory framework. These self energies are translated into effects on precision electroweak observables, and bounds are…
If the dynamics behind EWSB are of strongly-coupled nature, the Standard Model ceases to be renormalizable and should be instead understood as an effective field theory (EFT). Here I will discuss the systematics behind this effective field…
The first step in the counting operator analysis of the spectrum of any model Hamiltonian H is the choice of a Hermitean operator M in such a way that the third commutator with H is proportional to the first commutator. Next one calculates…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
The present review presents the authors previous results on the topic from the title in a new light. Most of the previous results were obtained using the techniques of antilinear Hilbert-Schmidt mappings of one Hilbert pace into another,…
We introduce a diagrammatic quantum field formalism for the evaluation of normalized expectation values of operators, and suitable for systems with localized electrons. It is used to develop a convergent series expansion for the energy in…