Related papers: Composite operators and algebra constraints: a for…
We present the Composite Operator Method (COM) as a modern approach to the study of strongly correlated electronic systems, based on the equation of motion and Green's function method. COM uses propagators of composite operators as building…
The Green's function formalism in Condensed Matter Physics is reviewed within the equation of motion approach. Composite operators and their Green's functions naturally appear as building blocks of generalized perturbative approaches and…
The Composite Operator Method (COM) is formulated, its internals illustrated in detail and some of its most successful applications reported. COM endorses the emergence, in strongly correlated systems (SCS), of composite operators,…
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…
Cooperative constraint solving is an area of constraint programming that studies the interaction between constraint solvers with the aim of discovering the interaction patterns that amplify the positive qualities of individual solvers.…
A well-established method to deal with highly correlated systems is based on the expansion of the Green's function in terms of spectral moments. In the context of the Composite Operator Method one approximation is proposed: a set of n…
At present an algebra of strongly interacting fields is unknown. In this paper it is assumed that the operators of strongly nonlinear field can form a non-associative algebra. It is shown that such algebra can be described as an algebra of…
An operator formalism for bosonic $\beta-\gamma$ systems on arbitrary algebraic curves is introduced. The classical degrees of freedom are identified and their commutation relations are postulated. The explicit realization of the algebra…
This paper provides a description of an algebraic setting for the Lagrangian formalism over graded algebras and is intended as the necessary first step towards the noncommutative C-spectral sequence (variational bicomplex). A noncommutative…
While the properties of materials at microscopic scales are well described by fundamental quantum mechanical equations and electronic structure theories, the emergent behavior of mesoscopic or macroscopic composites is no longer governed…
In this paper, we introduce product interactions, an algebraic formalism in which neural network layers are constructed from compositions of a multiplication operator defined over suitable algebras. Product interactions provide a principled…
The constraint operators belonging to a generally covariant system are found out within the framework of the BRST formalism. The result embraces quadratic Hamiltonian constraints whose potential can be factorized as a never null function…
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…
Some well-known examples of constrained quantum systems commonly quantized via Feynman path integrals are re-examined using the notion of conditional integrators introduced in [1]. The examples yield some new perspectives on old results. As…
We present a concise, but systematic, review of the ergodicity issue in strongly correlated systems. After giving a brief historical overview, we analyze the issue within the Green's function formalism by means of the equations of motion…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
Graph rewrite formalisms are a powerful approach to modeling complex molecular systems. They capture the intrinsic concurrency of molecular interactions, thereby enabling a formal notion of mechanism (a partially ordered set of events) that…
In this paper we propose an algebraic formalization of connectors in the quantitative setting, in order to address their non-functional features in architectures of component-based systems. We firstly present a weighted Algebra of…
In this work, we study the t-J model using a two-pole approximation within the composite operator method. We choose a basis of two composite operators -- the constrained electrons and their spin-fluctuation dressing -- and approximate their…