Related papers: Composite operators and algebra constraints: a for…
We study the aspects of constructing the interactions for the higher spin fields in the framework of BRST approach. The main object of such an approach is BRST operator acting in the appropriate Fock space and building on the base of…
We give a formula for the derivatives of a correlation function of composite operators with respect to the parameters (i.e., the strong fine structure constant and the quark mass) of QCD in four-dimensional euclidean space. The formula is…
Central issues of the Dirac constraint formalism are discussed in relation to the algorithmic methods of commutative algebra based on the Groebner basis techniques. For a wide class of finite dimensional polynomial degenerate Lagrangian…
We study the effective potential for composite operators. Introducing a source coupled to the composite operator, we define the effective potential by a Legendre transformation. We find that in three or fewer dimensions, one can use the…
Compositional Explanations is a method for identifying logical formulas of concepts that approximate the neurons' behavior. However, these explanations are linked to the small spectrum of neuron activations (i.e., the highest ones) used to…
Autonomous systems require the management of several model views to assure properties such as safety and security among others. A crucial issue in autonomous systems design assurance is the notion of emergent behavior; we cannot use their…
The $\beta\gamma$ system is generalized by complex(rational) powers of the fields, which leads to a corresponding extension on the Fock space. Two different approaches to compute the Green functions of the physical operators are proposed.…
A comprehensive approach to the theory of higher spin gauge fields is proposed. By explicitly separating out details of implementation from general principles, it becomes possible to focus on the bare minimum of requirements that such a…
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…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
We develop a framework for multiscale analysis of elliptic operators with high-contrast random coefficients. For a general class of such operators, we provide a detailed spectral analysis of the corresponding homogenised limit operator.…
This paper presents an analytical treatment of economic systems with an arbitrary number of agents that keeps track of the systems' interactions and agents' complexity. This formalism does not seek to aggregate agents. It rather replaces…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
We establish elements of a new approch to ellipticity and parametrices within operator algebras on a manifold with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales…
In this paper, we give a multiplication operator representation of bounded self-adjoint operators T on a Hilbert space H such that -- is a frame for H, for some -- . We state a necessary condition in order for a frame -- to have a…
In this paper, we propose to consider various models of pattern recognition. At the same time, it is proposed to consider models in the form of two operators: a recognizing operator and a decision rule. Algebraic operations are introduced…
A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems,…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…