Related papers: Constructive Field Theory and Applications: Perspe…
We look for a deep connection between mathematics and physics. Our approach is to propose a set theory T which leads to a concise mathematical description of physical fields and to a finite unit of action. The concept of "definability" of…
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
A selection of open problems in the theory of composites is presented. Particular attention is drawn to the question of whether two-dimensional, two-phase, composites with general geometries have the same set of possible effective tensors…
Two major learning theories have dominated recent literature on optimizing knowledge acquisition: constructivism and cognitive load theory. Constructivism, on the one hand, gives preeminent value to the development of students'…
There is growing interest in nuclear physics applications of effective field theory. I give a brief account of some of the latest developments in this area. I also describe interplay between this new approach and the traditional nuclear…
What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and…
Effective field theory is considered to provide a highly useful framework for connecting nuclear physics with the symmetries and dynamics of the underlying theory of strong interactions, QCD. Of many issues that are of great current…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
This short article is devoted to the dynamics of controlled (and, therefore, open) systems. The internal forces, which appear only in the presence of external free controls and depend explicitely on them, are considered. Such interactive…
Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…
I review the construction of an action for open superstring field theory which does not suffer from the contact term problems of other approaches. I also discuss a possible generalization of this action for closed superstring field theory.
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
For a wide class of nonlinear equations a perturbative solution is constructed. This class includes equations of motion of field theories. The solution possesses a graphical representation in terms of diagrams. To illustrate the formalism…
Research on spatially-structured light has seen an explosion in activity over the past decades, powered by technological advances for generating such light, and driven by questions of fundamental science as well as engineering applications.…
The central theme of this thesis is to study some aspects of noncommutative quantum mechanics and noncommutative quantum field theory. We explore how noncommutative structures can emerge and study the consequences of such structures in…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field…
A confluence of theoretical and technological developments are beginning to make possible contributions to nuclear physics from lattice QCD. Effective field theory plays a critical role in these advances. I give several examples.
I review basic concepts of chiral effective field theories guided by an historical perspective: from the first ideas to the merging with other effective frameworks, and to the interplay with lattice field theory. The impact of recent…