Related papers: Symplectic field theory: an overview
The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of…
A rough overview is given over the most essential structures underlying all working quantum theoretical models as well as axiomatic and algebraic quantum field theory .
We give two definitions of relative symplectic Steinberg group and show that they coincide.
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
After briefly reviewing basic concepts of perturbative string theory, we explain in simple terms some of the new findings that created excitement among the string physicists. These developments include non-perturbative dualities and a…
Bielavsky introduced and investigated the class of symmetric symplectic spaces, that is, symmetric spaces endowed with a symplectic form invariant with respect to symmetries. Since the theory of symmetric spaces has generalizations, we ask…
This is a survey of various types of Floer theories (both in symplectic geometry and gauge theory) and relations among them.
This paper summarizes the results in Integral Biomathics obtained to this moment and provides an outlook for future research in the field.
In this talk I describe a recently introduced field-theoretical approach that can be used as an alternative framework to study one-dimensional systems of highly correlated particles.
We provide a short and non-technical summary of our current knowledge and some possible perspectives on the group field theory formalism for quantum gravity, in the form of a (partial) FAQ (with answers). Some of the questions and answers…
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory.…
This review summarizes Effective Field Theory techniques, which are the modern theoretical tools for exploiting the existence of hierarchies of scale in a physical problem. The general theoretical framework is described, and explicitly…
We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the…
We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum…
We discuss a few selected topics in finite temperature field theory.
Over the past decade, Finite Temperature Quantum Field Theories have benefitted from impressive developments, while an increasing number of intriguing points were made. Some of them are presented here, recent and older, in a non exhaustive…
New types of maximal symplectic partial spreads are constructed.
String Field Theory is a formulation of String Theory as a Quantum Field Theory in target space. It allows to tame the infrared divergences of String Theory and to approach its non-perturbative structure and background independence. This…
We discuss some aspects of the theory of subelliptic estimates.