Related papers: The Capitulation Problem in Class Field Theory
We review main features and problems of higher spin field theory and flash some ways along which it has been developed over last decades.
We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and…
This article is an overview of the vanishing cycles method in number theory over function fields. We first explain how this works in detail in a toy example, and then give three examples which are relevant to current research. The focus…
A new method for derivation of the equation of motion from the field equation is proposed. The problem of embedding the singularities in a field satisfying the field equations is discussed.
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
This is a set of introductory lecture notes devoted to the Wess-Zumino-Witten model of two-dimensional conformal field theory. We review the construction of the exact solution of the model from the functional integral point of view. The…
These lecture notes provide a relatively self-contained introduction to field theoretic methods employed in the study of classical and quantum phase transitions.
The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of…
This article defines and formulates the problem of observation learning in robotic systems.
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
This is a PhD thesis on a categorical generalization of the $BF$ model called the $BFCG$ theory. The new theory is equivalent to General Relativity at the classical level but, at the quantum level, seeks to address the problem of 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 present the proof of the equivalence theorem in quantum field theory which is based on a formulation of this problem in the field-antifield formalism. As an example, we consider a model in which a different choices of natural finite…
We give a new approach for the local class field theory of Serre and Hazewinkel. We also discuss two-dimensional local class field theory in this framework.
This master thesis seeks to understand what happens to a Quantum Field Theory when we are in the high multiplicity regime. The motivation for this study comes from a newly (2017) proposed mechanism that would happen in scalar theories in…
This paper outlines a deceptively complex problem in classical mechanics which the paper names the "Falling Astronaut Problem," and it explores a method for teachers to implement this problem in an undergraduate classroom. The paper…
The vector field problem is an important and classical problem in differential topology. In this survey we shall consider the vector field problem focusing mainly on the class of compact homogeneous spaces.
We revisit the problem of relaxation in scalar gravitational field theory proposing a novel numerical solution to the problem.
Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link…