Related papers: Categories and the Foundations of Classical Field …
Finding solutions to non-linear field theories, such as Yang-Mills theories or general relativity, is usually difficult. The field equations of Yang-Mills theories and general relativity are known to share some mathematical similarities,…
We make a short review of the formalism that describes Higgs and Yang Mills fields as two particular cases of an appropriate generalization of the notion of connection. We also comment about the several variants of this formalism, their…
The study of complex systems through the lens of category theory consistently proves to be a powerful approach. We propose that cognition deserves the same category-theoretic treatment. We show that by considering a highly-compact cognitive…
Generalized Yang-Mills theories are constructed, that can use fields other than vector as gauge fields. Their geometric interpretation is studied. An application to the Glashow-Weinberg-Salam model is briefly review, and some related…
A bivertical classical field theory include the Newtonian mechanics and Maxwell's electromagnetic field theory as the special cases. This unification allows to recognize the formal analogies among the notions of Newtonian mechanics and…
A mass distribution is analyzed in terms of classical gravitational field theory. Newton's law of gravitation is consistently applied on the assumption that the equivalence of energy and mass according to Einstein's theory of relativity is…
Modern formulations of equivalence principles provide the foundation for an efficient approach to understanding and organizing the structural features of gravitation field theories. Since theories' predictions reflect differences in their…
A retrospective analysis of the field theory of gravitation, describing gravitational field in the same way as other fields of matter in the flat space-time, is done. The field approach could be called "quantum gravidynamics" to distinguish…
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…
We formulate and explore the physical implications of a new translation gauge theory of gravity in flat space-time with a new Yang-Mills action, which involves quadratic gauge curvature and fermions. The theory shows that the presence of an…
Classical and quantum field theory provide not only realistic examples of extant notions of empirical equivalence, but also new notions of empirical equivalence, both modal and occurrent. A simple but modern gravitational case goes back to…
This survey paper is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativity theory. In the second (section 3), I discuss three special topics: (i) the status of the relative…
We consider the Hamiltonian constraint formulation of classical field theories, which treats spacetime and the space of fields symmetrically, and utilizes the concept of momentum multivector. The gauge field is introduced to compensate for…
We provide, explicitly, equivalences and dual equivalences between categories of abstract quadratic forms theories and subcategories of multifields and multirings, that will bring new perspectives and methods to the abstract theories of…
We consider various homotopy algebras related to Yang-Mills theory and two-dimensional conformal field theory (CFT). Our main objects of study are Yang-Mills $L_{\infty}$ and $C_{\infty}$ algebras and their relation to the certain algebraic…
We use category theory to propose a unified approach to the Schur-Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras…
We discuss qualitative features of the conformal relation between certain classes of gravity theories and general relativity, common to different themes such as $f(R)$, Brans-Dicke-type, and string theories. We focus primarily on the frame…
In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field. The field strength of gravitational gauge field has both gravitational electric component and gravitational magnetic component. In…
A basic problem of classical field theory, which has attracted growing attention over the past decade, is to find and classify all nonlinear deformations of linear abelian gauge theories. The first part of this paper summarizes and…
A classification of gravitating Yang--Mills systems in all dimensions is presented. These systems are set up so that they support finite energy solutions. Both regular and black hole solutions are considered, the former being the limit of…