Related papers: Matrix Gauge Fields and Noether's theorem
A general method is presented to build all gauge-invariant terms in gauge field theories, including quantum electrodynamics and quantum chromodynamics. It is applied to two experiments, light-by-light scattering and deep inelastic…
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is…
This paper presents a formulation of Noether's theorem for fractional classical fields. We extend the variational formulations for fractional discrete systems to fractional field systems. By applying the variational principle to a…
The scope of this review is to give a pedagogical introduction to some new calculations and methods developed by the author in the context of quantum groups and their applications. The review is self- contained and serves as a "first aid…
We discuss the theory of electromagnetic fields, with an emphasis on aspects relevant to radiofrequency systems in particle accelerators. We begin by reviewing Maxwell's equations and their physical significance. We show that in free space,…
We survey certain accessible aspects of Grothendieck's theory of motives in arithmetic algebraic geometry for mathematical physicists, focussing on areas that have recently found applications in quantum field theory. An appendix (by Matilde…
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
Puts forward a complete scenario for interpreting nonlinear field theories highlighting the role played by gravitational self--energy in enabling a consistent revival of the Schroedinger approach to unifying micro and macro physics.
Modifications of General Relativity usually include extra dynamical degrees of freedom, which to date remain undetected. Here we explore the possibility of modifying Einstein's theory by adding solely nondynamical fields. With the minimal…
Elementary particle scatterings and decays in presence of a background magnetic field are very common in physics, specially after the observation that the core of the neutron stars can sustain a magnetic field of the order of $10^{13} {\rm…
In this paper (Part I of a series of three papers) an axiomatic formulation of GR is given, here use is made of the concept of pre-radar charts. These charts have "infinitesimally" the same properties as the true radar charts used in…
Using a generalised Noether prescription we are able to extract all the currents and their conservation laws in space dependent shift symmetric theories. Various identities among the currents in the matter sector are found that form the…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
Those articles (versions) explore a non conventional pregeometrical model encompassing quantics and geometrodynamics (a stochastic graph relational theory). Some key points are : 1) the use of simple boolean atom-like far subquantum…
We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar…
This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe…
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…
We present a formalism for analysis of linear Cauchy data on a Kottler metric. Our method removes redundancy due to gauge transformations and constraints. A set of four gauge-invariant, scalar functions on the Cauchy surface is produced and…
This article focuses on three main contributions. Firstly, we provide an in-depth overview of the nonlocal Lagrangian formalism. Secondly, we introduce an extended version of the second Noether's theorem tailored for nonlocal Lagrangians.…
Noether's theorem and the invariances of the Willmore functional are used to derive conservation laws that are satisfied by the critical points of the Willmore energy subject to generic constraints. We recover in particular previous results…