Related papers: A new approach to gauge fields
The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…
We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
In this talk we describe our recent work on discrete quantum theory based on Galois fields. In particular, we discuss how discrete quantum theory sheds new light on the foundations of quantum theory and we review an explicit model of…
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…
Gauge field theories may quite generally be defined as describing the coupling of a matter-field to an interaction-field, and they are suitably represented in the mathematical framework of fiber bundles. Their underlying principle is the…
Simulating magnetic effects with cold gases of neutral atoms is a challenge. Since these atoms have no charge, one needs to create artificial gauge fields by taking advantage of the geometric phases that can result for instance from…
We discuss the physical meaning and the geometric interpretation of causality implementation in classical field theories. Causality is normally implemented through kinematical constraints on fields but we show that in a zero-distance limit…
Recently a manifestly gauge invariant formalism for calculating amplitudes in quantum electrodynamics was outlined in which the field strength, rather than the gauge potential, is used as the propagating field. To demonstrate the utility of…
We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the…
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…
Discretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is over a century old. However there is no general theory or methodology in the literature, despite the ubiquitous use of…
We make a systematic development of the non-Abelian formulation of two-form gauge fields with topological coupling with the Yang-Mills one-form connection. An analysis of the gauge structure, reducibility conditions and physical degrees of…
The notion of gauge transform has its origin in Physics (Field Theory). In the present note we discuss -- from a purely mathematical perspective -- special gauge transforms of autonomous first order ODE's and their special properties.…
The symmetry reduction of dynamical systems that are invariant under changes of global scale is well-understood for classical theories of particles, and fields. The excision of the superfluous degree of freedom generating such rescalings…
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…
Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…
The nature of gravitational singularities has been questioned by some recent research, challenging the notion that classical determinism breaks down at these points. By allowing for dynamic changes in the orientation of spatial…
We discuss a remarkable new approach initiated by Cachazo, Svrcek and Witten for calculating gauge theory amplitudes. The formalism amounts to an effective scalar perturbation theory which in many cases offers a much simpler alternative to…