Related papers: A new approach to gauge fields

We provide an action for gauge theories discretized on simplicial meshes, inspired by finite element methods. The action is discretely gauge invariant and we give a proof of consistency. A discrete Noether's theorem that can be applied to…

Gravitation theory is formulated as gauge theory on natural bundles with spontaneous symmetry breaking where gauge symmetries are general covariant transformations, gauge fields are general linear connections, and Higgs fields are…

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…

Following recent developments in discrete gravity, we study geometrical variables (angles and forms) of simplices in the discrete geometry point of view. Some of our relatively new results include: new ways of writing a set of simplices…

We consider the linear space of composite fields as an infinite dimensional vector bundle over the theory space whose coordinates are simply the parameters of a renormalized field theory. We discuss a geometrical expression for the short…

Lattice gauge theory is now well into its third decade as a major subfield of theoretical particle physics. I open these lattice sessions with a brief review of the motivations for this formulation of quantum field theory. I then comment on…

We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…

This is the second paper in a series on the dynamics of matter fields in the causal set approach to quantum gravity. We start with the usual expression for the Lagrangian of a charged scalar field coupled to a SU(n) Yang-Mills field, in…

Sen's formalism is a mechanism for eliminating constraints on the dynamical fields that are imposed independently from equations of motion by employing spurious free fields. In this note a cyclic homotopy associative algebra underlying…

We equip the whole space of fields of the triplectic formalism of Lagrangian quantization with an even supersymplectic structure and clarify its geometric meaning. We also discuss its relation to a closed two-form arising naturally in the…

Many models of beyond Standard Model physics connect flavor symmetry with a discrete group. Having this symmetry arise spontaneously from a gauge theory maintains compatibility with quantum gravity and can be used to systematically prevent…

For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…

We review a recent proposal for the construction of a quantum theory of the gravitational field. The proposal is based on approximating the continuum theory by a discrete theory that has several attractive properties, among them, the fact…

It is shown that the local completeness condition introduced in the analysis of the locality of the gauge fixed action in the antifield formalism plays also a key role in the proof of unitarity.

In this paper, we show how information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely…

The action for self-dual gauge fields that emerges from the recently constructed superstring field theory is found. The new superstring field theory reduces to that of Sen in a certain limit, and in this limit the new action for self-dual…

The quantization of the gravitational field is discussed within the exact uncertainty approach. The method may be described as a Hamilton-Jacobi quantization of gravity. It differs from previous approaches that take the classical…

Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This theory has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge…

In fundamentally discrete approaches to quantum gravity such as loop quantum gravity, spin-foam models, group field theories or Regge calculus observables are functions on discrete geometries. We present a bra-ket formalism of function…

We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…