Related papers: Effective Field Theories on the Jet Bundle
We investigate the ghostfree scalar-tensor theory with a timelike scalar field, with derivatives of the scalar field up to the third order and with the Riemann tensor up to the quadratic order. We build two types of linear spaces. One is…
This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes with connection and their morphisms, and explain…
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to $L_VY$, the bundle of vertically adapted linear frames over the…
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.
Dynamical symmetries of Born-Infeld theory associated with its maximal field strength are encoded in a geometry on the tangent bundle of spacetime manifolds. The resulting extension of general relativity respecting a finite upper bound on…
We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group $G$. As coefficients, we allow $E_\infty$-algebras with $G$-action. For this homology theory, we establish an equivariant…
We give in this paper which is the fifth in a series of eight a theory of covariant derivatives of multivector and extensor fields based on the geometric calculus of an arbitrary smooth manifold M, and the notion of a connection extensor…
We demonstrate that it is conceptually and computationally favorable to regard spin-weighted spherical harmonics as vector valued functions on the total space $SO(3)$ of the Hopf bundle, satisfying a covariance condition with respect to the…
We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
I briefly review my proposal about how to extend the geometric Hamilton-Jacobi theory to higher derivative field theories on fiber bundles.
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
In this paper we introduce a generalization of Hamiltonian mechanics that replaces configuration spaces, conventionally regarded simply as smooth manifolds, with line bundles over smooth manifolds. Classical observables are then identified…
This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
Consider a fiber bundle in which the total space, the base space and the fiber are all symplectic manifolds. We study the relations between the quantization of these spaces. In particular, we discuss the geometric quantization of a vector…
We consider the geometric formulation of the Hamiltonian formalism for field theory in terms of {\em Hamiltonian connections} and {\em multisymplectic forms}. In this framework the covariant Hamilton equations for Mechanics and field theory…
We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…
Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…
We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…