Related papers: Geometric Hamilton-Jacobi Field Theory
We propose a new class of filtered vector bundles, which is related to variation of (mixed) Hodge structures and give a slight generalization of the Fujita--Zucker--Kawamata semipositivity theorem.
We explain how to construct a cohomology theory on the category of separated quasi-compact smooth rigid spaces over $\mathbf{C}_p$ (or more general base fields), taking values in the category of vector bundles on the Fargues-Fontaine curve,…
Hamilton-Jacobi theory provides a natural starting point for a covariant description of the gravitational field. Using a spatial gradient expansion, one may solve for the phase of the wavefunction by using a line-integral in superspace.…
We present a systematic treatment of line bundle geometry and Jacobi manifolds with an application to geometric mechanics that has not been noted in the literature. We precisely identify categories that generalise the ordinary categories of…
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 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…
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…
In this paper, we will give the polyhedron property role to satisfy fiber homotopically equivalent relation in fiber bundle theory over suspensions of polyhedron space.
We consider a family of vector fields and we assume a horizontal regularity on their derivatives. We discuss the notion of commutator showing that different definitions agree. We apply our results to the proof of a ball-box theorem and…
To understand in detail duality between heterotic string and F theory compactifications, it is important to understand the construction of holomorphic G bundles over elliptic Calabi-Yau manifolds, for various groups G. In this paper, we…
In this survey, we review the classical Hamilton Jacobi theory from a geometric point of view in different geometric backgrounds. We propose a Hamilton Jacobi equation for different geometric structures attending to one particular…
The Hamilton-Jacobi formalism generalized to 2-dimensional field theories according to Lepage's canonical framework is applied to several relativistic real scalar fields, e.g. massless and massive Klein-Gordon, Sinh and Sine-Gordon,…
This paper contains a long summary of the basic properties of higher FR torsion. An attempt is made to simplify the constructions from my book Higher Franz-Reidemeister Torsion (IP/AMS Studies in Advanced Math 31). Some new basic theorems…
Hyperbolic lattices underlie a new form of quantum matter with potential applications to quantum computing and simulation and which, to date, have been engineered artificially. A corresponding hyperbolic band theory has emerged, extending…
This is a continuation of the work initiated in a previous paper on so-called driven cofactor systems, which are partially decoupling second-order differential equations of a special kind. The main purpose in that paper was to obtain an…
Classical constrained Hamiltonian theory assumes complete observability of system states, but in reality only partial state information is often available. This paper establishes a complete geometric theoretical framework for handling such…
The fibre bundle formulation of gauge theory is generally accepted. The jet manifold machinery completes this formulation and provides the adequate mathematical description of dynamics of fields represented by sections of fibre bundles.…
We develop a constructive procedure for arriving at the Hamilton-Jacobi framework for the so-called affine in acceleration theories by analysing the canonical constraint structure. We find two scenarios in dependence of the order of the…
For higher derivative theories, using the approach of Caratheodory's equivalent Lagrangian, we show that there exist novel formulations of Hamilton-Jacobi equations, which are different from the formulations derived from Hamilton's…
The Hamilton-Jacobi equation for a Hamiltonian section on a Lie affgebroid is introduced and some examples are discussed.