Related papers: Evolution of Ehresmann's jet theory

Even though jet substructure was not an original design consideration for the Large Hadron Collider (LHC) experiments, it has emerged as an essential tool for the current physics program. We examine the role of jet substructure on the…

The purpose of this essay is to trace the historical development of geometry while focusing on how we acquired mathematical tools for describing the "shape of the universe." More specifically, our aim is to consider, without a claim to…

We formulate higher order variations of a Lagrangian in the geometric framework of jet prolongations of fibered manifolds. Our formalism applies to Lagrangians which depend on an arbitrary number of independent and dependent variables,…

The jet shape is a simple measure of how widely a jet's energy is spread. At present jet shape distributions have only been calculated to leading order in perturbative QCD. In this paper we consider how much these predictions should be…

Recent progress in the perturbative analysis of hadronic jets, especially in the context of hadron colliders, is discussed. The characteristic feature of this work is the emergence of a level of precision in the study of the strong…

The idea of a unified model for quasars and micro-quasars has been considered for a long time, despite the different environments and physical conditions where both classes of objects reside. Here we show the existence of a simple scaling…

We investigate closed ideals in the Grassmann algebra serving as bases of Lie-invariant geometric objects studied before by E. Cartan. Especially, the E. Cartan theory is enlarged for Lax integrable nonlinear dynamical systems to be treated…

We show how to map gravitational theories formulated in the Jordan frame to the Einstein frame at the quantum field theoretical level considering quantum fields in curved space-time. As an example, we consider gravitational theories in the…

These notes provide an introduction to the algebra and geometry of differential operators and jet bundles. Their point of view is guided by the leitmotiv that higher-spin gravity theories call for higher-order generalisations of Lie…

A classical derivation of Betz's law is first presented along with some insights. The extended Betz's theory is deduced for a rotor with axis orthogonal to the direction of an ideal fluid in uniform motion. The conceptual design used to…

We shall here propose a class of relativistic theories of gravitation, based on a foundational paper of Ehlers Pirani and Schild (EPS).All "extended theories of gravitation" (also known as f(R) theories) in Palatini formalism are shown to…

This thesis studies modified theories of gravity from a geometric viewpoint. We review the motivations for considering alternatives to General Relativity and cover the mathematical foundations of gravitational theories in Riemannian and…

We introduce a new class of event shapes to characterize the jet-like structure of an event. Like traditional event shapes, our observables are infrared/collinear safe and involve a sum over all hadrons in an event, but like a jet…

The statement of the Riemann hypothesis makes sense for all global fields, not just the rational numbers. For function fields, it has a natural restatement in terms of the associated curve. Weil's work on the Riemann hypothesis for curves…

We provide an easy approach to the geodesic distance on the general linear group GL(n) for left-invariant Riemannian metrics which are also right-O(n)-invariant. The parametrization of geodesic curves and the global existence of length…

Einstein gravitation theory can be extended by preserving its geometrical nature but changing the relation between curvature and energy-momentum tensors. This change accounts for radiative corrections, replacing the Newton gravitation…

The Einstein-Cartan-Saa theory of torsion modifies the spacetime volume element so that it is compatible with the connection. The condition of connection compatibility gives constraints on torsion, which are also necessary for the…

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…

We construct a theory of particles moving in curved both momentum space and spacetime, being a generalization of Relative Locality. We find that in order to construct such theory, with desired symmetries, including the general coordinate…

With the explosion of data on jet based observables in relativistic heavy-ion collisions at the Large Hadron Collider and the Relativistic Heavy-Ion Collider, perturbative QCD based simulations of these processes, often interacting with an…