Related papers: Geometric aspects of higher order variational prin…
Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent geometry of the surface and the curve. In this paper, we study…
The fourth paper of our series of papers entitled "Differential Geometry of Microlinear Frolicher Spaces is concerned with jet bundles. We present three distinct approaches together with transmogrifications of the first into the second and…
This paper contains a set of lecture notes on manifolds with boundary and corners, with particular attention to the space of quantum states. A geometrically inspired way of dealing with these kind of manifolds is presented,and explicit…
This note is intended to provide a general reference for jet spaces and jet differentials, valid in maximal generality (at the level of EGA). The approach is rather concrete, using Hasse-Schmidt (divided) higher differentials. Discussion of…
There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such…
Jet substructure in heavy-ion collisions is a rapidly evolving area with lots of intriguing new measurements. This contribution presents a selection of recent jet-substructure measurements from experiments at the LHC, in particular,…
We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally…
Reconstructing jets, which provide vital insights into the properties and histories of subatomic particles produced in high-energy collisions, is a main problem in data analyses in collider physics. This intricate task deals with estimating…
The process by which jet algorithms construct jets and subjets is inherently ambiguous and equally well motivated algorithms often return very different answers. The Qjets procedure was introduced by the authors to account for this…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
Current phenomenological studies of jet observables at colliders are clearly limited by the theoretical uncertainties inherent in the next-to-leading order QCD description. We discuss the recent progress made towards the calculation of QCD…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
In this review I summarise the status of observational research into relativistic jets from X-ray binaries, highlighting four areas in particular: (i) How relativistic are the jets ?, (ii) The disc : jet coupling, (iii) the nature of the…
This paper describes the foundations of a differential geometry of a quaternionic curves. The Frenet-Serret equations and the evolutes and evolvents of a particular quaternionic curve are accordingly determined. This new formulation takes…
This paper shows how properties of jet schemes relate to those of the singularity on the base scheme. We will see that the jet scheme's properties of being Q-factorial, Q-Gorenstein, canonical, terminal and so on are inherited by the base…
Variational and divergence symmetries are studied in this paper for linear equations of maximal symmetry in canonical form, and the associated first integrals are given in explicit form. All the main results obtained are formulated as…
A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…
In this paper, we explore the use of jet substructure as a way of probing phenomena which break the isotropic behavior of jets, such as jet propagation through an anisotropically flowing quark-gluon plasma or spin correlations. We introduce…
Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are…