Related papers: Higher prequantum geometry
In this paper we introduce the concepts of higher equivariant and invariant topological complexity; and study their properties. Then we compare them with equivariant LS-category. We give lower and upper bounds for these new invariants. We…
The first aim of this paper is to study the $p$-local higher homotopy commutativity of Lie groups in the sense of Sugawara. The second aim is to apply this result to the $p$-local higher homotopy commutativity of gauge groups. Although the…
We develop the framework for augmented homotopical algebraic geometry. This is an extension of homotopical algebraic geometry, which itself is a homotopification of classical algebraic geometry. To do so, we define the notion of…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q-manifolds…
The Hamiltonian operator describing a quantum particle on a path often extends holomorphically to a complex neighborhood of the path. When it does, it can be seen as the local expression of a complex projective structure, and its…
These notes are an introduction to higher dimensional local fields and higher dimensional adeles. As well as the foundational theory, we summarise the theory of topologies on higher dimensional local fields and higher dimensional local…
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…
In this chapter we describe a selection of mathematical techniques and results that suggest interesting links between the theory of gratings and the theory of homogenization, including a brief introduction to the latter. By no means do we…
The method of higher covariant derivative regularization of gauge theories is reviewed. The objections raised in the literature last years are discussed and the consistency of the method is proven. New approach to regularization of…
This is an invited survey article on higher gauge theory for the Encyclopedia of Mathematical Physics, 2nd edition. In particular, we provide a lightning introduction to higher structures and to the construction of the kinematical data of…
The main content of this treatise is a new concept in nonperturbative non-Lagrangian QFT which explains and extends the ad hoc constructions in low-dimensional models and incorporates them together with the higher dimensional theories into…
Using supervector fields and graded forms along a morphism, we study the geometry of ordinary differential superequations, extend the formalism of higher order Lagrangian mechanics to the graded context and prove a generalization of…
The paper is concerned with the development of a gravitational field theory having locally a covariant version of the Galilei group. We show that this Galilean gravity can be used to study the advance of perihelion of a planet, following in…
The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi…
The author explains local and global model structures on higher orbifolds which are truncated \'{e}tale differentiable higher stacks, and discuss the application of the model structures to quantum cohomology of higher and derived orbifolds.
Higher derivative scalar field theories have received considerable attention for the potentially explanations of the initial state of the universe or the current cosmic acceleration which they might offer. They have also attracted many…
In this note we study the local projective model structure on presheaves of complexes on a site, i.e. we describe its classes of cofibrations, fibrations and weak equivalences. In particular, we prove that the fibrant objects are those…
In this paper, I present a novel, purely differential geometric approach to the quantization of scalar fields, with a special focus on the familiar case of Minkowski spacetimes. This approach is based on using the natural geometric…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…