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Connections on locally trivial quantum principal fibre bundles [PDF]
Journal of Geometry and Physics, 2000 Following the approach of Budzy\'nski and Kondracki, we define covariant differential algebras and connections on locally trivial quantum principal fibre bundles.
Brzezinski +10 more
core +6 more sources
Principal bundles and connections modelled by Lie group bundles [PDF]
Geometriae Dedicata, 2023 AbstractIn this work, generalized principal bundles modelled by Lie group bundle actions are investigated. In particular, the definition of equivariant connections in these bundles, associated to Lie group bundle connections, is provided, together with the analysis of their existence and their main properties. The final part gives some examples.
Castrillón López, Marco +1 more
arxiv +7 more sources
The Existence of Cartan Connections and Geometrizable Principal Bundles [PDF]
Archiv der Mathematik, 2004 The aim of this article is to proof a necessary and sufficient condition for the existence of a Cartan connection on a principal bundle. After collecting the essentially well known facts to fix the terminology, soldering forms and geometrizable principal
Barakat, Mohamed
core +6 more sources
A Discrete Theory of Connections on Principal Bundles
, 2005 Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion.
Leok, Melvin +2 more
core +5 more sources
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space $E$, and then a connection is also defined on this bundle.
Durdevich, Micho, Sontz, Stephen Bruce
core +4 more sources
Can You hear the Shape of a Market? Geometric Arbitrage and Spectral Theory
Axioms, 2020 Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and
Farinelli, Simone, Takada, Hideyuki
core +3 more sources
Strong connections on quantum principal bundles [PDF]
Communications in Mathematical Physics, 1996 AMS-LaTeX, 40 pages, major revision including examples of connections over a quantum real projective ...
Piotr M. Hajac
openaire +7 more sources
Discrete connections on principal bundles: The discrete Atiyah sequence [PDF]
Journal of Geometry and Physics, 2022 In this work we study discrete analogues of an exact sequence of vector bundles introduced by M. Atiyah in 1957, associated to any smooth principal $G$-bundle $π:Q\rightarrow Q/G$. In the original setting, the splittings of the exact sequence correspond to connections on the principal bundle $π$.
Javier Fernández +2 more
openaire +3 more sources
On principal connection like bundles [PDF]
Czechoslovak Mathematical Journal, 2014 Let PBm be the category of all principal fibred bundles with m-dimensional bases and their principal bundle homomorphisms covering embeddings. We introduce the concept of the so called (r,m)-systems and describe all gauge bundle functors on PBm of order r by means of the (r,m)-systems.
openaire +3 more sources
A Categorical Equivalence between Generalized Holonomy Maps on a Connected Manifold and Principal Connections on Bundles over that Manifold [PDF]
, 2015 A classic result in the foundations of Yang-Mills theory, due to J. W. Barrett ["Holonomy and Path Structures in General Relativity and Yang-Mills Theory." Int. J. Th. Phys.
Bleecker D. +12 more
core +3 more sources