Pau Mir
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View article: Singularities and symmetries on the crossroads of geometry and physics
Singularities and symmetries on the crossroads of geometry and physics Open
(English) In this thesis we study several mathematical objects that are essential to formulate and model physical systems. Applying the tools provided by differential geometry, we develop and analyze different mathematical structures that …
View article: Constructions of <i>b</i>-semitoric systems
Constructions of <i>b</i>-semitoric systems Open
In this article, we introduce b-semitoric systems as a generalization of semitoric systems, specifically tailored for b-symplectic manifolds. The objective of this article is to furnish a collection of examples and investigate the distinct…
View article: Hamiltonian facets of classical gauge theories on <i>E</i>-manifolds
Hamiltonian facets of classical gauge theories on <i>E</i>-manifolds Open
Manifolds with boundary, with corners, b -manifolds and foliations model configuration spaces for particles moving under constraints and can be described as E -manifolds. E -manifolds were introduced in Nest and Tsygan (2001 Asian J. Math.…
View article: Constructions of b-semitoric systems
Constructions of b-semitoric systems Open
In this article, we introduce $b$-semitoric systems as a generalization of semitoric systems, specifically tailored for $b$-symplectic manifolds. The objective of this article is to furnish a collection of examples and investigate the dist…
View article: Bohr–Sommerfeld quantization of $b$-symplectic toric manifolds
Bohr–Sommerfeld quantization of $b$-symplectic toric manifolds Open
We define the Bohr-Sommerfeld quantization via T -modules for a b-symplectic toric manifold and show that it coincides with the formal geometric quantization of [Victor W. Guillemin, Eva Miranda, and Jonathan Weitsman. On geometric quantiz…
View article: Hamiltonian facets of classical gauge theories on $E$-manifolds
Hamiltonian facets of classical gauge theories on $E$-manifolds Open
Manifolds with boundary, with corners, $b$-manifolds and foliations model configuration spaces for particles moving under constraints and can be described as $E$-manifolds. $E$-manifolds were introduced in [NT01] and investigated in depth …
View article: Singular cotangent models and complexity in fluids with dissipation
Singular cotangent models and complexity in fluids with dissipation Open
In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a $b$-cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in $b$-c…
View article: Bohr-Sommerfeld quantization of $b$-symplectic toric manifolds
Bohr-Sommerfeld quantization of $b$-symplectic toric manifolds Open
We define the Bohr-Sommerfeld quantization via $T$-modules for a $b$-symplectic toric manifold and show that it coincides with the formal geometric quantization of [GMW18b]. In particular, we prove that its dimension is given by a signed c…
View article: Geometric quantization via cotangent models
Geometric quantization via cotangent models Open
In this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the cotangent models in…