11 citations · 40 across the 15 of their papers we have counts for
15 papers
Symplectic Reduction in Infinite Dimensions
Tobias Diez, Gerd Rudolph
This paper develops a theory of symplectic reduction in the infinite-dimensional setting, covering both the regular and singular case. Extending the classical work of Marsden, Wein…
Cartan Geometry and Infinite-Dimensional Kempf-Ness Theory
Tobias Diez, Akito Futaki, Tudor Ratiu
We pioneer the development of a rigorous infinite-dimensional framework for the Kempf-Ness theorem, addressing the significant challenge posed by the absence of a complexification…
Norm-squared of the momentum map in infinite dimensions with applications to Kähler geometry and symplectic connections
Tobias Diez, Tudor S. Ratiu
We initiate the study of the norm-squared of the momentum map as a rigorous tool in infinite dimensions. In particular, we calculate the Hessian at a critical point, show that it i…
Expectation values of polynomials and moments on general compact Lie groups
Tobias Diez, Lukas Miaskiwskyi
We develop a powerful framework to calculate expectation values of polynomials and moments on compact Lie groups based on elementary representation-theoretic arguments and an integ…
Normal form of equivariant maps in infinite dimensions
Tobias Diez, Gerd Rudolph
Local normal form theorems for smooth equivariant maps between infinite-dimensional manifolds are established. These normal form results are new even in finite dimensions. The proo…
Induced differential characters on nonlinear Graßmannians
Tobias Diez, Bas Janssens, Karl-Hermann Neeb +1
Using a nonlinear version of the tautological bundle over Graßmannians, we construct a transgression map for differential characters from to the nonlinear Graßmannians $\mathrm…
Group-valued momentum maps for actions of automorphism groups
Tobias Diez, Tudor S. Ratiu
The space of smooth sections of a symplectic fiber bundle carries a natural symplectic structure. We provide a general framework to determine the momentum map for the action of the…
Realizing the Teichmüller space as a symplectic quotient
Tobias Diez, Tudor S. Ratiu
Given a closed surface endowed with a volume form, we equip the space of compatible Riemannian structures with the structure of an infinite-dimensional symplectic manifold. We show…
Normal Form of Equivariant Maps and Singular Symplectic Reduction in Infinite Dimensions with Applications to Gauge Field Theory
Tobias Diez
A local normal form theorem for smooth equivariant maps between Fréchet manifolds is established. Moreover, an elliptic version of this theorem is obtained. The proof these normal…
Central extensions of Lie groups preserving a differential form
Tobias Diez, Bas Janssens, Karl-Hermann Neeb +1
Let be a manifold with a closed, integral -form , and let be a Fréchet-Lie group acting on . As a generalization of the Kostant-Souriau extension for sympl…
Singular symplectic cotangent bundle reduction of gauge field theory
Tobias Diez, Gerd Rudolph
We prove a theorem on singular symplectic cotangent bundle reduction in the Fréchet setting and apply it to Yang-Mills-Higgs theory with special emphasis on the Higgs sector of the…
Slice theorem and orbit type stratification in infinite dimensions
Tobias Diez, Gerd Rudolph
We establish a general slice theorem for the action of a locally convex Lie group on a locally convex manifold, which generalizes the classical slice theorem of Palais to infinite…
Clebsch-Lagrange variational principle and geometric constraint analysis of relativistic field theories
Tobias Diez, Gerd Rudolph
Inspired by the Clebsch optimal control problem, we introduce a new variational principle that is suitable for capturing the geometry of relativistic field theories with constraint…
Yang-Mills moduli spaces over an orientable closed surface via Fréchet reduction
Tobias Diez, Johannes Huebschmann
Given a principal bundle on an orientable closed surface with compact connected structure group, we endow the space of based gauge equivalence classes of smooth connections relativ…
Slice theorem for Fréchet group actions and covariant symplectic field theory
Tobias Diez
A general slice theorem for the action of a Fréchet Lie group on a Fréchet manifolds is established. The Nash-Moser theorem provides the fundamental tool to generalize the result o…