相关论文: A Frame Bundle Generalization of Multisymplectic M…
General relativity uses curved space-time to describe accelerating frames. The movement of particles in different curved space-times can be regarded as equivalent physical processes based on the covariant transformation between different…
We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for near complete generality, the Hamiltonian is formulated using any fixed…
We study Hamiltonian field theories on the multisymplectic bundle of a principal G-bundle with Hamiltonian densities invariant under a subgroup $H\subset G$. Using the covariant bracket formulation, we reduce the polysymplectic space and…
General Relativity can be reformulated as a geometrodynamical theory, called Shape Dynamics, that is not based on spacetime (in particular refoliation) symmetry but on spatial diffeomorphism and local spatial conformal symmetry. This leads…
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed…
Field theoretical models with first order Lagrangean can be formulated in a covariant Hamiltonian formalism. In this article, the geometrical construction of the Gerstenhaber structure that encodes the equations of motion is explained for…
We consider generalized (possibly depending on fields as well as on space-time variables) gauge transformations and gauge symmetries in the context of general -- that is, possibly non variational nor covariant -- differential equations. In…
We introduce an extension of the standard Local-to-Global Principle used in the proof of the convexity theorems for the momentum map to handle closed maps that take values in a length metric space. This extension is used to study the…
We study the implications of a change of coordinatization of momentum space for theories with curved momentum space. We of course find that after a passive diffeomorphism the theory yields the same physical predictions, as one would expect…
A geometric multisymplectic formulation of the classical BRST symmetry of constrained first-order classical field theories is described. To effect this we introduce graded analogues of the bundles and manifolds of the multisymplectic…
Multisymplectic geometry is an adequate formalism to geometrically describe first order classical field theories. The De Donder-Weyl equations are treated in the framework of multisymplectic geometry, solutions are identified as integral…
A generalized moment map is proposed for arbitrary symplectic actions of compact connected Lie groups on closed symplectic manifolds, in the spirit of the circle -valued maps introduced by D. McDuff in the case of non-Hamiltonian circle…
We present a class of three-dimensional quantum field theories whose ordinary global symmetries mix with higher-form symmetries to form a continuous 2-group. All these models can be obtained by performing a gauging procedure in a parent…
Recent work in the literature has shown that general relativity can be formulated in terms of a jet bundle which, in local coordinates, has five entries: local coordinates on Lorentzian space-time, tetrads, connection one-forms,…
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first…
We introduce and analyze Generalized Time Domain Velocity Vector (GTVV), an extension of the previously presented acoustic multipath footprint extracted from the Ambisonic recordings. GTVV is better adapted to adverse acoustic conditions,…
Gauge fields of mixed symmetry, corresponding to arbitrary representations of the local Lorentz group of the background spacetime, arise as massive modes in compactifications of superstring theories. We describe bosonic gauge field theories…
The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The…
Originating from the topology of the path-integral target space $Y$, solitonic symmetry describes the conservation law of topological solitons and the selection rule of defect operators. As Ref.~\cite{Chen:2022cyw} exemplifies, the…
In K\"ahler geometry, the Donaldson-Fujiki moment map picture interprets the scalar curvature of a K\"ahler metric as a moment map on the space of compatible almost complex structures on a fixed symplectic manifold. In this paper, we…