Related papers: Covariant phase space and $L_\infty$ algebras
This paper develops a symplectic bifurcation theory for integrable systems in dimension four. We prove that if an integrable system has no hyperbolic singularities and its bifurcation diagram has no vertical tangencies, then the fibers of…
In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of k-symplectic geometry. We discuss the relation between Lagrangian and Hamiltonian descriptions…
We review the basic features of a logarithmic conformal field theory that arise in the context of the scaling limit of lattice models. The theory of interest is the symplectic fermions, whose central charge is $-2$. We provide an explicit…
We introduce geometric quantization in the setting of shifted symplectic structures. We define Lagrangian fibrations and prequantizations of shifted symplectic stacks and their geometric quantization. In addition, we study many examples…
We construct integrable Hamiltonian systems with Lie bialgebras $({\bf g} , {\bf \tilde{g}})$ of the bi-symplectic type for which the Poisson-Lie groups ${\bf G}$ play the role of the phase spaces, and their dual Lie groups ${\bf {\tilde…
Many physically important mechanical systems may be described with a Lie group $G$ as configuration space. According to the well-known Noether's theorem, underlying symmetries of the Lie group may be used to considerably reduce the…
We propose a description of open universes in the Chern-Simons formulation of (2+1)-dimensional gravity where spatial infinity is implemented as a puncture. At this puncture, additional variables are introduced which lie in the cotangent…
It is conjectured that in the origin of space-time there lies a symplectic rather than metric structure. The complex symplectic symmetry Sp(2l,C), l\ge1 instead of the pseudo-orthogonal one SO(1,d-1), d\ge4 is proposed as the space-time…
We introduce the notion of a symplectic Lie affgebroid and their Lagrangian submanifolds in order to describe the Lagrangian (Hamiltonian) dynamics on a Lie affgebroid in terms of this type of structures. Several examples are discussed.
It is shown that the topological invariants associated with the two-dimensional world-surface in string theory have nontrivial fluctuations around their nonexistent classical dynamics. Additionally it is proved that the underlying…
Recently it has been argued, that Poincar\'{e} supersymmetric field theories admit an underlying loop space hamiltonian (symplectic) structure. Here shall establish this at the level of a general $N=1$ supermultiplet. In particular, we…
We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not…
We explain that when quantising phase spaces with varying symplectic structures, the bundle of quantum Hilbert spaces over the parameter space has a natural unitary connection. We then focus on symplectic vector spaces and their fermionic…
Exploring the concept of the extended Galilei group $\mathcal{G}$, a representation for the symplectic quantum mechanics in the manifold of $\mathcal{G}$, written in the light-cone of a five-dimensional De Sitter space-time, is derived…
The Lagrangian formulation of classical field theories and in particular general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the…
After explicitly constructing the symmetric space sigma model lagrangian in terms of the coset scalars of the solvable Lie algebra gauge in the current formalism we derive the field equations of the theory.
I argue that the Hodge structure on a Euclidean Clifford algebra $Cl(n)$ provides a way to generalise K\"ahler structure to higher dimensions, in the sense that the paired variables are now associated with $k-$ and $(n-k)-$ dimensional…
We investigate algebraic structure of light-cone string field theory which respects the spacetime supersymmetry su(2|2). Extracting building blocks from the explicit oscillator expressions of light-cone superstring field theory on the…
We perform a detailed study of the covariance properties of the symplectic potential of general relativity on a null hypersurface, and of the different polarizations that can be used to study conservative as well as leaky boundary…
We construct a complete type II superstring field theory that includes all the NS-NS, R-NS, NS-R and R-R sectors. As in the open and heterotic superstring cases, the R-NS, NS-R and R-R string fields are constrained by using the…