相关论文: Diffeomorphisms as Symplectomorphisms in History P…

We introduce the Quantum Holonomy-Diffeomorphism *-algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical…

We study Dirac structures associated with Manin pairs (\d,\g) and give a Dirac geometric approach to Hamiltonian spaces with D/G-valued moment maps, originally introduced by Alekseev and Kosmann-Schwarzbach in terms of quasi-Poisson…

A careful study of the induced transformations on spatial quantities due to 4-dimensional spacetime diffeomorphisms in the canonical formulation of general relativity is undertaken. Use of a general formalism, which indicates the role of…

We present the Dirac Hamiltonian formalism for a pair of $1$-form fields with a topological-like potential coupled to first-order gravity in three-dimensional spacetime. By considering the complete phase space, we derive the full structure…

Sen's action for a $p$-form gauge field with self-dual field strength coupled to a spacetime metric $g$ involves an explicit Minkowski metric and the presence of this raises questions as to whether the action is coordinate independent and…

A simple geometric description of T-duality is given by identifying the cotangent bundles of the original and the dual manifold. Strings propagate naturally in the cotangent bundle and the original and the dual string phase spaces are…

We review the recent generalization of the basic structures of classical analytical mechanics to field theory within the framework of the De Donder-Weyl (DW) covariant canonical theory. We start from the Poincar\'e-Cartan form and construct…

We write down a general action principle for spinning strings in 2+1 dimensional space-time without introducing Grassmann variables. The action is written solely in terms of coordinates taking values in the 2+1 Poincare group, and it has…

We consider two technical developments of the formalism of continuous-time histories. First, we provide an explicit description of histories of the simple harmonic oscillator on the classical histories phase space, comparing and contrasting…

We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of simple but restrictive rules of the game lead to conditions for an isomorphism between…

Classical mechanical systems are modeled by a symplectic manifold $(M,\omega)$, and their symmetries, encoded in the action of a Lie group $G$ on $M$ by diffeomorphisms that preserves $\omega$. These actions, which are called "symplectic",…

We investigate classical dynamics of the bosonic string in the background metric, antisymmetric and dilaton fields. We use canonical methods to find Hamiltonian in terms of energy-momentum tensor components. The later are secondary…

A Lie 2-algebra is a "categorified" version of a Lie algebra: that is, a category equipped with structures analogous those of a Lie algebra, for which the usual laws hold up to isomorphism. In the classical mechanics of point particles, the…

A Dirac Hamiltonian formulation of d-dimensional Einstein-Hilbert action in first order form, has shown that as well as secondary first class constraints, tertiary first class constraints also arise, with an unusual nonlocal Poisson bracket…

It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…

Local action principles on a manifold $\M$ are invariant (if at all) only under diffeomorphisms that preserve the boundary of $\M$. Suppose, however, that we wish to study only part of a system described by such a principle; namely, the…

As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present…

We consider the space of bilinear forms on a complex N-dimensional vector space endowed with the quadratic Poisson bracket studied in our previous paper arXiv:1012.5251. We classify all possible quadratic brackets on the set of pairs of…

We construct O(D,D) invariant actions for the bosonic string and RNS superstring, using Hamiltonian methods and ideas from double field theory. In this framework the doubled coordinates of double field theory appear as coordinates on phase…

In a natural way, the local diffeomorphisms of a manifold onto itself act on the reference frame bundles of any order and on the bundles associated with them. Due to the transitivity, the invariants by diffeomorphisms of an associated…