Related papers: Barnich-Troessaert Bracket as a Dirac Bracket on t…
The concept of Lagrange structure allows one to systematically quantize the Lagrangian and non-Lagrangian dynamics within the path-integral approach. In this paper, I show that any Lagrange structure gives rise to a covariant Poisson…
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among…
We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in $D$ dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first…
We single out a class of Lagrangians on a group manifold, for which one can introduce non-canonical coordinates in the phase space, which simplify the construction of the Poisson structure without explicitly calculating the Dirac bracket.…
We analyse the problem of boundary conditions for the Poisson-Sigma model and extend previous results showing that non-coisotropic branes are allowed. We discuss the canonical reduction of a Poisson structure to a submanifold, leading to a…
We apply the Dirac bracket quantization to open strings attached to branes in the presence of background antisymmetric field and recover an inherent noncommutativity in the internal coordinates of the brane.
Dirac's conjecture, that secondary first-class constraints generate transformations that do not change the physical system's state, has various counterexamples. Since no matching gauge conditions can be imposed, the Dirac bracket cannot be…
Free initial data for general relativity on a pair of intersecting null hypersurfaces are well known, but the lack of a Poisson bracket and concerns about caustics have stymied the development of a constraint free canonical theory. Here it…
We analyze the backreaction of a class of scalar field self-interactions with the possibility of evolving from an AdS vacuum to a fixed point where the scalar field potential vanishes. Exact solutions which interpolate between these…
We consider (2+1)-gravity with vanishing cosmological constant as a constrained dynamical system. By applying Dirac's gauge fixing procedure, we implement the constraints and determine the Dirac bracket on the gauge-invariant phase space.…
We generalize previous works on the Dirac eigenvalues as dynamical variables of the Euclidean gravity and N=1 D=4 supergravity to on-shell N=2 D=4 Euclidean supergravity. The covariant phase space of the theory is defined as as the space of…
Dirac's method for variations of a brane embedded in co-dimension one is demonstrated. The variation in the location of the brane invokes a rest frame formulation of the 'sandwiched' brane action. We first demonstrate the necessity of this…
The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically…
In the study of alternative or extended theories of gravity, Dirac's Hamiltonian constraint algorithm is invaluable for enumerating the propagating modes and gauge symmetries. For gravity, this canonical approach is frequently applied as a…
In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than…
Based on the non-Abelian Lie algebra, a generalized geometric Lie bracket on vector space is proposed to further realize the generalized structural Poisson bracket, and then we briefly discuss the second order equations of the generalized…
We present a general definition of the Poisson bracket between differential forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories and, more generally, on exact multisymplectic…
The Schouten bracket (or antibracket) plays a central role in the Poisson formalism and the Batalin-Vilkovisky quantization of gauge systems. There are several (in)equivalent ways to realize this concept on jet spaces. In this paper, we…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
Within the framework of geodetic brane gravity, the Universe is described as a 4-dimensional extended object evolving geodetically in a higher dimensional flat background. In this paper, by introducing a new pair of canonical fields…