411 research outputs found
Scalar and tensorial topological matter coupled to (2+1)-dimensional gravity:A.Classical theory and global charges
We consider the coupling of scalar topological matter to (2+1)-dimensional
gravity. The matter fields consist of a 0-form scalar field and a 2-form tensor
field. We carry out a canonical analysis of the classical theory, investigating
its sectors and solutions. We show that the model admits both BTZ-like
black-hole solutions and homogeneous/inhomogeneous FRW cosmological
solutions.We also investigate the global charges associated with the model and
show that the algebra of charges is the extension of the Kac-Moody algebra for
the field-rigid gauge charges, and the Virasoro algebrafor the diffeomorphism
charges. Finally, we show that the model can be written as a generalized
Chern-Simons theory, opening the perspective for its formulation as a
generalized higher gauge theory.Comment: 40 page
Hamiltonian analysis of SO(4,1) constrained BF theory
In this paper we discuss canonical analysis of SO(4,1) constrained BF theory.
The action of this theory contains topological terms appended by a term that
breaks the gauge symmetry down to the Lorentz subgroup SO(3,1). The equations
of motion of this theory turn out to be the vacuum Einstein equations. By
solving the B field equations one finds that the action of this theory contains
not only the standard Einstein-Cartan term, but also the Holst term
proportional to the inverse of the Immirzi parameter, as well as a combination
of topological invariants. We show that the structure of the constraints of a
SO(4,1) constrained BF theory is exactly that of gravity in Holst formulation.
We also briefly discuss quantization of the theory.Comment: 9 page
The spectrum of states of Ba~nados-Teitelboim-Zanelli black hole formed by a collapsing dust shell
We perform canonical analysis of an action in which 2+1-dimensional gravity
with negative cosmological constant is coupled to cylindrically symmetric dust
shell. The resulting phase space is finite dimensional having geometry of SO(2;
2) group manifold. Representing the Poisson brackets by commutators results in
the algebra of observables which is a quantum double D(SL(2)q). Deformation
parameter q is real when the total energy of the system is below the threshold
of a black hole formation, and a root of unity when it is above. Inside the
black hole the spectra of the shell radius and time operator are discrete and
take on a finite set of values. The Hilbert space of the black hole is thus
finite-dimensional.Comment: 8 page
MacDowell-Mansouri gravity and Cartan geometry
The geometric content of the MacDowell-Mansouri formulation of general
relativity is best understood in terms of Cartan geometry. In particular,
Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick
of combining the Levi-Civita connection and coframe field, or soldering form,
into a single physical field. The Cartan perspective allows us to view physical
spacetime as tangentially approximated by an arbitrary homogeneous "model
spacetime", including not only the flat Minkowski model, as is implicitly used
in standard general relativity, but also de Sitter, anti de Sitter, or other
models. A "Cartan connection" gives a prescription for parallel transport from
one "tangent model spacetime" to another, along any path, giving a natural
interpretation of the MacDowell-Mansouri connection as "rolling" the model
spacetime along physical spacetime. I explain Cartan geometry, and "Cartan
gauge theory", in which the gauge field is replaced by a Cartan connection. In
particular, I discuss MacDowell-Mansouri gravity, as well as its more recent
reformulation in terms of BF theory, in the context of Cartan geometry.Comment: 34 pages, 5 figures. v2: many clarifications, typos correcte
Kinematics of a relativistic particle with de Sitter momentum space
We discuss kinematical properties of a free relativistic particle with
deformed phase space in which momentum space is given by (a submanifold of) de
Sitter space. We provide a detailed derivation of the action, Hamiltonian
structure and equations of motion for such free particle. We study the action
of deformed relativistic symmetries on the phase space and derive explicit
formulas for the action of the deformed Poincare' group. Finally we provide a
discussion on parametrization of the particle worldlines stressing analogies
and differences with ordinary relativistic kinematics.Comment: RevTeX, 12 pages, no figure
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