1,100 research outputs found
Lorentzian homogeneous spaces admitting a homogeneous structure of type T1+T3
We show that a Lorentzian homogeneous space admitting a homogeneous structure
of type T1 + T3 is either a (locally) symmetric space or a singular homogeneous
plane wave.Comment: 7 pages, Latex2e, a small note and a reference adde
A topological limit of gravity admitting an SU(2) connection formulation
We study the Hamiltonian formulation of the generally covariant theory
defined by the Lagrangian 4-form L=e_I e_J F^{IJ}(\omega) where e^I is a tetrad
field and F^{IJ} is the curvature of a Lorentz connection \omega^{IJ}. This
theory can be thought of as the limit of the Holst action for gravity for the
Newton constant G goes to infinity and Immirzi parameter goes to zero, while
keeping their product fixed. This theory has for a long time been conjectured
to be topological. We prove this statement both in the covariant phase space
formulation as well as in the standard Dirac formulation. In the time gauge,
the unconstrained phase space of theory admits an SU(2) connection formulation
which makes it isomorphic to the unconstrained phase space of gravity in terms
of Ashtekar-Barbero variables. Among possible physical applications, we argue
that the quantization of this topological theory might shed new light on the
nature of the degrees of freedom that are responsible for black entropy in loop
quantum gravity.Comment: Appendix added where moldels leading to boundary degrees of freedom
are constructed. This version will appear in PRD
Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter
We perform the Lorentz-covariant Hamiltonian analysis of two Lagrangian
action principles that describe general relativity as a constrained BF theory
and that include the Immirzi parameter. The relation between these two
Lagrangian actions has been already studied through a map among the fields
involved. The main difference between these is the way the Immirzi parameter is
included, since in one of them the Immirzi parameter is included explicitly in
the BF terms, whereas in the other (the CMPR action) it is in the constraint on
the B fields. In this work we continue the analysis of their relationship but
at the Hamiltonian level. Particularly, we are interested in seeing how the
above difference appears in the constraint structure of both action principles.
We find that they both possess the same number of first-class and second-class
constraints and satisfy a very similar (off-shell) Poisson-bracket algebra on
account of the type of canonical variables employed. The two algebras can be
transformed into each other by making a suitable change of variablesComment: LaTeX file, no figure
Quantum mechanics without spacetime II : noncommutative geometry and the free point particle
In a recent paper we have suggested that a formulation of quantum mechanics
should exist, which does not require the concept of time, and that the
appropriate mathematical language for such a formulation is noncommutative
differential geometry. In the present paper we discuss this formulation for the
free point particle, by introducing a commutation relation for a set of
noncommuting coordinates. The sought for background independent quantum
mechanics is derived from this commutation relation for the coordinates. We
propose that the basic equations are invariant under automorphisms which map
one set of coordinates to another- this is a natural generalization of
diffeomorphism invariance when one makes a transition to noncommutative
geometry. The background independent description becomes equivalent to standard
quantum mechanics if a spacetime manifold exists, because of the proposed
automorphism invariance. The suggested basic equations also give a quantum
gravitational description of the free particle.Comment: 8 page
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