9,501 research outputs found
Spin Networks and Recoupling in Loop Quantum Gravity
I discuss the role played by the spin-network basis and recoupling theory (in
its graphical tangle-theoretic formulation) and their use for performing
explicit calculations in loop quantum gravity. In particular, I show that
recoupling theory allows the derivation of explicit expressions for the
eingenvalues of the quantum volume operator. An important side result of these
computations is the determination of a scalar product with respect to which
area and volume operators are symmetric, and the spin network states are
orthonormal.Comment: 8 pages, LaTeX3e, To appear in the Proceedings of the 2nd Conference
on Constrained Dynamics and Quantum Gravity, Santa Margherita, Italy, 17-21
September 199
The physical hamiltonian in nonperturbative quantum gravity
A quantum hamiltonian which evolves the gravitational field according to time
as measured by constant surfaces of a scalar field is defined through a
regularization procedure based on the loop representation, and is shown to be
finite and diffeomorphism invariant. The problem of constructing this
hamiltonian is reduced to a combinatorial and algebraic problem which involves
the rearrangements of lines through the vertices of arbitrary graphs. This
procedure also provides a construction of the hamiltonian constraint as a
finite operator on the space of diffeomorphism invariant states as well as a
construction of the operator corresponding to the spatial volume of the
universe.Comment: Latex, 11 pages, no figures, CGPG/93/
Did Growth and Reforms Increase Citizens’ Support for the Transition?
How did post-communist transformations affect people’s perceptions of their economic and political systems? We model a pseudo-panel with 89 country-year clusters, based on 13 countries observed between 1991 and 2004, to identify the macro and institutional drivers of the public opinion. Our main findings are: (i) When the economy is growing, on average people appreciate more extensive reforms; they dislike unbalanced reforms. (ii) Worsening of income distribution and higher inflation interact with an increasing share of the private sector in aggravating nostalgia for the past regime. (iii) Cross-country differences in the attitudes towards the present and future (both in the economic and political dimensions) are largely explained by differences in the institutional indicators for the rule of law and corruption. (iv) Cross-country differences in the extent of nostalgia towards the past are mainly related to differences in the deterioration of standards of living.
The century of the incomplete revolution: searching for general relativistic quantum field theory
In fundamental physics, this has been the century of quantum mechanics and
general relativity. It has also been the century of the long search for a
conceptual framework capable of embracing the astonishing features of the world
that have been revealed by these two ``first pieces of a conceptual
revolution''. I discuss the general requirements on the mathematics and some
specific developments towards the construction of such a framework. Examples of
covariant constructions of (simple) generally relativistic quantum field
theories have been obtained as topological quantum field theories, in
nonperturbative zero-dimensional string theory and its higher dimensional
generalizations, and as spin foam models. A canonical construction of a general
relativistic quantum field theory is provided by loop quantum gravity.
Remarkably, all these diverse approaches have turn out to be related,
suggesting an intriguing general picture of general relativistic quantum
physics.Comment: To appear in the Journal of Mathematical Physics 2000 Special Issu
Compatibility of radial, Lorenz and harmonic gauges
We observe that the radial gauge can be consistently imposed \emph{together}
with the Lorenz gauge in Maxwell theory, and with the harmonic traceless gauge
in linearized general relativity. This simple observation has relevance for
some recent developments in quantum gravity where the radial gauge is
implicitly utilized.Comment: 9 pages, minor changes in the bibliograph
Finite, diffeomorphism invariant observables in quantum gravity
Two sets of spatially diffeomorphism invariant operators are constructed in
the loop representation formulation of quantum gravity. This is done by
coupling general relativity to an anti- symmetric tensor gauge field and using
that field to pick out sets of surfaces, with boundaries, in the spatial three
manifold. The two sets of observables then measure the areas of these surfaces
and the Wilson loops for the self-dual connection around their boundaries. The
operators that represent these observables are finite and background
independent when constructed through a proper regularization procedure.
Furthermore, the spectra of the area operators are discrete so that the
possible values that one can obtain by a measurement of the area of a physical
surface in quantum gravity are valued in a discrete set that includes integral
multiples of half the Planck area. These results make possible the construction
of a correspondence between any three geometry whose curvature is small in
Planck units and a diffeomorphism invariant state of the gravitational and
matter fields. This correspondence relies on the approximation of the classical
geometry by a piecewise flat Regge manifold, which is then put in
correspondence with a diffeomorphism invariant state of the gravity-matter
system in which the matter fields specify the faces of the triangulation and
the gravitational field is in an eigenstate of the operators that measure their
areas.Comment: Latex, no figures, 30 pages, SU-GP-93/1-
Quantum Loop Representation for Fermions coupled to Einstein-Maxwell field
Quantization of the system comprising gravitational, fermionic and
electromagnetic fields is developed in the loop representation. As a result we
obtain a natural unified quantum theory. Gravitational field is treated in the
framework of Ashtekar formalism; fermions are described by two Grassmann-valued
fields. We define a -algebra of configurational variables whose
generators are associated with oriented loops and curves; ``open'' states --
curves -- are necessary to embrace the fermionic degrees of freedom. Quantum
representation space is constructed as a space of cylindrical functionals on
the spectrum of this -algebra. Choosing the basis of ``loop'' states we
describe the representation space as the space of oriented loops and curves;
then configurational and momentum loop variables become in this basis the
operators of creation and annihilation of loops and curves. The important
difference of the representation constructed from the loop representation of
pure gravity is that the momentum loop operators act in our case simply by
joining loops in the only compatible with their orientaiton way, while in the
case of pure gravity this action is more complicated.Comment: 28 pages, REVTeX 3.0, 15 uuencoded ps-figures. The construction of
the representation has been changed so that the representation space became
irreducible. One part is removed because it developed into a separate paper;
some corrections adde
Relational evolution of the degrees of freedom of generally covariant quantum theories
We study the classical and quantum dynamics of generally covariant theories
with vanishing a Hamiltonian and with a finite number of degrees of freedom. In
particular, the geometric meaning of the full solution of the relational
evolution of the degrees of freedom is displayed, which means the determination
of the total number of evolving constants of motion required. Also a method to
find evolving constants is proposed. The generalized Heinsenberg picture needs
M time variables, as opposed to the Heisenberg picture of standard quantum
mechanics where one time variable t is enough. As an application, we study the
parameterized harmonic oscillator and the SL(2,R) model with one physical
degree of freedom that mimics the constraint structure of general relativity
where a Schrodinger equation emerges in its quantum dynamics.Comment: 25 pages, no figures, Latex file. Revised versio
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