1,845 research outputs found
Canonical ``Loop'' Quantum Gravity and Spin Foam Models
The canonical ``loop'' formulation of quantum gravity is a mathematically
well defined, background independent, non perturbative standard quantization of
Einstein's theory of General Relativity. Some among the most meaningful results
of the theory are: 1) the complete calculation of the spectrum of geometric
quantities like the area and the volume and the consequent physical predictions
about the structure of the space-time at the Plank scale; 2) a microscopical
derivation of the Bekenstein-Hawking black-hole entropy formula. Unfortunately,
despite recent results, the dynamical aspect of the theory (imposition of the
Wheller-De Witt constraint) remains elusive.
After a short description of the basic ideas and the main results of loop
quantum gravity we show in which sence the exponential of the super Hamiltonian
constraint leads to the concept of spin foam and to a four dimensional
formulation of the theory. Moreover, we show that some topological field
theories as the BF theory in 3 and 4 dimension admits a spin foam formulation.
We argue that the spin-foams/spin-networks formalism it is the natural
framework to discuss loop quantum gravity and topological field theory.Comment: 17 pages, LaTeX2e, 7 figures. To appear in the proceeding of the
XXIII SIGRAV conference, Monopoli (ITALY), September 21st-25th, 1998. Minor
correction
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 planar spectrum in U(N)-invariant quantum mechanics by Fock space methods: I. The bosonic case
Prompted by recent results on Susy-U(N)-invariant quantum mechanics in the
large N limit by Veneziano and Wosiek, we have examined the planar spectrum in
the full Hilbert space of U(N)-invariant states built on the Fock vacuum by
applying any U(N)-invariant combinations of creation-operators. We present
results about 1) the supersymmetric model in the bosonic sector, 2) the
standard quartic Hamiltonian. This latter is useful to check our techniques
against the exact result of Brezin et al. The SuSy case is where Fock space
methods prove to be the most efficient: it turns out that the problem is
separable and the exact planar spectrum can be expressed in terms of the
single-trace spectrum. In the case of the anharmonic oscillator, on the other
hand, the Fock space analysis is quite cumbersome due to the presence of large
off-diagonal O(N) terms coupling subspaces with different number of traces;
these terms should be absorbed before taking the planar limit and recovering
the known planar spectrum. We give analytical and numerical evidence that good
qualitative information on the spectrum can be obtained this way.Comment: 17 pages, 4 figures, uses youngtab.sty. Final versio
A Gaussian Weave for Kinematical Loop Quantum Gravity
Remarkable efforts in the study of the semi-classical regime of kinematical
loop quantum gravity are currently underway. In this note, we construct a
``quasi-coherent'' weave state using Gaussian factors. In a similar fashion to
some other proposals, this state is peaked in both the connection and the spin
network basis. However, the state constructed here has the novel feature that,
in the spin network basis, the main contribution for this state is given by the
fundamental representation, independently of the value of the parameter that
regulates the Gaussian width.Comment: 15 pages, 3 figures, Revtex file. Comments added and references
updated. Final version to appear in IJMP-
The basis of the physical Hilbert space of lattice gauge theories
Non-linear Fourier analysis on compact groups is used to construct an
orthonormal basis of the physical (gauge invariant) Hilbert space of
Hamiltonian lattice gauge theories. In particular, the matrix elements of the
Hamiltonian operator involved are explicitly computed. Finally, some
applications and possible developments of the formalism are discussed.Comment: 14 pages, LaTeX (Using amsmath
Relationship between resistivity and specific heat in a canonical non-magnetic heavy fermion alloy system: UPt_5-xAu_x
UPt_(5-x)Au_x alloys form in a single crystal structure, cubic AuBe_5-type,
over a wide range of concentrations from x = 0 to at least x = 2.5. All
investigated alloys, with an exception for x = 2.5, were non-magnetic. Their
electronic specific heat coefficient varies from about 60 (x = 2) to
about 700 mJ/mol K^2 (x = 1). The electrical resistivity for all alloys has a
Fermi-liquid-like temperature variation, \rho = \rho_o + AT^2, in the limit of
T -> 0 K. The coefficient A is strongly enhanced in the heavy-fermion regime in
comparison with normal and transition metals. It changes from about 0.01 (x =
0) to over 2 micro-ohm cm/K^2 (x = 1). A/\gamma^2, which has been postulated to
have a universal value for heavy-fermions, varies from about 10^-6 (x = 0, 0.5)
to 10^-5 micro-ohm cm (mol K/mJ)^2 (x > 1.1), thus from a value typical of
transition metals to that found for some other heavy-fermion metals. This ratio
is unaffected, or only weakly affected, by chemical or crystallographic
disorder. It correlates with the paramagnetic Curie-Weiss temperature of the
high temperature magnetic susceptibility.Comment: 5 pages, 5 eps figures, RevTe
A Model for QCD at High Density and Large Quark Mass
We study the high density region of QCD within an effective model obtained in
the frame of the hopping parameter expansion and choosing Polyakov type of
loops as the main dynamical variables representing the fermionic matter. To get
a first idea of the phase structure, the model is analyzed in strong coupling
expansion and using a mean field approximation. In numerical simulations, the
model still shows the so-called sign problem, a difficulty peculiar to non-zero
chemical potential, but it permits the development of algorithms which ensure a
good overlap of the Monte Carlo ensemble with the true one. We review the main
features of the model and present calculations concerning the dependence of
various observables on the chemical potential and on the temperature, in
particular of the charge density and the diquark susceptibility, which may be
used to characterize the various phases expected at high baryonic density. We
obtain in this way information about the phase structure of the model and the
corresponding phase transitions and cross over regions, which can be considered
as hints for the behaviour of non-zero density QCD.Comment: 21 pages, 29 figure
Geometry eigenvalues and scalar product from recoupling theory in loop quantum gravity
We summarize the basics of the loop representation of quantum gravity and describe the main aspects of the formalism, including its latest developments, in a reorganized and consistent form. Recoupling theory, in its graphical tangle-theoretic Temperley-Lieb formulation, provides a powerful calculation tool in this context. We describe its application to the loop representation in detail. Using recoupling theory, we derive general expressions for the spectrum of the quantum area and the quantum volume operators. We compute several volume eigenvalues explicitly. We introduce a scalar product with respect to which area and volume are symmetric operators, and (the trivalent expansions of) the spin network states are orthonormal
Gauging kinematical and internal symmetry groups for extended systems: the Galilean one-time and two-times harmonic oscillators
The possible external couplings of an extended non-relativistic classical
system are characterized by gauging its maximal dynamical symmetry group at the
center-of-mass. The Galilean one-time and two-times harmonic oscillators are
exploited as models. The following remarkable results are then obtained: 1) a
peculiar form of interaction of the system as a whole with the external gauge
fields; 2) a modification of the dynamical part of the symmetry
transformations, which is needed to take into account the alteration of the
dynamics itself, induced by the {\it gauge} fields. In particular, the
Yang-Mills fields associated to the internal rotations have the effect of
modifying the time derivative of the internal variables in a scheme of minimal
coupling (introduction of an internal covariant derivative); 3) given their
dynamical effect, the Yang-Mills fields associated to the internal rotations
apparently define a sort of Galilean spin connection, while the Yang-Mills
fields associated to the quadrupole momentum and to the internal energy have
the effect of introducing a sort of dynamically induced internal metric in the
relative space.Comment: 32 pages, LaTex using the IOP preprint macro package (ioplppt.sty
available at: http://www.iop.org/). The file is available at:
http://www.fis.unipr.it/papers/1995.html The file is a uuencoded tar gzip
file with the IOP preprint style include
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