630 research outputs found
Real and complex connections for canonical gravity
Both real and complex connections have been used for canonical gravity: the
complex connection has SL(2,C) as gauge group, while the real connection has
SU(2) as gauge group. We show that there is an arbitrary parameter
which enters in the definition of the real connection, in the Poisson brackets,
and therefore in the scale of the discrete spectra one finds for areas and
volumes in the corresponding quantum theory. A value for could be could
be singled out in the quantum theory by the Hamiltonian constraint, or by the
rotation to the complex Ashtekar connection.Comment: 8 pages, RevTeX, no figure
Constraints and restraints in crystal structure analysis
The restraint-based procedure in least-squares refinement is critiqued and the advantages of using internal coordinates are discussed
The simplest Regge calculus model in the canonical form
Dynamics of a Regge three-dimensional (3D) manifold in a continuous time is
considered. The manifold is closed consisting of the two tetrahedrons with
identified corresponding vertices. The action of the model is that obtained via
limiting procedure from the general relativity (GR) action for the completely
discrete 4D Regge calculus. It closely resembles the continuous general
relativity action in the Hilbert-Palatini (HP) form but possesses finite number
of the degrees of freedom. The canonical structure of the theory is described.
Central point is appearance of the new relations with time derivatives not
following from the Lagrangian but serving to ensure completely discrete 4D
Regge calculus origin of the system. In particular, taking these into account
turns out to be necessary to obtain the true number of the degrees of freedom
being the number of linklengths of the 3D Regge manifold at a given moment of
time.Comment: LaTeX, 7 page
Fuzzy Nambu-Goldstone Physics
In spacetime dimensions larger than 2, whenever a global symmetry G is
spontaneously broken to a subgroup H, and G and H are Lie groups, there are
Nambu-Goldstone modes described by fields with values in G/H. In
two-dimensional spacetimes as well, models where fields take values in G/H are
of considerable interest even though in that case there is no spontaneous
breaking of continuous symmetries. We consider such models when the world sheet
is a two-sphere and describe their fuzzy analogues for G=SU(N+1),
H=S(U(N-1)xU(1)) ~ U(N) and G/H=CP^N. More generally our methods give fuzzy
versions of continuum models on S^2 when the target spaces are Grassmannians
and flag manifolds described by (N+1)x(N+1) projectors of rank =< (N+1)/2.
These fuzzy models are finite-dimensional matrix models which nevertheless
retain all the essential continuum topological features like solitonic sectors.
They seem well-suited for numerical work.Comment: Latex, 18 pages; references added, typos correcte
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