3,125 research outputs found
Chern-Simons Forms in Gravitation Theories
The Chern-Simons (CS) form evolved from an obstruction in mathematics into an
important object in theoretical physics. In fact, the presence of CS terms in
physics is more common than one may think: they seem to play an important role
in high Tc superconductivity and in recently discovered topological insulators.
In classical physics, the minimal coupling in electromagnetism and to the
action for a mechanical system in Hamiltonian form are examples of CS
functionals. CS forms are also the natural generalization of the minimal
coupling between the electromagnetic field and a point charge when the source
is not point-like but an extended fundamental object, a membrane. They are
found in relation with anomalies in quantum field theories, and as Lagrangians
for gauge fields, including gravity and supergravity. A cursory review of the
role of CS forms in gravitation theories is presented at an introductory level.Comment: Author-created, un-copyedited version of an article published in CQG;
41 pages, no figure
Chern-Simons Gravity: From 2+1 to 2n+1 Dimensions
These lectures provide an elementary introduction to Chern Simons Gravity and
Supergravity in dimensions.Comment: 17 pages, two columns, latex, no figures, Lectures presented at the
XX Encontro de Fisica de Particulas e Campos, Sao Lourenco, Brazil, October
1999, and at the Fifth La Hechicera School, Merida, Venezuela, November 199
Reflections on Cosmology: an Outsider's Point of View
Some of the assumptions of cosmology, as based on the simplest version of
General Relativity, are discussed. It is argued that by slight modifications of
standard gravitation theory, our notion of the sources of gravity {the right
hand side of Einstein's equations{, could be something radically different from
what is usually expected. One example is exhibited to prove the point, and some
consequences are discussed
Torsional Topological Invariants (and their relevance for real life)
The existence of topological invariants analogous to Chern/Pontryagin classes
for a standard or connection, but constructed out of the
torsion tensor, is discussed. These invariants exhibit many of the features of
the Chern/Pontryagin invariants: they can be expressed as integrals over the
manifold of local densities and take integer values on compact spaces without
boundary; their spectrum is determined by the homotopy groups
and .
These invariants are not solely determined by the connection bundle but
depend also on the bundle of local orthonormal frames on the tangent space of
the manifold. It is shown that in spacetimes with nonvanishing torsion there
can occur topologically stable configurations associated with the frame bundle
which are independent of the curvature.
Explicit examples of topologically stable configurations carrying
nonvanishing instanton number in four and eight dimensions are given, and they
can be conjectured to exist in dimension . It is also shown that the chiral
anomaly in a spacetime with torsion receives a contribution proportional to
this instanton number and hence, chiral theories in -dimensional spacetimes
with torsion are potentially anomalous.Comment: Lecture presented at the Meeting on Trends in Theoretical Physics
held at La Plata, April 28-May 6, 1997. Minor correction
Bose-Fermi Transformation In Three Dimensional Space
A generalization of the Jordan-Wigner transformation to three (or higher)
dimensions is constructed. The nonlocal mapping of spin to fermionic variables
is expressed as a gauge transformation with topological charge equal to one.
The resulting fermionic theory is minimally coupled to a nonabelian gauge field
in a spontaneously broken phase containing monopoles.Comment: 11 pages, ReVTe
Chern-Simons Supergravities with Off-Shell Local Superalgebras
A new family of supergravity theories in odd dimensions is presented. The
Lagrangian densities are Chern-Simons forms for the connection of a
supersymmetric extension of the anti-de Sitter algebra. The superalgebras are
the supersymmetric extensions of the AdS algebra for each dimension, thus
completing the analysis of van Holten and Van Proeyen, which was valid for N=1
and for D=2,3,4,mod 8. The Chern-Simons form of the Lagrangian ensures
invariance under the gauge supergroup by construction and, in particular, under
local supersymmetry. Thus, unlike standard supergravity, the local
supersymmetry algebra closes off-shell and without requiring auxiliary fields.
The Lagrangian is explicitly given for D=5, 7 and 11. In all cases the
dynamical field content includes the vielbein, the spin connection, N
gravitini, and some extra bosonic ``matter'' fields which vary from one
dimension to another. The superalgebras fall into three families: osp(m|N) for
D=2,3,4, mod 8, osp(N|m) for D=6,7,8, mod 8, and su(m-2,2|N) for D=5 mod 4,
with m=2^{[D/2]}. The possible connection between the D=11 case and M-Theory is
also discussed.Comment: 13pages, RevTeX, no figures, two column
Geometric approach to the Hamilton-Jacobi equation and global parametrices for the Schr\"odinger propagator
We construct a family of Fourier Integral Operators, defined for arbitrary
large times, representing a global parametrix for the Schr\"odinger propagator
when the potential is quadratic at infinity. This construction is based on the
geometric approach to the corresponding Hamilton-Jacobi equation and thus
sidesteps the problem of the caustics generated by the classical flow.
Moreover, a detailed study of the real phase function allows us to recover a
WKB semiclassical approximation which necessarily involves the multivaluedness
of the graph of the Hamiltonian flow past the caustics
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