197 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 $d=2n+1$ 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

### Three aspects of bosonized supersymmetry and linear differential field equation with reflection

Recently it was observed by one of the authors that supersymmetric quantum
mechanics (SUSYQM) admits a formulation in terms of only one bosonic degree of
freedom. Such a construction, called the minimally bosonized SUSYQM, appeared
in the context of integrable systems and dynamical symmetries. We show that the
minimally bosonized SUSYQM can be obtained from Witten's SUSYQM by applying to
it a nonlocal unitary transformation with a subsequent reduction to one of the
eigenspaces of the total reflection operator. The transformation depends on the
parity operator, and the deformed Heisenberg algebra with reflection,
intimately related to parabosons and parafermions, emerges here in a natural
way. It is shown that the minimally bosonized SUSYQM can also be understood as
supersymmetric two-fermion system. With this interpretation, the bosonization
construction is generalized to the case of N=1 supersymmetry in 2 dimensions.
The same special unitary transformation diagonalises the Hamiltonian operator
of the 2D massive free Dirac theory. The resulting Hamiltonian is not a square
root like in the Foldy-Wouthuysen case, but is linear in spatial derivative.
Subsequent reduction to `up' or `down' field component gives rise to a linear
differential equation with reflection whose `square' is the massive
Klein-Gordon equation. In the massless limit this becomes the self-dual Weyl
equation. The linear differential equation with reflection admits
generalizations to higher dimensions and can be consistently coupled to gauge
fields. The bosonized SUSYQM can also be generated applying the nonlocal
unitary transformation to the Dirac field in the background of a nonlinear
scalar field in a kink configuration.Comment: 18 pages, LaTeX, minor typos corrected, ref updated, to appear in
Nucl. Phys.

### 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 $SO(D)$ or $SU(N)$ 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
$\pi_{D-1}(SO(D))$ and $\pi_{D-1}(SO(D+1))$.
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 $4k$. 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 $4k$-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

### Irregular Hamiltonian Systems

Hamiltonian systems with linearly dependent constraints (irregular systems),
are classified according to their behavior in the vicinity of the constraint
surface. For these systems, the standard Dirac procedure is not directly
applicable. However, Dirac's treatment can be slightly modified to obtain, in
some cases, a Hamiltonian description completely equivalent to the Lagrangian
one. A recipe to deal with the different cases is provided, along with a few
pedagogical examples.Comment: To appear in Proceedings of the XIII Chilean Symposium of Physics,
Concepcion, Chile, November 13-15 2002. LaTeX; 5 pages; no figure

- âŠ