12 research outputs found

### The BMS/GCA correspondence

We find a surprising connection between asymptotically flat space-times and
non-relativistic conformal systems in one lower dimension. The BMS group is the
group of asymptotic isometries of flat Minkowski space at null infinity. This
is known to be infinite dimensional in three and four dimensions. We show that
the BMS algebra in 3 dimensions is the same as the 2D Galilean Conformal
Algebra which is of relevance to non-relativistic conformal symmetries. We
further justify our proposal by looking at a Penrose limit of a radially
infalling null ray inspired by non-relativistic scaling and obtain a flat
metric. The 4D BMS algebra is also discussed and found to be the same as
another class of GCA, called the semi-GCA, in three dimensions. We propose a
general BMS/GCA correspondence. Some consequences are discussed.Comment: 17 page

### Unconstrained Hamiltonian Formulation of SU(2) Gluodynamics

SU(2) Yang-Mills field theory is considered in the framework of the
generalized Hamiltonian approach and the equivalent unconstrained system is
obtained using the method of Hamiltonian reduction. A canonical transformation
to a set of adapted coordinates is performed in terms of which the
Abelianization of the Gauss law constraints reduces to an algebraic operation
and the pure gauge degrees of freedom drop out from the Hamiltonian after
projection onto the constraint shell. For the remaining gauge invariant fields
two representations are introduced where the three fields which transform as
scalars under spatial rotations are separated from the three rotational fields.
An effective low energy nonlinear sigma model type Lagrangian is derived which
out of the six physical fields involves only one of the three scalar fields and
two rotational fields summarized in a unit vector. Its possible relation to the
effective Lagrangian proposed recently by Faddeev and Niemi is discussed.
Finally the unconstrained analog of the well-known nonnormalizable groundstate
wave functional which solves the Schr\"odinger equation with zero energy is
given and analysed in the strong coupling limit.Comment: 20 pages REVTEX, no figures; final version to appear in Phys. Rev. D;
minor changes, notations simplifie

### On the Dynamics of Bianchi IX cosmological models

A cosmological description of the universe is proposed in the context of
Hamiltonian formulation of a Bianchi IX cosmology minimally coupled to a
massless scalar field. The classical and quantum results are studied with
special attention to the case of closed Friedmann-Robertson-Walker model.Comment: 11 pages, 1 figur

### Euler-Calogero-Moser system from SU(2) Yang-Mills theory

The relation between SU(2) Yang-Mills mechanics, originated from the
4-dimensional SU(2) Yang-Mills theory under the supposition of spatial
homogeneity of the gauge fields, and the Euler-Calogero-Moser model is
discussed in the framework of Hamiltonian reduction. Two kinds of reductions of
the degrees of freedom are considered: due to the gauge invariance and due to
the discrete symmetry. In the former case, it is shown that after elimination
of the gauge degrees of freedom from the SU(2) Yang-Mills mechanics the
resulting unconstrained system represents the ID_3 Euler-Calogero-Moser model
with an external fourth-order potential. Whereas in the latter, the IA_6
Euler-Calogero-Moser model embedded in an external potential is derived whose
projection onto the invariant submanifold through the discrete symmetry
coincides again with the SU(2) Yang-Mills mechanics. Based on this connection,
the equations of motion of the SU(2) Yang-Mills mechanics in the limit of the
zero coupling constant are presented in the Lax form.Comment: Revtex, 14 pages, no figures. Abstract changed, strata analysis have
been included, typos corrected, references adde