141 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
On the Groundstate of Yang-Mills Quantum Mechanics
A systematic method to calculate the low energy spectrum of SU(2) Yang-Mills
quantum mechanics with high precision is given and applied to obtain the
energies of the groundstate and the first few excited states.Comment: 4 pages REVTEX twocolumn, no figures; important calculational mistake
corrected which considerably changes the conclusions; references adde
Description of Friedmann Observables in Quantum Universe
The solution of the problem of describing the Friedmann observables (the
Hubble law, the red shift, etc.) in quantum cosmology is proposed on the basis
of the method of gaugeless Hamiltonian reduction in which the gravitational
part of the energy constraint is considered as a new momentum. We show that the
conjugate variable corresponding to the new momentum plays a role of the
invariant time parameter of evolution of dynamical variables in the sector of
the Dirac observables of the general Hamiltonian approach. Relations between
these Dirac observables and the Friedmann observables of the expanding Universe
are established for the standard Friedmann cosmological model with dust and
radiation. The presented reduction removes an infinite factor from the
functional integral, provides the normalizability of the wave function of the
Universe and distinguishes the conformal frame of reference where the Hubble
law is caused by the alteration of the conformal dust mass.Comment: 10 pages, LaTe
Mass of a quantum 't Hooft-Polyakov monopole
The quantum mechanical mass of 't Hooft-Polyakov monopoles in the
four-dimensional Georgi-Glashow is calculated non-perturbatively using lattice
Monte Carlo simulations. This is done by imposing twisted boundary conditions
that ensure there is one unit of magnetic charge on the lattice, and measuring
the free energy difference between this ensemble and the vacuum. In the
weak-coupling limit, the results can be used to determine the quantum
correction to the classical mass, once renormalisation of couplings is taken
properly into account. The methods can also be used to study the masses at
strong coupling, i.e., near the critical point, where there are hints of a
possible electric-magnetic duality.Comment: 17 pages, 4 figures. Typos corrected, one reference adde
Time and Dirac Observables in Friedmann Cosmologies
A cosmological time variable is emerged from the Hamiltonian formulation of
Friedmann model to measure the evolution of dynamical observables in the
theory. A set of observables has been identified for the theory on the null
hypersurfaces that its evolution is with respect to the volume clock introduced
by the cosmological time variable.Comment: 11 page
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
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