417 research outputs found

### Dynamics of a self-gravitating shell of matter

Dynamics of a self-gravitating shell of matter is derived from the Hilbert
variational principle and then described as an (infinite dimensional,
constrained) Hamiltonian system. A method used here enables us to define
singular Riemann tensor of a non-continuous connection {\em via} standard
formulae of differential geometry, with derivatives understood in the sense of
distributions. Bianchi identities for the singular curvature are proved. They
match the conservation laws for the singular energy-momentum tensor of matter.
Rosenfed-Belinfante and Noether theorems are proved to be still valid in case
of these singular objects. Assumption about continuity of the four-dimensional
spacetime metric is widely discussed.Comment: publishe

### Dynamics of a self gravitating light-like matter shell: a gauge-invariant Lagrangian and Hamiltonian description

A complete Lagrangian and Hamiltonian description of the theory of
self-gravitating light-like matter shells is given in terms of
gauge-independent geometric quantities. For this purpose the notion of an
extrinsic curvature for a null-like hypersurface is discussed and the
corresponding Gauss-Codazzi equations are proved. These equations imply Bianchi
identities for spacetimes with null-like, singular curvature. Energy-momentum
tensor-density of a light-like matter shell is unambiguously defined in terms
of an invariant matter Lagrangian density. Noether identity and
Belinfante-Rosenfeld theorem for such a tensor-density are proved. Finally, the
Hamiltonian dynamics of the interacting system: ``gravity + matter'' is derived
from the total Lagrangian, the latter being an invariant scalar density.Comment: 20 pages, RevTeX4, no figure

### Charge Superselection Sectors for Scalar QED on the Lattice

The lattice model of scalar quantum electrodynamics (Maxwell field coupled to
a complex scalar field) in the Hamiltonian framework is discussed.
It is shown that the algebra of observables ${\cal O}({\Lambda})$ of this
model is a $C^*$-algebra, generated by a set of gauge-invariant elements
satisfying the Gauss law and some additional relations. Next, the faithful,
irreducible and non-degenerate representations of ${\cal O}({\Lambda})$ are
found. They are labeled by the value of the total electric charge, leading to a
decomposition of the physical Hilbert space into charge superselection sectors.
In the Appendices we give a unified description of spinorial and scalar quantum
electrodynamics and, as a byproduct, we present an interesting example of
weakly commuting operators, which do not commute strongly

### Gauge Invariant Formulation and Bosonisation of the Schwinger Model

The functional integral of the massless Schwinger model in $(1+1)$ dimensions
is reduced to an integral in terms of local gauge invariant quantities. It
turns out that this approach leads to a natural bosonisation scheme, yielding,
in particular the famous `bosonisation rule'' and giving some deeper insight
into the nature of the bosonisation phenomenon. As an application, the chiral
anomaly is calculated within this formulation.Comment: LaTeX, 8 page

### Energy-minimizing two black holes initial data

An attempt to construct the ``ground state'' vacuum initial data for the
gravitational field surrounding two black holes is presented. The ground state
is defined as the gravitational initial data minimizing the ADM mass within the
class of data for which the masses of the holes and their distance are fixed.
To parameterize different geometric arrangements of the two holes (and,
therefore, their distance) we use an appropriately chosen scale factor. A
method for analyzing the variations of the ADM mass and the masses (areas) of
the horizons in terms of gravitational degrees of freedom is proposed. The
Misner initial data are analyzed in this context: it is shown that they do not
minimize the ADM mass.Comment: Minor corrections, 2 references adde

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