913 research outputs found
Classical electrodynamics of point charges
A simple mathematical procedure is introduced which allows redefining in an
exact way divergent integrals and limits that appear in the basic equations of
classical electrodynamics with point charges. In this way all divergences are
at once removed without affecting the locality and the relativistic covariance
of the theory, and with no need for mass renormalization. The procedure is
first used to obtain a finite expression for the electromagnetic
energy-momentum of the system. We show that the relativistic Lorentz-Dirac
equation can be deduced from the conservation of this electromagnetic
energy-momentum plus the usual mechanical term. Then we derive a finite
lagrangian, which depends on the particle variables and on the actual
electromagnetic potentials at a given time. From this lagrangian the equations
of motion of both particles and fields can be derived via Hamilton's
variational principle. The hamiltonian formulation of the theory can be
obtained in a straightforward way. This leads to an interesting comparison
between the resulting divergence-free expression of the hamiltonian functional
and the standard renormalization rules for perturbative quantum
electrodynamics.Comment: 46 pages, REVTeX . Revised version with added comments and reference
The Riemann-Lovelock Curvature Tensor
In order to study the properties of Lovelock gravity theories in low
dimensions, we define the kth-order Riemann-Lovelock tensor as a certain
quantity having a total 4k-indices, which is kth-order in the Riemann curvature
tensor and shares its basic algebraic and differential properties. We show that
the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions
2k \le D <4k. In D=2k+1 this identity implies that all solutions of pure
kth-order Lovelock gravity are `Riemann-Lovelock' flat. It is verified that the
static, spherically symmetric solutions of these theories, which are missing
solid angle space times, indeed satisfy this flatness property. This
generalizes results from Einstein gravity in D=3, which corresponds to the k=1
case. We speculate about some possible further consequences of Riemann-Lovelock
curvature.Comment: 12 page
Gauge Invariance for Generally Covariant Systems
Previous analyses on the gauge invariance of the action for a generally
covariant system are generalized. It is shown that if the action principle is
properly improved, there is as much gauge freedom at the endpoints for an
arbitrary gauge system as there is for a system with ``internal'' gauge
symmetries. The key point is to correctly identify the boundary conditions for
the allowed histories and to include the appropriate end-point contribution in
the action. The path integral is then discussed. It is proved that by employing
the improved action, one can use time-independent canonical gauges even in the
case of generally covariant theories. From the point of view of the action and
the path integral, there is thus no conceptual difference between general
covariance and ``ordinary gauge invariance''. The discussion is illustrated in
the case of the point particle, for which various canonical gauges are
considered.Comment: 41 pages, ULB-PMIF-92-0
Decay of the Cosmological Constant. Equivalence of Quantum Tunneling and Thermal Activation in Two Spacetime Dimensions
We study the decay of the cosmological constant in two spacetime dimensions
through production of pairs. We show that the same nucleation process looks as
quantum mechanical tunneling (instanton) to one Killing observer and as thermal
activation (thermalon) to another. Thus, we find another striking example of
the deep interplay between gravity, thermodynamics and quantum mechanics which
becomes apparent in presence of horizons.Comment: 11 pages, 6 figure
Dyonic Anomalies
We consider the problem of coupling a dyonic p-brane in d = 2p+4 space-time
dimensions to a prescribed (p+2)-form field strength. This is particularly
subtle when p is odd. For the case p = 1, we explicitly construct a coupling
functional, which is a sum of two terms: one which is linear in the prescribed
field strength, and one which describes the coupling of the brane to its
self-field and takes the form of a Wess-Zumino term depending only on the
embedding of the brane world-volume into space-time. We then show that this
functional is well-defined only modulo a certain anomaly, related to the Euler
class of the normal bundle of the brane world-volume.Comment: 7 pages; reference adde
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