3,863 research outputs found
The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - I: Dynamical Synchronization and Generalized Inertial Effects
This is the first of a couple of papers in which, by exploiting the
capabilities of the Hamiltonian approach to general relativity, we get a number
of technical achievements that are instrumental both for a disclosure of
\emph{new} results concerning specific issues, and for new insights about
\emph{old} foundational problems of the theory. The first paper includes: 1) a
critical analysis of the various concepts of symmetry related to the
Einstein-Hilbert Lagrangian viewpoint on the one hand, and to the Hamiltonian
viewpoint, on the other. This analysis leads, in particular, to a
re-interpretation of {\it active} diffeomorphisms as {\it passive and
metric-dependent} dynamical symmetries of Einstein's equations, a
re-interpretation which enables to disclose the (nearly unknown) connection of
a subgroup of them to Hamiltonian gauge transformations {\it on-shell}; 2) a
re-visitation of the canonical reduction of the ADM formulation of general
relativity, with particular emphasis on the geometro-dynamical effects of the
gauge-fixing procedure, which amounts to the definition of a \emph{global
(non-inertial) space-time laboratory}. This analysis discloses the peculiar
\emph{dynamical nature} that the traditional definition of distant simultaneity
and clock-synchronization assume in general relativity, as well as the {\it
gauge relatedness} of the "conventions" which generalize the classical
Einstein's convention.Comment: 45 pages, Revtex4, some refinements adde
Efficiency optimization and symmetry-breaking in a model of ciliary locomotion
A variety of swimming microorganisms, called ciliates, exploit the bending of
a large number of small and densely-packed organelles, termed cilia, in order
to propel themselves in a viscous fluid. We consider a spherical envelope model
for such ciliary locomotion where the dynamics of the individual cilia are
replaced by that of a continuous overlaying surface allowed to deform
tangentially to itself. Employing a variational approach, we determine
numerically the time-periodic deformation of such surface which leads to
low-Reynolds locomotion with minimum rate of energy dissipation (maximum
efficiency). Employing both Lagrangian and Eulerian points of views, we show
that in the optimal swimming stroke, individual cilia display weak asymmetric
beating, but that a significant symmetry-breaking occurs at the organism level,
with the whole surface deforming in a wave-like fashion reminiscent of
metachronal waves of biological cilia. This wave motion is analyzed using a
formal modal decomposition, is found to occur in the same direction as the
swimming direction, and is interpreted as due to a spatial distribution of
phase-differences in the kinematics of individual cilia. Using additional
constrained optimizations, as well as a constructed analytical ansatz, we
derive a complete optimization diagram where all swimming efficiencies,
swimming speeds, and amplitude of surface deformation can be reached, with the
mathematically optimal swimmer, of efficiency one half, being a singular limit.
Biologically, our work suggests therefore that metachronal waves may allow
cilia to propel cells forward while reducing the energy dissipated in the
surrounding fluid.Comment: 29 pages, 20 figure
Brane Induced Gravity: From a No-Go to a No-Ghost Theorem
Numerous claims in the literature suggest that gravity induced on a higher
co-dimensional surface violates unitarity in the weak coupling regime. However,
it remained unclear, why a conserved source localized on this surface and
giving rise to an induced gravity term at low energies would absorb and emit
the associated ghost, given a consistent source-free theory. In this article it
is shown that the appearance of the induced Einstein Hilbert term does not
threaten the unitarity of the theory. The physics arguments behind this
statement are presented in a semi-covariant language, but the detailed proof is
given using Dirac's constraint analysis. It is shown that the would-be ghost
highlighted in previous works is non-dynamical and therefore not associated
with a state in the Hilbert space. As a result of these investigations, brane
induced gravity goes without a ghost, opening an exciting window of opportunity
for consistent deformations of gravity at the largest observable distances.Comment: 13 pages, v2: matches version published in Physical Review
Classical and Quantum Evolutions of the de Sitter and the anti-de Sitter Universes in 2+1 dimensions
Two canonical formulations of the Einstein gravity in 2+1 dimensions, namely,
the ADM formalism and the Chern-Simons gravity, are investigated in the case of
nonvanishing cosmological constant. General arguments for reducing phase spaces
of the two formalisms are given when spatial hypersurface is compact. In
particular when the space has the topology of a sphere or a torus
, the spacetimes constructed from these two formulations can be
identified and the classical equivalence between the ADM and the CSG is shown.
Moreover in the case the relations between their phase spaces, and
therefore between their quantizations, are given in almost the same form as
that in the case when the cosmological constant vanishes. There are, however,
some modifications, the most remarkable one of which is that the phase space of
the CSG is in 1 to 2 correspondence with the one of the ADM when the
cosmological constant is negative.Comment: 37pages Latex (6 figures not included
Integrable theories and loop spaces: fundamentals, applications and new developments
We review our proposal to generalize the standard two-dimensional flatness
construction of Lax-Zakharov-Shabat to relativistic field theories in d+1
dimensions. The fundamentals from the theory of connections on loop spaces are
presented and clarified. These ideas are exposed using mathematical tools
familiar to physicists. We exhibit recent and new results that relate the
locality of the loop space curvature to the diffeomorphism invariance of the
loop space holonomy. These result are used to show that the holonomy is abelian
if the holonomy is diffeomorphism invariant.
These results justify in part and set the limitations of the local
implementations of the approach which has been worked out in the last decade.
We highlight very interesting applications like the construction and the
solution of an integrable four dimensional field theory with Hopf solitons, and
new integrability conditions which generalize BPS equations to systems such as
Skyrme theories. Applications of these ideas leading to new constructions are
implemented in theories that admit volume preserving diffeomorphisms of the
target space as symmetries. Applications to physically relevant systems like
Yang Mills theories are summarized. We also discuss other possibilities that
have not yet been explored.Comment: 64 pages, 8 figure
Special Geometry of Euclidean Supersymmetry I: Vector Multiplets
We construct the general action for Abelian vector multiplets in rigid
4-dimensional Euclidean (instead of Minkowskian) N=2 supersymmetry, i.e., over
space-times with a positive definite instead of a Lorentzian metric. The target
manifolds for the scalar fields turn out to be para-complex manifolds endowed
with a particular kind of special geometry, which we call affine special
para-Kahler geometry. We give a precise definition and develop the mathematical
theory of such manifolds. The relation to the affine special Kahler manifolds
appearing in Minkowskian N=2 supersymmetry is discussed. Starting from the
general 5-dimensional vector multiplet action we consider dimensional reduction
over time and space in parallel, providing a dictionary between the resulting
Euclidean and Minkowskian theories. Then we reanalyze supersymmetry in four
dimensions and find that any (para-)holomorphic prepotential defines a
supersymmetric Lagrangian, provided that we add a specific four-fermion term,
which cannot be obtained by dimensional reduction. We show that the Euclidean
action and supersymmetry transformations, when written in terms of
para-holomorphic coordinates, take exactly the same form as their Minkowskian
counterparts. The appearance of a para-complex and complex structure in the
Euclidean and Minkowskian theory, respectively, is traced back to properties of
the underlying R-symmetry groups. Finally, we indicate how our work will be
extended to other types of multiplets and to supergravity in the future and
explain the relevance of this project for the study of instantons, solitons and
cosmological solutions in supergravity and M-theory.Comment: 74 page
Spontaneous breakdown of Lorentz symmetry in scalar QED with higher order derivatives
Scalar QED is studied with higher order derivatives for the scalar field
kinetic energy. A local potential is generated for the gauge field due to the
covariant derivatives and the vacuum with non-vanishing expectation value for
the scalar field and the vector potential is constructed in the leading order
saddle point expansion. This vacuum breaks the global gauge and Lorentz
symmetry spontaneously. The unitarity of time evolution is assured in the
physical, positive norm subspace and the linearized equations of motion are
calculated. Goldstone theorem always keeps the radiation field massless. A
particular model is constructed where the the full set of standard Maxwell
equations is recovered on the tree level thereby relegating the effects of
broken Lorentz symmetry to the level of radiative corrections.Comment: 14 pages, to appear in Phys. Rev.
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