3,478 research outputs found
On the evolutionary form of the constraints in electrodynamics
The constraint equations in Maxwell theory are investigated. In analogy with
some recent results on the constraints of general relativity it is shown,
regardless of the signature and dimension of the ambient space, that the
"divergence of a vector field" type constraints can always be put into linear
first order hyperbolic form for which global existence and uniqueness of
solutions to an initial-boundary value problem is guaranteed.Comment: 10 pages, 1 figure; The published version contains several updates of
former one. The introduction is extended, and new sections with an explicit
example and with concluding remarks had also been adde
Multi-Hamiltonian formulations and stability of higher-derivative extensions of Chern-Simons
Most general third-order linear gauge vector field theory is considered.
The field equations involve, besides the mass, two dimensionless constant
parameters. The theory admits two-parameter series of conserved tensors with
the canonical energy-momentum being a particular representative of the series.
For a certain range of the model parameters, the series of conserved tensors
include bounded quantities. This makes the dynamics classically stable, though
the canonical energy is unbounded in all the instances. The free third-order
equations are shown to admit constrained multi-Hamiltonian form with the
zero-zero components of conserved tensors playing the roles of corresponding
Hamiltonians. The series of Hamiltonians includes the canonical Ostrogradski's
one, which is unbounded. The Hamiltonian formulations with different
Hamiltonians are not connected by canonical transformations. This means, the
theory admits inequivalent quantizations at the free level. Covariant
interactions are included with spinor fields such that the higher-derivative
dynamics remains stable at interacting level if the bounded conserved quantity
exists in the free theory. In the first-order formalism, the interacting theory
remains Hamiltonian and therefore it admits quantization, though the vertices
are not necessarily Lagrangian in the third-order field equations.Comment: 19 page
Anomalous character of the axion-photon coupling in a magnetic field distorted by a pp-wave gravitational background
We study the problem of axion-photon coupling in the magnetic field
influenced by gravitational radiation. We focus on exact solutions to the
equations for axion electrodynamics in the pp-wave gravitational background for
two models with initially constant magnetic field. The first model describes
the response of an initially constant magnetic field in a gravitational-wave
vacuum with unit refraction index; the second model is characterized by a
non-unit refraction index prescribed to the presence of ordinary and/or dark
matter. We show that both models demonstrate anomalous behavior of the
electromagnetic field generated by the axion-photon coupling in the presence of
magnetic field, evolving in the gravitational wave background. The role of
axionic dark matter in the formation of the anomalous response of this
electrodynamic system is discussed.Comment: 26 pages, no figure
Nonlinear electrodynamics as a symmetric hyperbolic system
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a
Lagrangian formalism have dispersion relations in which propagation planes
factor into null planes corresponding to two effective metrics which depend on
the point-wise values of the electromagnetic field. These effective Lorentzian
metrics share the null (generically two) directions of the electromagnetic
field. We show that, the theory is symmetric hyperbolic if and only if the
cones these metrics give rise to have a non-empty intersection. Namely that
there exist families of symmetrizers in the sense of Geroch which are positive
definite for all covectors in the interior of the cones intersection. Thus, for
these theories, the initial value problem is well-posed. We illustrate the
power of this approach with several nonlinear models of physical interest such
as Born-Infeld, Gauss-Bonnet and Euler-Heisenberg
Non-minimal coupling of photons and axions
We establish a new self-consistent system of equations accounting for a
non-minimal interaction of gravitational, electromagnetic and axion fields. The
procedure is based on a non-minimal extension of the standard
Einstein-Maxwell-axion action. The general properties of a ten-parameter family
of non-minimal linear models are discussed. We apply this theory to the models
with pp-wave symmetry and consider propagation of electromagnetic waves
non-minimally coupled to the gravitational and axion fields. We focus on exact
solutions of electrodynamic equations, which describe quasi-minimal and
non-minimal optical activity induced by the axion field. We also discuss
empirical constraints on coupling parameters from astrophysical birefringence
and polarization rotation observations.Comment: 31 pages, 2 Tables; replaced with the final version published in
Classical and Quantum Gravit
Constrained Transport Algorithms for Numerical Relativity. I. Development of a Finite Difference Scheme
A scheme is presented for accurately propagating the gravitational field
constraints in finite difference implementations of numerical relativity. The
method is based on similar techniques used in astrophysical
magnetohydrodynamics and engineering electromagnetics, and has properties of a
finite differential calculus on a four-dimensional manifold. It is motivated by
the arguments that 1) an evolutionary scheme that naturally satisfies the
Bianchi identities will propagate the constraints, and 2) methods in which
temporal and spatial derivatives commute will satisfy the Bianchi identities
implicitly. The proposed algorithm exactly propagates the constraints in a
local Riemann normal coordinate system; {\it i.e.}, all terms in the Bianchi
identities (which all vary as ) cancel to machine roundoff
accuracy at each time step. In a general coordinate basis, these terms, and
those that vary as , also can be made to cancel, but
differences of connection terms, proportional to , will remain,
resulting in a net truncation error. Detailed and complex numerical experiments
with four-dimensional staggered grids will be needed to completely examine the
stability and convergence properties of this method.
If such techniques are successful for finite difference implementations of
numerical relativity, other implementations, such as finite element (and
eventually pseudo-spectral) techniques, might benefit from schemes that use
four-dimensional grids and that have temporal and spatial derivatives that
commute.Comment: 27 pages, 5 figure
Part I. The Cosmological Vacuum from a Topological Perspective
This article examines how the physical presence of field energy and
particulate matter can be interpreted in terms of the topological properties of
space-time. The theory is developed in terms of vector and matrix equations of
exterior differential systems, which are not constrained by tensor
diffeomorphic equivalences. The first postulate defines the field properties (a
vector space continuum) of the Cosmological Vacuum in terms of matrices of
basis functions that map exact differentials into neighborhoods of exterior
differential 1-forms (potentials). The second postulate requires that the field
equations must satisfy the First Law of Thermodynamics dynamically created in
terms of the Lie differential with respect to a process direction field acting
on the exterior differential forms that encode the thermodynamic system. The
vector space of infinitesimals need not be global and its compliment is used to
define particle properties as topological defects embedded in the field vector
space. The potentials, as exterior differential 1-forms, are not (necessarily)
uniquely integrable: the fibers can be twisted, leading to possible Chiral
matrix arrays of certain 3-forms defined as Topological Torsion and Topological
Spin. A significant result demonstrates how the coefficients of Affine Torsion
are related to the concept of Field excitations (mass and charge); another
demonstrates how thermodynamic evolution can describe the emergence of
topological defects in the physical vacuum.Comment: 70 pages, 5 figure
Electromagnetic field theory without divergence problems: 1. The Born Legacy
A fully consistent classical relativistic electrodynamics with spinless point
charges is constructed. The classical evolution of the electromagnetic fields
is governed by the nonlinear Maxwell--Born--Infeld field equations, the
classical evolution of the point charges by a many-body Hamilton--Jacobi law of
motion. The Pauli principle for bosons can be incorporated in the classical
Hamilton--Jacobi formalism. The Cauchy problem is explained and illustrated
with examples. The question of charge-free field solitons is addressed also and
it is shown that if they exist, their peak field strengths must be enormous.
The value The value of Born's constant is shown to be a subtle open issue.Comment: Minor corrections at galley stage incorporated. 66p; to appear in JSP
vol. 116, issue dedicated to Elliott H. Lieb on his 70th birthday. Part II is
math-ph/031103
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