1,462 research outputs found
Lagrangian Symmetries of Chern-Simons Theories
This paper analyses the Noether symmetries and the corresponding conservation
laws for Chern-Simons Lagrangians in dimension . In particular, we find an
expression for the superpotential of Chern-Simons gravity. As a by-product the
general discussion of superpotentials for 3rd order natural and quasi-natural
theories is also given.Comment: 16 pages in LaTeX, some comments and references added. to appear in
Journal of Physics A: Mathematical and Genera
Yang-Mills, Complex Structures and Chern's Last Theorem
Recently Shiing-Shen Chern suggested that the six dimensional sphere
has no complex structure. Here we explore the relations between
his arguments and Yang-Mills theories. In particular, we propose that Chern's
approach is widely applicable to investigate connections between the geometry
of manifolds and the structure of gauge theories. We also discuss several
examples of manifolds, both with and without a complex structure.Comment: Chern's proof remains incomplete, and we have edited some statements
in our article accordingl
Extension of the Poincar\'e Group and Non-Abelian Tensor Gauge Fields
In the recently proposed generalization of the Yang-Mills theory the group of
gauge transformation gets essentially enlarged. This enlargement involves an
elegant mixture of the internal and space-time symmetries. The resulting group
is an extension of the Poincar\'e group with infinitely many generators which
carry internal and space-time indices. This is similar to the super-symmetric
extension of the Poincar\'e group, where instead of an anti-commuting spinor
variable one should introduce a new vector variable. The construction of
irreducible representations of the extended Poincar\'e algebra identifies a
vector variable with the derivative of the Pauli-Lubanski vector over its
length. As a result of this identification the generators of the gauge group
have nonzero components only in the plane transversal to the momentum and are
projecting out non-Abelian tensor gauge fields into the transversal plane,
keeping only their positively definite space-like components.Comment: 21 page
On number fields with nontrivial subfields
What is the probability for a number field of composite degree to have a
nontrivial subfield? As the reader might expect the answer heavily depends on
the interpretation of probability. We show that if the fields are enumerated by
the smallest height of their generators the probability is zero, at least if
. This is in contrast to what one expects when the fields are enumerated
by the discriminant. The main result of this article is an estimate for the
number of algebraic numbers of degree and bounded height which generate
a field that contains an unspecified subfield of degree . If
we get the correct asymptotics as the height tends to
infinity
The causal structure of spacetime is a parameterized Randers geometry
There is a by now well-established isomorphism between stationary
4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries -
these Randers geometries being a particular case of the more general class of
3-dimensional Finsler geometries. We point out that in stably causal
spacetimes, by using the (time-dependent) ADM decomposition, this result can be
extended to general non-stationary spacetimes - the causal structure (conformal
structure) of the full spacetime is completely encoded in a parameterized
(time-dependent) class of Randers spaces, which can then be used to define a
Fermat principle, and also to reconstruct the null cones and causal structure.Comment: 8 page
Seismic Safety Analysis of Earth Dam — Case History Studies
The method of seismic safety analysis for earth dam was examined by using actual performances of earth dams during the Chi-Chi Earthquake. Results of analysis under design earthquakes were also collected and compared with the performance records of earth dams. From the results of these studies, it appears that the Seed-Lee-Idriss approach can provide reasonable predictions on the dynamic responses and post-earthquake performance of well-compacted earth dam
Conditional linearizability criteria for a system of third-order ordinary differential equations
We provide linearizability criteria for a class of systems of third-order
ordinary differential equations (ODEs) that is cubically semi-linear in the
first derivative, by differentiating a system of second-order quadratically
semi-linear ODEs and using the original system to replace the second
derivative. The procedure developed splits into two cases, those where the
coefficients are constant and those where they are variables. Both cases are
discussed and examples given
The geometric sense of R. Sasaki connection
For the Riemannian manifold two special connections on the sum of the
tangent bundle and the trivial one-dimensional bundle are constructed.
These connections are flat if and only if the space has a constant
sectional curvature . The geometric explanation of this property is
given. This construction gives a coordinate free many-dimensional
generalization of the connection from the paper: R. Sasaki 1979 Soliton
equations and pseudospherical surfaces, Nuclear Phys., {\bf 154 B}, pp.
343-357. It is shown that these connections are in close relation with the
imbedding of into Euclidean or pseudoeuclidean -dimension
spaces.Comment: 7 pages, the key reference to the paper of Min-Oo is included in the
second versio
Two universal results for Wilson loops at strong coupling
We present results for Wilson loops in strongly coupled gauge theories. The
loops may be taken around an arbitrarily shaped contour and in any field theory
with a dual IIB geometry of the form M x S^5. No assumptions about
supersymmetry are made. The first result uses D5 branes to show how the loop in
any antisymmetric representation is computed in terms of the loop in the
fundamental representation. The second result uses D3 branes to observe that
each loop defines a rich sequence of operators associated with minimal surfaces
in S^5. The action of these configurations are all computable. Both results
have features suggesting a connection with integrability.Comment: 1+12 pages. LaTeX. No figure
A covariant formalism for Chern-Simons gravity
Chern--Simons type Lagrangians in dimensions are analyzed from the
point of view of their covariance and globality. We use the transgression
formula to find out a new fully covariant and global Lagrangian for
Chern--Simons gravity: the price for establishing globality is hidden in a
bimetric (or biconnection) structure. Such a formulation allows to calculate
from a global and simpler viewpoint the energy-momentum complex and the
superpotential both for Yang--Mills and gravitational examples.Comment: 12 pages,LaTeX, to appear in Journal of Physics
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