Do physical laws limit the speed of "all data processing systems, manmade as
well as biological"? This question proposed and positively answered by H. J.
Bremermann in 1962, should be corrected to make it compatible with Einstein's
theory o...
The shortest way to the geodesics of spheres
September 20, 2009
|
Mathematics
General Mathematics
General Mathematics
In this paper, we prove, using only elementary geometric arguments and only
assuming that the curves are continuous, that the geodesics on a sphere are the
minor arcs of the great circles. Our result are valid for any sphere in any
inner pr...
Probability Bracket Notation, Wick-Matsubara Relation, Density
Operators, and Microscopic Probability Modeling
September 7, 2009
Mathematics
Physics
Probability
Mathematical Physics
Mathematical Physics
Following the Dirac vector bracket notation (VBN), we proposed the
probability bracket notation (PBN) in our previous paper. We mentioned that
under the special Wick rotation (imaginary time), a stationary Schrodinger
equation in the Hilber...
Improved simulation of non-Gaussian temperature and polarization CMB
maps
August 31, 2009
|
Physics
Cosmology and Nongalactic Astrophysics
We describe an algorithm to generate temperature and polarization maps of the
cosmic microwave background radiation containing non-Gaussianity of arbitrary
local type. We apply an optimized quadrature scheme that allows us to predict
and co...
Representations of Hermitian Commutative *-Algebras by Unbounded
Operators
August 22, 2009
Mathematics
Operator Algebras
Representation Theory
We give a spectral theorem for unital representations of Hermitian
commutative unital *-algebras by possibly unbounded operators in a pre-Hilbert
space. A better result is known for the case in which the *-algebra is
countably generated....
Classification of abelian complex structures on 6-dimensional Lie
algebras
August 21, 2009
| |
Mathematics
Rings and Algebras
Differential Geometry
We classify the 6-dimensional Lie algebras that can be endowed with an
abelian complex structure and parameterize, on each of these algebras, the
space of such structures up to holomorphic isomorphism....
Quantum Zeno, Hamlet and similar effects
August 10, 2009
Physics
Quantum Physics
Simply speaking quantum Zeno effect for an unstable quantum system represents
total decay probability decrease by frequent decay detection. Analogously
simply speaking quantum anti-Zeno effect for an unstable quantum system
represents total...
Towards a Post Reductionist Science: The Open Universe
July 15, 2009
|
Physics
General Physics
In this paper we consider clumped baryonic matter as a spherically symmetric
barotropic fluid associated with a compact four-dimensional Einstein manifold
with a four-radius that is determined by the fluid density. We further
investigate th...
Discrete Linear Groups containing Arithmetic Groups
May 12, 2009
| | |
Mathematics
Group Theory
Group Theory
We prove in a large number of cases, that a Zariski dense discrete subgroup
of a simple real algebraic group G which contains a higher rank lattice is a
lattice in the group G. For example, we show that a Zariski dense subgroup of
$SL_n...
Quantum action, non-locality and coherence from classical perception, a
new facet of Lagrangian formalism for relativistic dynamics
April 14, 2009
Physics
Classical Physics
Classical and quantum mechanical descriptions of physical world are
seamlessly abridged within the framework of Lagrangian formalism which, besides
revealing the essence of nonlocally correlated dynamic evolution, helps
understanding abrupt...