37 research outputs found
Cartan Pairs
A new notion of Cartan pairs as a substitute of notion of vector fields in
noncommutative geometry is proposed. The correspondence between Cartan pairs
and differential calculi is established.Comment: 7 pages in LaTeX, to be published in Czechoslovak Journal of Physics,
presented at the 5th Colloquium on Quantum Groups and Integrable Systems,
Prague, June 199
Fibre bundle formulation of nonrelativistic quantum mechanics: I. Introduction. The evolution transport
We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. Its evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
The present first part of this investigation is devoted to the introduction
of basic concepts on which the fibre bundle approach to quantum mechanics
rests. We show that the evolution of pure quantum-mechanical states can be
described as a suitable linear transport along paths, called evolution
transport, of the state sections in the Hilbert fibre bundle of states of a
considered quantum system.Comment: 26 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and
amsfonts are required. Revised: new material, references, and comments are
added. Minor style chages. Continuation of quan-ph/9803083. For continuation
of the this series see http://www.inrne.bas.bg/mathmod/bozhome
The algebra of Grassmann canonical anti-commutation relations (GAR) and its applications to fermionic systems
We present an approach to a non-commutative-like phase space which allows to
analyze quasi-free states on the CAR algebra in analogy to quasi-free states on
the CCR algebra. The used mathematical tools are based on a new algebraic
structure the "Grassmann algebra of canonical anti-commutation relations" (GAR
algebra) which is given by the twisted tensor product of a Grassmann and a CAR
algebra. As a new application, the corresponding theory provides an elegant
tool for calculating the fidelity of two quasi-free fermionic states which is
needed for the study of entanglement distillation within fermionic systems.Comment: 25 page
On Conformal Infinity and Compactifications of the Minkowski Space
Using the standard Cayley transform and elementary tools it is reiterated
that the conformal compactification of the Minkowski space involves not only
the "cone at infinity" but also the 2-sphere that is at the base of this cone.
We represent this 2-sphere by two additionally marked points on the Penrose
diagram for the compactified Minkowski space. Lacks and omissions in the
existing literature are described, Penrose diagrams are derived for both,
simple compactification and its double covering space, which is discussed in
some detail using both the U(2) approach and the exterior and Clifford algebra
methods. Using the Hodge * operator twistors (i.e. vectors of the
pseudo-Hermitian space H_{2,2}) are realized as spinors (i.e., vectors of a
faithful irreducible representation of the even Clifford algebra) for the
conformal group SO(4,2)/Z_2. Killing vector fields corresponding to the left
action of U(2) on itself are explicitly calculated. Isotropic cones and
corresponding projective quadrics in H_{p,q} are also discussed. Applications
to flat conformal structures, including the normal Cartan connection and
conformal development has been discussed in some detail.Comment: 38 pages, 8 figures, late
Determination of electromagnetic medium from the Fresnel surface
We study Maxwell's equations on a 4-manifold where the electromagnetic medium
is described by an antisymmetric -tensor . In this setting,
the Tamm-Rubilar tensor density determines a polynomial surface of fourth order
in each cotangent space. This surface is called the Fresnel surface and acts as
a generalisation of the light-cone determined by a Lorentz metric; the Fresnel
surface parameterises electromagnetic wave-speed as a function of direction.
Favaro and Bergamin have recently proven that if has only a principal
part and if the Fresnel surface of coincides with the light cone for a
Lorentz metric , then is proportional to the Hodge star operator of
. That is, under additional assumptions, the Fresnel surface of
determines the conformal class of . The purpose of this paper is
twofold. First, we provide a new proof of this result using Gr\"obner bases.
Second, we describe a number of cases where the Fresnel surface does not
determine the conformal class of the original -tensor . For
example, if is invertible we show that and have
the same Fresnel surfaces.Comment: 23 pages, 1 figur
Wave propagation in linear electrodynamics
The Fresnel equation governing the propagation of electromagnetic waves for
the most general linear constitutive law is derived. The wave normals are found
to lie, in general, on a fourth order surface. When the constitutive
coefficients satisfy the so-called reciprocity or closure relation, one can
define a duality operator on the space of the two-forms. We prove that the
closure relation is a sufficient condition for the reduction of the fourth
order surface to the familiar second order light cone structure. We finally
study whether this condition is also necessary.Comment: 13 pages. Phys. Rev. D, to appea
On Uniqueness of the Jump Process in Quantum Measurement Theory
We prove that, contrary to the standard quantum theory of continuous
observation, in the formalism of Event Enhanced Quantum Theory the stochastic
process generating individual sample histories of pairs (observed quantum
system, observing classical apparatus) is unique. This result gives a rigorous
basis to the previous heuristic argument of Blanchard and Jadczyk. Possible
implications of this result are discussed.Comment: 31 pages, LaTeX, article; e-mail contact [email protected]
Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles
The EPRB experiment with massive partcles can be formulated if one defines
spin in a relativistic way. Two versions are discussed: The one using the spin
operator defined via the relativistic center-of-mass operator, and the one
using the Pauli-Lubanski vector. Both are shown to lead to the SAME prediction
for the EPRB experiment: The degree of violation of the Bell inequality
DECREASES with growing velocity of the EPR pair of spin-1/2 particles. The
phenomenon can be physically understood as a combined effect of the Lorentz
contraction and the Moller shift of the relativistic center of mass. The effect
is therefore stronger than standard relativistic phenomena such as the Lorentz
contraction or time dilatation. The fact that the Bell inequality is in general
less violated than in the nonrelativistic case will have to be taken into
account in tests for eavesdropping if massive particles will be used for a key
transfer.Comment: Figures added as appeared in PRA, two typos corrected (one important
in the formula for eigenvector in Sec. IV); link to the unpublished 1984
paper containing the results (without typos!) of Sec. IV is adde
The Schroedinger Problem, Levy Processes Noise in Relativistic Quantum Mechanics
The main purpose of the paper is an essentially probabilistic analysis of
relativistic quantum mechanics. It is based on the assumption that whenever
probability distributions arise, there exists a stochastic process that is
either responsible for temporal evolution of a given measure or preserves the
measure in the stationary case. Our departure point is the so-called
Schr\"{o}dinger problem of probabilistic evolution, which provides for a unique
Markov stochastic interpolation between any given pair of boundary probability
densities for a process covering a fixed, finite duration of time, provided we
have decided a priori what kind of primordial dynamical semigroup transition
mechanism is involved. In the nonrelativistic theory, including quantum
mechanics, Feyman-Kac-like kernels are the building blocks for suitable
transition probability densities of the process. In the standard "free" case
(Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered.
In the framework of the Schr\"{o}dinger problem, the "free noise" can also be
extended to any infinitely divisible probability law, as covered by the
L\'{e}vy-Khintchine formula. Since the relativistic Hamiltonians
and are known to generate such laws, we focus on
them for the analysis of probabilistic phenomena, which are shown to be
associated with the relativistic wave (D'Alembert) and matter-wave
(Klein-Gordon) equations, respectively. We show that such stochastic processes
exist and are spatial jump processes. In general, in the presence of external
potentials, they do not share the Markov property, except for stationary
situations. A concrete example of the pseudodifferential Cauchy-Schr\"{o}dinger
evolution is analyzed in detail. The relativistic covariance of related waveComment: Latex fil
Circulating Very Small Embryonic-Like Stem Cells in Cardiovascular Disease
Very small embryonic-like cells (VSELs) are a population of stem cells residing in the bone marrow (BM) and several organs, which undergo mobilization into peripheral blood (PB) following acute myocardial infarction and stroke. These cells express markers of pluripotent stem cells (PSCs), such as Oct-4, Nanog, and SSEA-1, as well as early cardiac, endothelial, and neural tissue developmental markers. VSELs can be effectively isolated from the BM, umbilical cord blood, and PB. Peripheral blood and BM-derived VSELs can be expanded in co-culture with C2C12 myoblast feeder layer and undergo differentiation into cells from all three germ layers, including cardiomyocytes and vascular endothelial cells. Isolation of VSLEs using fluorescence-activated cell sorting multiparameter live cell sorting system is dependent on gating strategy based on their small size and expression of PSC and absence of hematopoietic lineage markers. VSELs express early cardiac and endothelial lineages markers (GATA-4, Nkx2.5/Csx, VE-cadherin, and von Willebrand factor), SDF-1 chemokine receptor CXCR4, and undergo rapid mobilization in acute MI and ischemic stroke. Experiments in mice showed differentiation of BM-derived VSELs into cardiac myocytes and effectiveness of expanded and pre-differentiated VSLEs in improvement of left ventricular ejection fraction after myocardial infarction