8,465 research outputs found
Relativistic Partial Wave Analysis Using the Velocity Basis of the Poincare Group
The velocity basis of the Poincare group is used in the direct product space
of two irreducible unitary representations of the Poincare group. The velocity
basis with total angular momentum j will be used for the definition of
relativistic Gamow vectors.Comment: 14 pages; revte
Time Asymmetric Quantum Theory - II. Relativistic Resonances from S-Matrix Poles
Relativistic resonances and decaying states are described by representations
of Poincar\'e transformations, similar to Wigner's definition of stable
particles. To associate decaying state vectors to resonance poles of the
-matrix, the conventional Hilbert space assumption (or asymptotic
completeness) is replaced by a new hypothesis that associates different dense
Hardy subspaces to the in- and out-scattering states. Then one can separate the
scattering amplitude into a background amplitude and one or several
``relativistic Breit-Wigner'' amplitudes, which represent the resonances per
se. These Breit-Wigner amplitudes have a precisely defined lineshape and are
associated to exponentially decaying Gamow vectors which furnish the
irreducible representation spaces of causal Poincar\'e transformations into the
forward light cone.Comment: 57 pages, 6 figure
Time Asymmetric Quantum Theory - III. Decaying States and the Causal Poincare Semigroup
A relativistic resonance which was defined by a pole of the -matrix, or by
a relativistic Breit-Wigner line shape, is represented by a generalized state
vector (ket) which can be obtained by analytic extension of the relativistic
Lippmann-Schwinger kets. These Gamow kets span an irreducible representation
space for Poincar\'e transformations which, similar to the Wigner
representations for stable particles, are characterized by spin (angular
momentum of the partial wave amplitude) and complex mass (position of the
resonance pole). The Poincar\'e transformations of the Gamow kets, as well as
of the Lippmann-Schwinger plane wave scattering states, form only a semigroup
of Poincar\'e transformations into the forward light cone. Their transformation
properties are derived. From these one obtains an unambiguous definition of
resonance mass and width for relativistic resonances. The physical
interpretation of these transformations for the Born probabilities and the
problem of causality in relativistic quantum physics is discussed.Comment: 49 pages, 1 figur
Resonances, Unstable Systems and Irreversibility: Matter Meets Mind
The fundamental time-reversal invariance of dynamical systems can be broken
in various ways. One way is based on the presence of resonances and their
interactions giving rise to unstable dynamical systems, leading to well-defined
time arrows. Associated with these time arrows are semigroups bearing time
orientations. Usually, when time symmetry is broken, two time-oriented
semigroups result, one directed toward the future and one directed toward the
past. If time-reversed states and evolutions are excluded due to resonances,
then the status of these states and their associated backwards-in-time oriented
semigroups is open to question. One possible role for these latter states and
semigroups is as an abstract representation of mental systems as opposed to
material systems. The beginnings of this interpretation will be sketched.Comment: 9 pages. Presented at the CFIF Workshop on TimeAsymmetric Quantum
Theory: The Theory of Resonances, 23-26 July 2003, Instituto Superior
Tecnico, Lisbon, Portugal; and at the Quantum Structures Association Meeting,
7-22 July 2004, University of Denver. Accepted for publication in the
Internation Journal of Theoretical Physic
Misleading signposts along the de Broglie-Bohm road to quantum mechanics
Eighty years after de Broglie's, and a little more than half a century after
Bohm's seminal papers, the de Broglie--Bohm theory (a.k.a. Bohmian mechanics),
which is presumably the simplest theory which explains the orthodox quantum
mechanics formalism, has reached an exemplary state of conceptual clarity and
mathematical integrity. No other theory of quantum mechanics comes even close.
Yet anyone curious enough to walk this road to quantum mechanics is soon being
confused by many misleading signposts that have been put up, and not just by
its detractors, but unfortunately enough also by some of its proponents.
This paper outlines a road map to help navigate ones way.Comment: Dedicated to Jeffrey Bub on occasion of his 65th birthday. Accepted
for publication in Foundations of Physics. A "slip of pen" in the
bibliography has been corrected -- thanks go to Oliver Passon for catching
it
Strings, T-duality breaking, and nonlocality without the shortest distance
T-duality of string theory suggests nonlocality manifested as the shortest
possible distance. As an alternative, we suggest a nonlocal formulation of
string theory that breaks T-duality at the fundamental level and does not
require the shortest possible distance. Instead, the string has an objective
shape in spacetime at all length scales, but different parts of the string
interact in a nonlocal Bohmian manner.Comment: 7 pages, revised, to appear in Eur. Phys. J.
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