7,872 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
A Note on the Topology of Space-time in Special Relativity
We show that a topology can be defined in the four dimensional space-time of
special relativity so as to obtain a topological semigroup for time. The
Minkowski 4-vector character of space-time elements as well as the key
properties of special relativity are still the same as in the standard theory.
However, the new topological structure allows the possibility of an intrinsic
asymmetry in the time evolution of physical systems
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
Measurement of the total energy of an isolated system by an internal observer
We consider the situation in which an observer internal to an isolated system
wants to measure the total energy of the isolated system (this includes his own
energy, that of the measuring device and clocks used, etc...). We show that he
can do this in an arbitrarily short time, as measured by his own clock. This
measurement is not subjected to a time-energy uncertainty relation. The
properties of such measurements are discussed in detail with particular
emphasis on the relation between the duration of the measurement as measured by
internal clocks versus external clocks.Comment: 7 pages, 1 figur
Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics
We discuss some basic properties of Lie group representations in rigged
Hilbert spaces. In particular, we show that a differentiable representation in
a rigged Hilbert space may be obtained as the projective limit of a family of
continuous representations in a nested scale of Hilbert spaces. We also
construct a couple of examples illustrative of the key features of group
representations in rigged Hilbert spaces. Finally, we establish a simple
criterion for the integrability of an operator Lie algebra in a rigged Hilbert
space
On Epstein's trajectory model of non-relativistic quantum mechanics
In 1952 Bohm presented a theory about non-relativistic point-particles moving
along deterministic trajectories and showed how it reproduces the predictions
of standard quantum theory. This theory was actually presented before by de
Broglie in 1926, but Bohm's particular formulation of the theory inspired
Epstein to come up with a different trajectory model. The aim of this paper is
to examine the empirical predictions of this model. It is found that the
trajectories in this model are in general very different from those in the de
Broglie-Bohm theory. In certain cases they even seem bizarre and rather
unphysical. Nevertheless, it is argued that the model seems to reproduce the
predictions of standard quantum theory (just as the de Broglie-Bohm theory).Comment: 12 pages, no figures, LaTex; v2 minor improvement
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