10,460 research outputs found
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
Topological Aspects of the Non-adiabatic Berry Phase
The topology of the non-adiabatic parameter space bundle is discussed for
evolution of exact cyclic state vectors in Berry's original example of split
angular momentum eigenstates. It turns out that the change in topology occurs
at a critical frequency. The first Chern number that classifies these bundles
is proportional to angular momentum. The non-adiabatic principal bundle over
the parameter space is not well-defined at the critical frequency.Comment: 14 pages, Dep. of Physics, Uni. of Texas at Austin, Austin, Texas
78712, to appear in J. Physics
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
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
Irreversible Quantum Mechanics in the Neutral K-System
The neutral Kaon system is used to test the quantum theory of resonance
scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with
complex Hamiltonian is obtained by truncating the complex basis vector
expansion of the exact theory in Rigged Hilbert space. This can be done for K_1
and K_2 as well as for K_S and K_L, depending upon whether one chooses the
(self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP.
As an unexpected curiosity one can show that the exact theory (without
truncation) predicts long-time 2 pion decays of the neutral Kaon system even if
the Hamiltonian conserves CP.Comment: 36 pages, 1 PostScript figure include
The Higgs Boson Mass in Split Supersymmetry at Two-Loops
The mass of the Higgs boson in the Split Supersymmetric Standard Model is
calculated, including all one-loop threshold effects and the renormalization
group evolution of the Higgs quartic coupling through two-loops. The two-loop
corrections are very small (<<1 GeV), while the one-loop threshold corrections
generally push the Higgs mass down several GeV.Comment: 17 pages. 4 figures. Improved discussion and notation. Corrected
typos. Added references. Added plots. Main results unchange
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
Topological insulators and metal-insulator transition in the pyrochlore iridates
The possible existence of topological insulators in cubic pyrochlore iridates
AIrO (A = Y or rare-earth elements) is investigated by taking
into account the strong spin-orbit coupling and trigonal crystal field effect.
It is found that the trigonal crystal field effect, which is always present in
real systems, may destabilize the topological insulator proposed for the ideal
cubic crystal field, leading to a metallic ground state. Thus the trigonal
crystal field is an important control parameter for the metal-insulator
changeover. We propose that this could be one of the reasons why distinct low
temperature ground states may arise for the pyrochlore iridates with different
A-site ions. On the other hand, examining the electron-lattice coupling, we
find that softening of the =0 modes corresponding to trigonal or
tetragonal distortions of the Ir pyrochlore lattice leads to the resurrection
of the strong topological insulator. Thus, in principle, a finite temperature
transition to a low-temperature topological insulator can occur via structural
changes. We also suggest that the application of the external pressure along
[111] or its equivalent directions would be the most efficient way of
generating strong topological insulators in pyrochlore iridates.Comment: 10 pages, 11 figures, 2 table
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
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