53 research outputs found
Energy Gaps in a Spacetime Crystal
This paper presents an analysis of the band structure of a spacetime
potential lattice created by a standing electromagnetic wave. We show that
there are energy band gaps. We estimate the effect, and propose a measurement
that could confirm the existence of such phenomena.Comment: 8 pages. 2 figure
Equilibrium Relativistic Mass Distribution
The relativistic Maxwell-Boltzmann distribution for the system of events
with motion in space-time parametrized by an invariant ``historical time''
is considered without the simplifying approximation ,
where is a given intrinsic property of the events. The relativistic mass
distribution is obtained and the average values of and are
calculated. The average value of the energy in nonrelativistic limit gives a
correction of the order of 10\% to the Dulong-Petit law. Expressions for the
pressure and the density of events are obtained and the ideal gas law is
recovered.Comment: TAUP-2048-9
A New Relativistic High Temperature Bose-Einstein Condensation
We discuss the properties of an ideal relativistic gas of events possessing
Bose-Einstein statistics. We find that the mass spectrum of such a system is
bounded by where is the usual chemical
potential, is an intrinsic dimensional scale parameter for the motion of an
event in space-time, and is an additional mass potential of the
ensemble. For the system including both particles and antiparticles, with
nonzero chemical potential the mass spectrum is shown to be bounded by
and a special type of high-temperature
Bose-Einstein condensation can occur. We study this Bose-Einstein condensation,
and show that it corresponds to a phase transition from the sector of
continuous relativistic mass distributions to a sector in which the boson mass
distribution becomes sharp at a definite mass This phenomenon
provides a mechanism for the mass distribution of the particles to be sharp at
some definite value.Comment: Latex, 22 page
Stark Effect in Lax-Phillips Theory
The scattering theory of Lax and Phillips, originally developed to describe
resonances associated with classical wave equations, has been recently extended
to apply as well to the case of the Schroedinger equation in the case that the
wave operators for the corresponding Lax-Phillips theory exist. It is known
that the bound state levels of an atom become resonances (spectral
enhancements) in the continuum in the presence of an electric field (in all
space) in the quantum mechanical Hilbert space. Such resonances appear as
states in the extended Lax-Phillips Hilbert space. We show that for a simple
version of the Stark effect, these states can be explicitly computed, and
exhibit the (necessarily) semigroup property of decay in time. The widths and
location of the resonances are those given by the poles of the resolvent of the
standard quantum mechanical form.Comment: Plain TeX, 19 page
Discrete Symmetries of Off-Shell Electromagnetism
We discuss the discrete symmetries of the Stueckelberg-Schrodinger
relativistic quantum theory and its associated 5D local gauge theory, a
dynamical description of particle/antiparticle interactions, with monotonically
increasing Poincare-invariant parameter. In this framework, worldlines are
traced out through the parameterized evolution of spacetime events, advancing
or retreating with respect to the laboratory clock, with negative energy
trajectories appearing as antiparticles when the observer describes the
evolution using the laboratory clock. The associated gauge theory describes
local interactions between events (correlated by the invariant parameter)
mediated by five off-shell gauge fields. These gauge fields are shown to
transform tensorially under under space and time reflections, unlike the
standard Maxwell fields, and the interacting quantum theory therefore remains
manifestly Lorentz covariant. Charge conjugation symmetry in the quantum theory
is achieved by simultaneous reflection of the sense of evolution and the fifth
scalar field. Applying this procedure to the classical gauge theory leads to a
purely classical manifestation of charge conjugation, placing the CPT
symmetries on the same footing in the classical and quantum domains. In the
resulting picture, interactions do not distinguish between particle and
antiparticle trajectories -- charge conjugation merely describes the
interpretation of observed negative energy trajectories according to the
laboratory clock.Comment: 26 page
On the Thermodynamics of Hot Hadronic Matter
The equation of state of hot hadronic matter is obtained, by taking into
account the contribution of the massive states with the help of the resonance
spectrum justified by the authors in previous papers. This
equation of state is in agreement with that provided by the low-temperature
expansion for the pion intracting gas. It is shown that in this picture the
deconfinement phase transition is absent, in agreement with lattice gauge
calculations which show the only phase transition of chiral symmetry
restoration. The latter is modelled with the help of the restriction of the
number of the effective degrees of freedom in the hadron phase to that of the
microscopic degrees of freedom in the quark-gluon phase, through the
corresponding truncation of the hadronic resonance spectrum, and the decrease
of the effective hadron masses with temperature, predicted by Brown and Rho.
The results are in agreement with lattice gauge data and show a smooth
crossover in the thermodynamic variables in a temperature range MeV.Comment: 21 pages, LaTeX, 3 postscript figure
Common Space of Spin and Spacetime
Given Lorentz invariance in Minkowski spacetime, we investigate a common
space of spin and spacetime. To obtain a finite spinor representation of the
non-compact homogeneous Lorentz group including Lorentz boosts, we introduce an
indefinite inner product space (IIPS) with a normalized positive probability.
In this IIPS, the common momentum and common variable of a massive fermion turn
out to be ``doubly strict plus-operators''. Due to this nice property, it is
straightforward to show an uncertainty relation between fermion mass and proper
time. Also in IIPS, the newly-defined Lagrangian operators are self-adjoint,
and the fermion field equations are derivable from the Lagrangians. Finally,
the nonlinear QED equations and Lagrangians are presented as an example.Comment: 17 pages, a reference corrected, final version published on
Foundations of Physics Letters in June of 2005, as a personal tribute to
Einstein and Dira
Finding Shuffle Words That Represent Optimal Scheduling of Shared Memory Access
In the present paper, we introduce and study the problem
of computing, for any given finite set of words, a shuffle word with a
minimum so-called scope coincidence degree. The scope coincidence degree is the maximum number of different symbols that parenthesise any
position in the shuffle word. This problem is motivated by an application of a new automaton model and can be regarded as the problem of
scheduling shared memory accesses of some parallel processes in a way
that minimises the number of memory cells required. We investigate the
complexity of this problem and show that it can be solved in polynomial
time
Glimpses of the Octonions and Quaternions History and Todays Applications in Quantum Physics
Before we dive into the accessibility stream of nowadays indicatory
applications of octonions to computer and other sciences and to quantum physics
let us focus for a while on the crucially relevant events for todays revival on
interest to nonassociativity. Our reflections keep wandering back to the
two square identity and then via the four
square identity up to the eight square identity.
These glimpses of history incline and invite us to retell the story on how
about one month after quaternions have been carved on the bridge
octonions were discovered by , jurist and
mathematician, a friend of . As for today we just
mention en passant quaternionic and octonionic quantum mechanics,
generalization of equations for octonions and triality
principle and group in spinor language in a descriptive way in order not
to daunt non specialists. Relation to finite geometries is recalled and the
links to the 7stones of seven sphere, seven imaginary octonions units in out of
the cave reality applications are appointed . This way we are welcomed
back to primary ideas of , and other distinguished
fathers of quantum mechanics and quantum gravity foundations.Comment: 26 pages, 7 figure
A Statistical Mechanical Problem in Schwarzschild Spacetime
We use Fermi coordinates to calculate the canonical partition function for an
ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the
validity of the results we prove theorems for limiting cases. We recover the
Newtonian gas law subject only to tidal forces in the Newtonian limit.
Additionally we recover the special relativistic gas law as the radius of the
orbit increases to infinity. We also discuss how the method can be extended to
the non ideal gas case.Comment: Corrected an equation misprint, added four references, and brief
comments on the system's center of mass and the thermodynamic limi
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