57 research outputs found
A Massive Non-Abelian Vector Model
The introduction of a Lagrange multiplier field to ensure that the classical
equations of motion are satisfied serves to restrict radiative corrections in a
model to being only one loop. The consequences of this for a massive
non-Abelian vector model are considered.Comment: 8 pages, LaTeX format; further comments added; accepted for
publication at the Canadian Journal of Physic
Gravitational Repulsion within a Black-Hole using the Stueckelberg Quantum Formalism
We wish to study an application of Stueckelberg's relativistic quantum theory
in the framework of general relativity. We study the form of the wave equation
of a massive body in the presence of a Schwarzschild gravitational field. We
treat the mathematical behavior of the wavefunction also around and beyond the
horizon (r=2M). Classically, within the horizon, the time component of the
metric becomes spacelike and distance from the origin singularity becomes
timelike, suggesting an inevitable propagation of all matter within the horizon
to a total collapse at r=0. However, the quantum description of the wave
function provides a different understanding of the behavior of matter within
the horizon. We find that a test particle can almost never be found at the
origin and is more probable to be found at the horizon. Matter outside the
horizon has a very small wave length and therefore interference effects can be
found only on a very small atomic scale. However, within the horizon, matter
becomes totally "tachionic" and is potentially "spread" over all space. Small
location uncertainties on the atomic scale become large around the horizon, and
different mass components of the wave function can therefore interfere on a
stellar scale. This interference phenomenon, where the probability of finding
matter decreases as a function of the distance from the horizon, appears as an
effective gravitational repulsion.Comment: 20 pages, 6 figure
The renormalization of the effective Lagrangian with spontaneous symmetry breaking: the SU(2) case
We study the renormalization of the nonlinear effective SU(2) Lagrangian up
to with spontaneous symmetry breaking. The Stueckelberg
transformation, the background field gauge, the Schwinger proper time and heat
kernel method, and the covariant short distance expansion technology, guarantee
the gauge covariance and incooperate the Ward indentities in our calculations.
The renormalization group equations of the effective couplings are derived and
analyzed. We find that the difference between the results gotten from the
direct method and the renormalization group equation method can be quite large
when the Higgs scalar is far below its decoupling limit.Comment: ReVTeX, 12 figures, 22 pages, some bugs are kicked off from programs,
numerical analysis is renew
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
Effects of nonlinear sweep in the Landau-Zener-Stueckelberg effect
We study the Landau-Zener-Stueckelberg (LZS) effect for a two-level system
with a time-dependent nonlinear bias field (the sweep function) W(t). Our main
concern is to investigate the influence of the nonlinearity of W(t) on the
probability P to remain in the initial state. The dimensionless quantity
epsilon = pi Delta ^2/(2 hbar v) depends on the coupling Delta of both levels
and on the sweep rate v. For fast sweep rates, i.e., epsilon << l and
monotonic, analytic sweep functions linearizable in the vicinity of the
resonance we find the transition probability 1-P ~= epsilon (1+a), where a>0 is
the correction to the LSZ result due to the nonlinearity of the sweep. Further
increase of the sweep rate with nonlinearity fixed brings the system into the
nonlinear-sweep regime characterized by 1-P ~= epsilon ^gamma with gamma neq 1
depending on the type of sweep function. In case of slow sweep rates, i.e.,
epsilon >>1 an interesting interference phenomenon occurs. For analytic W(t)
the probability P=P_0 e^-eta is determined by the singularities of sqrt{Delta
^2+W^2(t)} in the upper complex plane of t. If W(t) is close to linear, there
is only one singularity, that leads to the LZS result P=e^-epsilon with
important corrections to the exponent due to nonlinearity. However, for, e.g.,
W(t) ~ t^3 there is a pair of singularities in the upper complex plane.
Interference of their contributions leads to oscillations of the prefactor P_0
that depends on the sweep rate through epsilon and turns to zero at some
epsilon. Measurements of the oscillation period and of the exponential factor
would allow to determine Delta, independently.Comment: 11 PR pages, 12 figures. To be published in PR
A Supersymmetric Stueckelberg U(1) Extension of the MSSM
A Stueckelberg extension of the MSSM with only one abelian vector and one
chiral superfield as an alternative to an abelian extension with Higgs scalars
is presented. The bosonic sector contains a new gauge boson Z' which is a sharp
resonance, and a new CP-even scalar, which combines with the MSSM Higgs bosons
to produce three neutral CP-even massive states. The neutral fermionic sector
has two additional fermions which mix with the four MSSM neutralinos to produce
an extended 6x6 neutralino mass matrix. For the case when the LSP is composed
mostly of the Stueckelberg fermions, the LSP of the MSSM will be unstable,
which leads to exotic decays of sparticles with many leptons in final states.
Prospects for supersymmetry searches and for dark matter are discussed.Comment: 10 page
On the Resummation of the epe^+e^-$ Annihilation
The resummation of the non-singlet contributions is
performed for initial state QED corrections. As examples, the effect of the
resummation on neutral-current deep-inelastic scattering and the scattering cross section near the -peak is
investigated.Comment: 11 pages Latex, including 3 eps-figure
Covariant Gauge Fixing and Canonical Quantization
Theories that contain first class constraints possess gauge invariance which
results in the necessity of altering the measure in the associated quantum
mechanical path integral. If the path integral is derived from the canonical
structure of the theory, then the choice of gauge conditions used in
constructing Faddeev's measure cannot be covariant. This shortcoming is
normally overcome either by using the "Faddeev-Popov" quantization procedure,
or by the approach of Batalin-Fradkin-Fradkina-Vilkovisky, and then
demonstrating that these approaches are equivalent to the path integral
constructed from the canonical approach with Faddeev's measure. We propose in
this paper an alternate way of defining the measure for the path integral when
it is constructed using the canonical procedure for theories containing first
class constraints and that this new approach can be used in conjunction with
covariant gauges. This procedure follows the Faddeev-Popov approach, but rather
than working with the form of the gauge transformation in configuration space,
it employs the generator of the gauge transformation in phase space. We
demonstrate this approach to the path integral by applying it to Yang-Mills
theory, a spin-two field and the first order Einstein-Hilbert action in two
dimensions. The problems associated with defining the measure for theories
containing second-class constraints and ones in which there are fewer secondary
first class constraints than primary first class constraints are discussed.Comment: 31 page
Consistent histories of systems and measurements in spacetime
Traditional interpretations of quantum theory in terms of wave function
collapse are particularly unappealing when considering the universe as a whole,
where there is no clean separation between classical observer and quantum
system and where the description is inherently relativistic. As an alternative,
the consistent histories approach provides an attractive "no collapse"
interpretation of quantum physics. Consistent histories can also be linked to
path-integral formulations that may be readily generalized to the relativistic
case. A previous paper described how, in such a relativistic spacetime path
formalism, the quantum history of the universe could be considered to be an
eignestate of the measurements made within it. However, two important topics
were not addressed in detail there: a model of measurement processes in the
context of quantum histories in spacetime and a justification for why the
probabilities for each possible cosmological eigenstate should follow Born's
rule. The present paper addresses these topics by showing how Zurek's concepts
of einselection and envariance can be applied in the context of relativistic
spacetime and quantum histories. The result is a model of systems and
subsystems within the universe and their interaction with each other and their
environment.Comment: RevTeX 4; 37 pages; v2 is a revision in response to reviewer
comments, connecting the discussion in the paper more closely to consistent
history concepts; v3 has minor editorial corrections; accepted for
publication in Foundations of Physics; v4 has a couple minor typographical
correction
Properties of Physical Systems: Transient Singularities on Borders and Surface Transitive Zones
Certain alternative properties of physical systems are describable by
supports of arguments of response functions (e.g. light cone, borders of media)
and expressed by projectors; corresponding equations of restraints lead to
dispersion relations, theorems of counting, etc. As supports are measurable,
their absolutely strict borders contradict the spirit of quantum theory and
their quantum evolution leading to appearance of subtractions or certain needed
flattening would be considered. Flattening of projectors introduce transitive
zones that can be examined as a specification of adiabatic hypothesis or the
Bogoliubov regulatory function in QED. For demonstration of their possibilities
the phenomena of refraction and reflection of electromagnetic wave are
considered; they show, in particular, the inevitable appearing of double
electromagnetic layers on all surfaces that formerly were repeatedly
postulated, etc. Quantum dynamics of projectors proves the neediness of
subtractions that usually are artificially adding and express transient
singularities and zones in squeezed forms.Comment: 12 p
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