1,277 research outputs found
Implication of Compensator Field and Local Scale Invariance in the Standard Model
We introduce Weyl's scale symmetry into the standard model (SM) as a local
symmetry. This necessarily introduces gravitational interactions in addition to
the local scale invariance group \tilde U(1) and the SM groups SU(3) X SU(2) X
U(1). The only other new ingredients are a new scalar field \sigma and the
gauge field for \tilde U(1) we call the Weylon. A noteworthy feature is that
the system admits the St\" uckelberg-type compensator. The \sigma couples to
the scalar curvature as (-\zeta/2) \sigma^2 R, and is in turn related to a St\"
uckelberg-type compensator \varphi by \sigma \equiv M_P e^{-\varphi/M_P} with
the Planck mass M_P. The particular gauge \varphi = 0 in the St\" uckelberg
formalism corresponds to \sigma = M_P, and the Hilbert action is induced
automatically. In this sense, our model presents yet another mechanism for
breaking scale invariance at the classical level. We show that our model
naturally accommodates the chaotic inflation scenario with no extra field.Comment: This work is to be read in conjunction with our recent comments
hep-th/0702080, arXiv:0704.1836 [hep-ph] and arXiv:0712.2487 [hep-ph]. The
necessary ingredients for describing chaotic inflation in the SM as
entertained by Bezrukov and Shaposhnikov [17] have been provided by our
original model [8]. We regret their omission in citing our original model [8
New results for the missing quantum numbers labeling the quadrupole and octupole boson basis
The many -pole boson states, with ,
realize the irreducible representation (IR) for the group reduction chains
. They have been analytically
studied and widely used for the description of nuclear systems. However, no
analytical expression for the degeneracy of the 's IR,
determined by the reduction , is available. Thus, the
number of distinct values taken by has been so far obtained by
solving some complex equations. Here we derive analytical expressions for the
degeneracy characterizing the octupole and quadrupole boson states,
respectively. The merit of this work consists of the fact that it completes the
analytical expressions for the -pole boson basis.Comment: 10page
Monomial integrals on the classical groups
This paper presents a powerfull method to integrate general monomials on the
classical groups with respect to their invariant (Haar) measure. The method has
first been applied to the orthogonal group in [J. Math. Phys. 43, 3342 (2002)],
and is here used to obtain similar integration formulas for the unitary and the
unitary symplectic group. The integration formulas turn out to be of similar
form. They are all recursive, where the recursion parameter is the number of
column (row) vectors from which the elements in the monomial are taken. This is
an important difference to other integration methods. The integration formulas
are easily implemented in a computer algebra environment, which allows to
obtain analytical expressions very efficiently. Those expressions contain the
matrix dimension as a free parameter.Comment: 16 page
Periodic and discrete Zak bases
Weyl's displacement operators for position and momentum commute if the
product of the elementary displacements equals Planck's constant. Then, their
common eigenstates constitute the Zak basis, each state specified by two phase
parameters. Upon enforcing a periodic dependence on the phases, one gets a
one-to-one mapping of the Hilbert space on the line onto the Hilbert space on
the torus. The Fourier coefficients of the periodic Zak bases make up the
discrete Zak bases. The two bases are mutually unbiased. We study these bases
in detail, including a brief discussion of their relation to Aharonov's modular
operators, and mention how they can be used to associate with the single degree
of freedom of the line a pair of genuine qubits.Comment: 15 pages, 3 figures; displayed abstract is shortened, see the paper
for the complete abstrac
Alternative linear structures for classical and quantum systems
The possibility of deforming the (associative or Lie) product to obtain
alternative descriptions for a given classical or quantum system has been
considered in many papers. Here we discuss the possibility of obtaining some
novel alternative descriptions by changing the linear structure instead. In
particular we show how it is possible to construct alternative linear
structures on the tangent bundle TQ of some classical configuration space Q
that can be considered as "adapted" to the given dynamical system. This fact
opens the possibility to use the Weyl scheme to quantize the system in
different non equivalent ways, "evading", so to speak, the von Neumann
uniqueness theorem.Comment: 32 pages, two figures, to be published in IJMP
Significant reduction in arc frequency biased solar cells: Observations, diagnostics, and mitigation technique(s)
A variety of experiments were performed which identify key factors contributing to the arcing of negatively biased high voltage solar cells. These efforts have led to reduction of greater than a factor of 100 in the arc frequency of a single cell following proper remediation procedures. Experiments naturally lead to and focussed on the adhesive/encapsulant that is used to bond the protective cover slip to the solar cell. An image-intensified charge coupled device (CCD) camera system recorded UV emission from arc events which occurred exclusively along the interfacial edge between the cover slip and the solar cell. Microscopic inspection of this interfacial region showed a bead of encapsulant along this entire edge. Elimination of this encapsulant bead reduced the arc frequency by two orders of magnitude. Water contamination was also identified as a key contributor which enhances arcing of the encapsulant bead along the solar cell edge. Spectrally resolved measurements of the observable UV light shows a feature assignable to OH(A-X) electronic emission, which is common for water contaminated discharges. Experiments in which the solar cell temperature was raised to 85 C showed a reduced arcing frequency, suggesting desorption of H2O. Exposing the solar cell to water vapor was shown to increase the arcing frequency. Clean dry gases such as O2, N2, and Ar show no enhancement of the arcing rate. Elimination of the exposed encapsulant eliminates any measurable sensitivity to H2O vapor
Conformal Spinning Quantum Particles in Complex Minkowski Space as Constrained Nonlinear Sigma Models in U(2,2) and Born's Reciprocity
We revise the use of 8-dimensional conformal, complex (Cartan) domains as a
base for the construction of conformally invariant quantum (field) theory,
either as phase or configuration spaces. We follow a gauge-invariant Lagrangian
approach (of nonlinear sigma-model type) and use a generalized Dirac method for
the quantization of constrained systems, which resembles in some aspects the
standard approach to quantizing coadjoint orbits of a group G. Physical wave
functions, Haar measures, orthonormal basis and reproducing (Bergman) kernels
are explicitly calculated in and holomorphic picture in these Cartan domains
for both scalar and spinning quantum particles. Similarities and differences
with other results in the literature are also discussed and an extension of
Schwinger's Master Theorem is commented in connection with closure relations.
An adaptation of the Born's Reciprocity Principle (BRP) to the conformal
relativity, the replacement of space-time by the 8-dimensional conformal domain
at short distances and the existence of a maximal acceleration are also put
forward.Comment: 33 pages, no figures, LaTe
See a Black Hole on a Shoestring
The modes of vibration of hanging and partially supported strings provide
useful analogies to scalar fields travelling through spacetimes that admit
conformally flat spatial sections. This wide class of spacetimes includes
static, spherically symmetric spacetimes. The modes of a spacetime where the
scale factor depends as a power-law on one of the coordinates provide a useful
starting point and yield a new classification of these spacetimes on the basis
of the shape of the string analogue. The family of corresponding strings follow
a family of curves related to the cycloid, denoted here as hypercycloids (for
reasons that will become apparent). Like the spacetimes that they emulate these
strings exhibit horizons, typically at their bottommost points where the string
tension vanishes; therefore, hanging strings may provide a new avenue for the
exploration of the quantum mechanics of horizons.Comment: 5 pages, 1 figure, extensive changes to refect version accepted to
PR
Representations of the -algebra and the loop representation in -dimensions
We consider the phase-space of Yang-Mills on a cylindrical space-time () and the associated algebra of gauge-invariant functions, the
-variables. We solve the Mandelstam identities both classically and
quantum-mechanically by considering the -variables as functions of the
eigenvalues of the holonomy and their associated momenta. It is shown that
there are two inequivalent representations of the quantum -algebra. Then we
compare this reduced phase space approach to Dirac quantization and find it to
give essentially equivalent results. We proceed to define a loop representation
in each of these two cases. One of these loop representations (for ) is
more or less equivalent to the usual loop representation.Comment: 15 pages, LaTeX, 1 postscript figure included, uses epsf.sty,
G\"oteborg ITP 93-3
Approximate quantum error correction, random codes, and quantum channel capacity
We work out a theory of approximate quantum error correction that allows us
to derive a general lower bound for the entanglement fidelity of a quantum
code. The lower bound is given in terms of Kraus operators of the quantum
noise. This result is then used to analyze the average error correcting
performance of codes that are randomly drawn from unitarily invariant code
ensembles. Our results confirm that random codes of sufficiently large block
size are highly suitable for quantum error correction. Moreover, employing a
lemma of Bennett, Shor, Smolin, and Thapliyal, we prove that random coding
attains information rates of the regularized coherent information.Comment: 29 pages, final version to appear in Phys. Rev. A, improved lower
bound for code entanglement fidelity, simplified proo
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