661 research outputs found
Non-Hermitian extension of gauge theories and implications for neutrino physics
An extension of QED is considered in which the Dirac fermion has both
Hermitian and anti-Hermitian mass terms, as well as both vector and
axial-vector couplings to the gauge field. Gauge invariance is restored when
the Hermitian and anti-Hermitian masses are of equal magnitude, and the theory
reduces to that of a single massless Weyl fermion. An analogous non-Hermitian
Yukawa theory is considered, and it is shown that this model can explain the
smallness of the light-neutrino masses and provide an additional source of
leptonic CP violation.Comment: 23 pages, 1 figure, JHEP style; corrections to match published
versio
On the consistency of a non-Hermitian Yukawa interaction
We study different properties of an anti-Hermitian Yukawa interaction,
motivated by a scenario of radiative anomalous generation of masses for the
right-handed sterile neutrinos. The model, involving either a pseudo-scalar or
a scalar, is consistent both at the classical and quantum levels, and
particular attention is given to its properties under improper Lorentz
transformations. The path integral is consistently defined with a Euclidean
signature, and we discuss the energetics of the model, which show that no
dynamical mass generation can occur, unless extra interactions are considered.Comment: 7 pages, comments adde
Calculation of the Characteristic Functions of Anharmonic Oscillators
The energy levels of quantum systems are determined by quantization
conditions. For one-dimensional anharmonic oscillators, one can transform the
Schrodinger equation into a Riccati form, i.e., in terms of the logarithmic
derivative of the wave function. A perturbative expansion of the logarithmic
derivative of the wave function can easily be obtained. The Bohr-Sommerfeld
quantization condition can be expressed in terms of a contour integral around
the poles of the logarithmic derivative. Its functional form is B_m(E,g) = n +
1/2, where B is a characteristic function of the anharmonic oscillator of
degree m, E is the resonance energy, and g is the coupling constant. A
recursive scheme can be devised which facilitates the evaluation of
higher-order Wentzel-Kramers-Brioullin (WKB) approximants. The WKB expansion of
the logarithmic derivative of the wave function has a cut in the tunneling
region. The contour integral about the tunneling region yields the instanton
action plus corrections, summarized in a second characteristic function
A_m(E,g). The evaluation of A_m(E,g) by the method of asymptotic matching is
discussed for the case of the cubic oscillator of degree m=3.Comment: 11 pages, LaTeX; three further typographical errors correcte
Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians
Two Non-Hermitian fermion models are proposed and analyzed by using Foldy-Wouthuysen transformations. One model has Lorentz symmetry breaking and the other has a non-Hermitian mass term. It is shown that each model has real energies in a given region of parameter space, where they have a locally conserved current
Kaluza-Klein towers in warped spaces with metric singularities
The version of the warp model that we proposed to explain the mass scale
hierarchy has been extended by the introduction of one or more singularities in
the metric. We restricted ourselves to a real massless scalar field supposed to
propagate in a five dimensional bulk with the extradimension being compactified
on a strip or on a circle. With the same emphasis on the hermiticity and
commutativity properties of the Kakuza Klein operators, we have established all
the allowed boundary conditions to be imposed on the fields. From them, for
given positions of the singularities, one can deduce either mass eigenvalues
building up a Kaluza Klein tower, or a tachyon, or a zero mass state. Assuming
the Planck mass to be the high mass scale and by a choice, unique for all
boundary conditions, of the major warp parameters, the low lying mass
eigenvalues are of the order of the TeV, in this way explaining the mass scale
hierarchy. In our model, the physical masses are related to the Kaluza Klein
eigenvalues, depending on the location of the physical brane which is an
arbitrary parameter of the model. Illustrative numerical calculations are given
to visualize the structure of Kaluza Klein mass eigenvalue towers. Observation
at high energy colliders like LHC of a mass tower with its characteristic
structure would be the fingerprint of the model.Comment: 33 pages, 1 figur
A nearly optimal algorithm to decompose binary forms
Accepted to JSCSymmetric tensor decomposition is an important problem with applications in several areas for example signal processing, statistics, data analysis and computational neuroscience. It is equivalent to Waring's problem for homogeneous polynomials, that is to write a homogeneous polynomial in n variables of degree D as a sum of D-th powers of linear forms, using the minimal number of summands. This minimal number is called the rank of the polynomial/tensor. We focus on decomposing binary forms, a problem that corresponds to the decomposition of symmetric tensors of dimension 2 and order D. Under this formulation, the problem finds its roots in invariant theory where the decompositions are known as canonical forms. In this context many different algorithms were proposed. We introduce a superfast algorithm that improves the previous approaches with results from structured linear algebra. It achieves a softly linear arithmetic complexity bound. To the best of our knowledge, the previously known algorithms have at least quadratic complexity bounds. Our algorithm computes a symbolic decomposition in arithmetic operations, where is the complexity of multiplying two polynomials of degree D. It is deterministic when the decomposition is unique. When the decomposition is not unique, our algorithm is randomized. We present a Monte Carlo version of it and we show how to modify it to a Las Vegas one, within the same complexity. From the symbolic decomposition, we approximate the terms of the decomposition with an error of , in arithmetic operations. We use results from Kaltofen and Yagati (1989) to bound the size of the representation of the coefficients involved in the decomposition and we bound the algebraic degree of the problem by min(rank, D â rank + 1). We show that this bound can be tight. When the input polynomial has integer coefficients, our algorithm performs, up to poly-logarithmic factors, bit operations, where is the maximum bitsize of the coefficients and is the relative error of the terms in the decomposition
Multi-Instantons and Exact Results III: Unified Description of the Resonances of Even and Odd Anharmonic Oscillators
This is the third article in a series of three papers on the resonance energy
levels of anharmonic oscillators. Whereas the first two papers mainly dealt
with double-well potentials and modifications thereof [see J. Zinn-Justin and
U. D. Jentschura, Ann. Phys. (N.Y.) 313 (2004), pp. 197 and 269], we here focus
on simple even and odd anharmonic oscillators for arbitrary magnitude and
complex phase of the coupling parameter. A unification is achieved by the use
of PT-symmetry inspired dispersion relations and generalized quantization
conditions that include instanton configurations. Higher-order formulas are
provided for the oscillators of degrees 3 to 8, which lead to subleading
corrections to the leading factorial growth of the perturbative coefficients
describing the resonance energies. Numerical results are provided, and
higher-order terms are found to be numerically significant. The resonances are
described by generalized expansions involving intertwined non-analytic
exponentials, logarithmic terms and power series. Finally, we summarize
spectral properties and dispersion relations of anharmonic oscillators, and
their interconnections. The purpose is to look at one of the classic problems
of quantum theory from a new perspective, through which we gain systematic
access to the phenomenologically significant higher-order terms.Comment: 51 pages, LaTeX, Latin2 font
Ladder Metamodeling & PLC Program Validation through Time Petri Nets
International audienceLadder Diagram (LD) is the most used programming language for Programmable Logical Controllers (PLCs). A PLC is a special purpose industrial computer used to automate industrial processes. Bugs in LD programs are very costly and sometimes are even a threat to human safety. We propose a model driven approach for formal verification of LD programs through model-checking. We provide a metamodel for a subset of the LD language. We define a time Petri net (TPN) semantics for LD programs through an ATL model transformation. Finally, we automatically generate behavioral properties over the LD models as LTL formulae which are then checked over the generated TPN using the model-checkers available in the Tina toolkit. We focus on race condition detection. This work is supported by the topcased project, part of the french cluster Aerospace Valley (granted by the french DGE), cf. http://www.topcased.or
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