A Krein quantization approach to Klein paradox

In this paper we first introduce the famous Klein tization approach and taking the negative modes into account densities could be achieved without confronting any paradox. paradox. Afterwards by proposing the Krein quan- , we will show that the expected and exact current     

PT symmetry and spontaneous symmetry breaking in a microwave billiard

We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.     

QED effective action in Krein space quantization

The one-loop effective action of QED is calculated by the Schwinger method in Krein space quantization. We show that the effective action is naturally finite and regularized. It also coincides with the renormalized solution which was derived by Schwinger.     

A Krein Space Approach to PT-symmetry

In this note we apply Krein space methods to PT-symmetric problems to obtain conditions for the spectrum to be real and estimates of the number of non-real spectral points. An erratum to this article is available at.     

A hidden local symmetry approach to rho-meson photoproduction

We study the photoproduction of r \rho -mesons in a model of hidden local symmetry. For this purpose, the r \rho -meson is introduced as a hidden-gauge boson in a non-linear sigma model. For charged r \rho -meson photoproduction, the model takes into account the r \rho -meson magnetic moments from the three-point vertex in the kinetic terms. We show that the magnetic interaction of the charged r \rho -meson has a significant effect on the total cross-sections through the r \rho -meson exchange process, which is proportional to the energy of the photon. The t -channel dominance may be used for the study of structures of various unstable particles.     

A basis-free approach to time-reversal for symmetry groups

We develop a basis-free approach to time-reversal for the quantal angular momentum group,SU2, and apply these methods to the physical symmetrySU2_isospin,SU3_flavor,SU3_nuclear and the nuclear collective symmetry groupSL(3,R) of Gell-Mann and Tomonaga.     

A new approach to spontaneously broken conformal symmetry

In this paper we present a new method for constructing theories of gravitation which exhibit spontaneously broken conformal symmetry. It does not require introducing nongeometric terms (i.e., auxiliary gauge fields or potential terms for the conformal field) into the Lagrangian. It is based on a theory which initially is locally both Lorentz invariant and Weyl gauge invariant inD dimensions. It is shown that, if the field Lagrangian contains terms quadratic in curvature in addition to the Ricci scalar, then the field equations allow both the dilation field and some connection components to have nonvanishing vacuum values. Both Lorentz and Weyl symmetries are thereby broken simultaneously.     

A complex minkowski space approach to twistors

This paper is basically a review of known results in twistor theory. Its value is intended to lie in the connections presented between twistor concepts and structures in complex Minkowski space. The relationship of twistor theory to complex null infinity and a new proof of the Kerr theorem are presented; these results are to some extent original.     

Higgsless approach to electroweak symmetry breaking

Higgsless models are an attempt to achieve a breaking of the electroweak symmetry via boundary conditions at the end-points of a fifth dimension compactified on an interval, as an alternative to the usual Higgs mechanism. There is no physical Higgs scalar in the spectrum and the perturbative unitarity violation scale is delayed via the exchange of massive spin-1 KK resonances. The correct mass spectrum is reproduced in a model in warped space, which inherits a custodial symmetry from a left–right gauge symmetry in the bulk. Phenomenological challenges as well as collider signatures are presented. From the AdS/CFT perspective, this model appears as a weakly coupled dual to walking technicolour models. To cite this article: C. Grojean, C. R. Physique 8 (2007).     

Stability boundaries of a Mathieu equation having PT symmetry

I have applied multiple-scale perturbation theory to a generalized complex PT-symmetric Mathieu equation in order to find the stability boundaries between bounded and unbounded solutions. The analysis suggests that the non-Hermitian parameter present in the equation can be used to control the shape and curvature of these boundaries. Although this was suggested earlier by several authors, analytic formulas for the boundary curves were not given. This paper is a first attempt to fill this gap in the theory.     

A symmetry adapted approach to vibrational excitations in atomic clusters

An algebraic method especially suited to describe the strongly anharmonic vibrational spectra in molecules may be an appropriate framework to study the vibrational spectra of Na _n ⁺ clusters, where nearly flat potential energy surfaces and the appearance of close lying isomers have been reported. As an illustration we describe the model and apply it to the Be₄, H ₃ ⁺ , Be₃ and Na ₃ ⁺ clusters. Presented by A. Frank at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997. This work was supported in part by the European Community under contract No. CI1*-CT94-0072, DGAPA-UNAM under project IN101997 and Spanish DGCYT under project PB92-0663.     

PT symmetry in a fractional Schrödinger equation

We investigate the fractional Schrödinger equation with a periodic ‐symmetric potential. In the inverse space, the problem transfers into a first‐order nonlocal frequency‐delay partial differential equation. We show that at a critical point, the band structure becomes linear and symmetric in the one‐dimensional case, which results in a nondiffracting propagation and conical diffraction of input beams. If only one channel in the periodic potential is excited, adjacent channels become uniformly excited along the propagation direction, which can be used to generate laser beams of high power and narrow width. In the two‐dimensional case, there appears conical diffraction that depends on the competition between the fractional Laplacian operator and the ‐symmetric potential. This investigation may find applications in novel on‐chip optical devices.

     

Structure of symmetry restoring interactions: A modified BCS plus rotational approach for a schematic model space

Symmetry restoring interactions are constructed for pairing and cranking Hamiltonians in a deformed single particle basis. The structure of the interactions is explicitly shown and the effective Hamiltonian is treated in the framework of a modified BCS + RPA approach. Numerical results for a schematic single particle basis, which consists of a splitj=3/2 multiplet, are discussed.     

A configuration space approach to the nuclear four-body problem

The derivation of a complete orthogonal system for the nuclear four-body problem is discussed, which will be especially useful in the case of identical particles. A method for dealing with four-body bound states is proposed. Part of the orthogonal system is given explicitly.     

A unified symmetry of nonholonomic mechanical systems in phase space

In this paper, we have studied the unified symmetry of a nonholonomic mechanical system in phase space. The definition and the criterion of a unified symmetry of the nonholonomic mechanical system in phase space are given under general infinitesimal transformations of groups in which time is variable. The Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity are obtained from the unified symmetry. An example is given to illustrate the application of the results.     

A unified approach to the effects of symmetry and periodicity on boundary-value problems

A generalized approach to the effects of symmetry and periodicity on boundary-value problems is presented, especially as it pertains to the guiding structures encountered in electromagnetics. Several examples of structures and their dispersion behavior are given, and the theory predicts well that other authors claim.     

相空间中离散完整系统的Noether对称性和Mei对称性

研究相空间中离散完整系统的Noether对称性、Mei对称性及其导致的守恒量.利用差分离散变分方法,给出相空间中离散完整系统的差分离散变分原理,建立系统的离散正则方程和能量演化方程;给出系统Noether对称性和Mei对称性的判定条件,得到系统离散形式的Noether守恒量和Mei守恒量及其存在的条件.举例说明结果的应用. 关键词： 相空间 离散完整系统 对称性 守恒量