N=4超对称量子力学

利用Clifford代数构造了N=4超对称量子力学的一般形式,并讨论了它的实现.     

BPS States of D=4 ␣N=1 Supersymmetry

We find the combinations of momentum and domain-wall charges corresponding to BPS states preserving 1/4, 1/2 or 3/4 of D=4 N=1 supersymmetry, and we show how the supersymmetry algebra implies their stability. These states form the boundary of the convex cone associated with the Jordan algebra of 4× 4 real symmetric matrices, and we explore some implications of the associated geometry. For the Wess–Zumino model we derive the conditions for preservation of 1/4 supersymmetry when one of two parallel domain-walls is rotated and in addition show that this model does not admit any classical configurations with 3/4 supersymmetry. Our analysis also provides information about BPS states of N=1 D=4 anti-de Sitter supersymmetry. Received: 6 April 2000/ Accepted: 10 September 2000     

Birkhoff’s Polytope and Unistochastic Matrices,N = 3 and N = 4

The set of bistochastic or doubly stochastic N×N matrices is a convex set called Birkhoff’s polytope, which we describe in some detail. Our problem is to characterize the set of unistochastic matrices as a subset of Birkhoff’s polytope. For N=3 we present fairly complete results. For N=4 partial results are obtained. An interesting difference between the two cases is that there is a ball of unistochastic matrices around the van der Waerden matrix for N=3, while this is not the case for N=4.     

New nonlinear σ-model with N=4 extended supersymmetry

A new nonlinear -model with N=4 supersymmetry in d=2 is constructed in terms of a N=2 tensor multiplet in d=4. Four equivalent formulations of the theory in superspace are obtained. The component structure of the model is considered by means of the Legendre transformation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 70–74, September, 1987.     

N=Z原子核性质的研究

论述了N=Z核实验和理论研究的历史和现状在,N=Z,是研究T=0对关联最好的核区,实验表明T=0和n-p对关联起着重要的作用,理论研究知心朋友同时包括T=0和T=1的对关联,是研究它们之间竞争及相变。 The history and current status of the study of N=Z nuclei are reviewed. T=0 n p pairing correlation is expected to play an important role in the structure of the nuclei along N=Z line. Both T=0 and T=1 pairing modes should be included in the theoretical models. Phenomena like possible competition and phase transition between different pairing modes are becoming important issues in nuclear structure.     

Variability of the atmospheric N2O line (J=3→4)

We analyze the results of observations of the radio emission of atmospheric N₂O in the line J=3→4 at frequency near 100.5 GHz. Observations aimed at monitoring the nitrous oxide content at altitudes h>20 km were performed in Nizhny Novgorod from March to May, 1997. We discover variations of the optical-depth decrement in the line, which can be explained by the redistribution of nitrous oxide over the altitude range h=20–55 km. This assumption does not contradict published data on in-situ measurements of N₂O density at h=5–35 km. Using the obtained data we calculate the rotational-line spectra of atmospheric N₂O. We point out that the measured decrements of the optical depths are greater than the calculated ones. We discuss observations of the N₂O lines in the mm-wave band as a promising method for monitoring the vertical mixing in the atmosphere. N. I. Lobachevsky State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 10, pp. 933–939, October 1999.     

Singular Dimensions¶of the N= 2 Superconformal Algebras II:¶The Twisted N= 2 Algebra

We introduce a suitable adapted ordering for the twisted N= 2 superconformal algebra (i.e. with mixed boundary conditions for the fermionic fields). We show that the ordering kernels for complete Verma modules have two elements and the ordering kernels for G-closed Verma modules just one. Therefore, spaces of singular vectors may be two-dimensional for complete Verma modules whilst for G-closed Verma modules they can only be one-dimensional. We give all singular vectors for the levels , 1, and for both complete Verma modules and G-closed Verma modules. We also give explicit examples of degenerate cases with two-dimensional singular vector spaces in complete Verma modules. General expressions are conjectured for the relevant terms of all (primitive) singular vectors, i.e. for the coefficients with respect to the ordering kernel. These expressions allow to identify all degenerate cases as well as all G-closed singular vectors. They also lead to the discovery of subsingular vectors for the twisted N= 2 superconformal algebra. Explicit examples of these subsingular vectors are given for the levels , 1, and . Finally, the multiplication rules for singular vector operators are derived using the ordering kernel coefficients. This sets the basis for the analysis of the twisted N= 2 embedding diagrams. Received: Received: 15 March 1999 / Accepted: 12 November 2000     

Four-loop β-function for the N = 1 and N = 2 supersymmetric non-linear sigma model in two dimensions

A superspace calculation of the four-loop β-function is presented for two-dimensional N= 1,2 supersymmetric non-linear σ-models. It is concluded that besides the one-loop contribution which vanishes on Ricci-flat manifolds, the β-function receives four-loop contributions which do not vanish in the Ricci-flat case. Implications for the superstring are discussed.     

The ΔTz = + 1 Gamow-Teller excitation of N = 28 isotones

Results of shell-model calculations of Gamow-Teller strength distributions are presented for ⁵⁰Ti → ⁵⁰Sc, ⁵²Cr → ⁵²V and ⁵⁴Fe → ⁵⁴Mn. The results support the previous shell-model estimates that a large fraction of Gamow-Teller strength is concentrated at low excitation energy in the daughter nuclei. The strength distributions are in fairly good agreement with those of forward-angle cross sections of T₀ + 1 isospin states of the intermediate-energy (p, p') reaction on N = 28 isotones. An estimate of quenching in the T₀ → T₀ + 1 τσ mode transition is attempted. Calculations are performed also for the first 2⁺ and 4⁺ parent states in the context of electron capture at the late stages of stellar evolution.     

N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution

We further investigate, in the planar limit of N=4 supersymmetric Yang–Mills theories, the high energy Regge behavior of six-point MHV scattering amplitudes. In particular, for the new Regge cut contribution found in our previous paper, we compute in the leading logarithmic approximation (LLA) the energy spectrum of the BFKL equation in the color octet channel, and we calculate explicitly the two-loop corrections to the discontinuities of the amplitudes for the transitions 2→4 and 3→3. We find an explicit solution of the BFKL equation for the octet channel for arbitrary momentum transfers and investigate the intercepts of the Regge singularities in this channel. As an important result we find that the universal collinear and infrared singularities of the BDS formula are not affected by this Regge-cut contribution. Any improvement of the BDS formula should reproduce this cut to all orders in the coupling.     

D=2 and D=4 realization of κ-conformal algebra

We describe the generators of-conformal transformations leaving invariant the-deformed d'Alembert equation. For the case D=4 the algebraic structure of the conformal extension of the off-shell spin zero realization of-Poincaré algebra is discussed. Then the D=2 off-shell realization of-conformal algebra for arbitrary spin and its commutation relations are studied.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.Supported by KBN grant 2P 302 087 06.     

丰中子Z=96—102同位素链的N=184闭壳

在相对论平均场理论框架下, 首先证明了对力强度存在明显的壳效应, 然后用此方法研究了Z=96—102区域内超重同位素链中中子壳封闭问题, 证明了在超重元素中,N=184处确实存在壳封闭. 并据此给出了一种检验壳封闭的新方法.     

围绕Z=56和N=88丰中子核区八极形变的研究

介绍了通过测量重核裂变产生的瞬发γ谱方法,对围绕Ｚ＝５６、Ｎ＝８８丰中子核区高自旋态八极形变的研究,并对Ｘｅ、Ｂａ、Ｃｅ和Ｌａ等丰中子核链的八极形变特性进行了讨Through study of the prompt γ rays in spontaneous fission, the octupole deformation in neutron rich Xe, Ba, Ce and La isotopes around Z =56, N =88 region was assigned. The properties of the octupole deformation in these nuclei were also discussed. 论．     

Structure of Ti N (N = 6–15) titanium cluster isomers

The atomic structures of various isomers of free Ti _N (N = 6–15) titanium clusters have been studied by molecular dynamics using the many-body interaction potential in the tight binding model. The following parameters of the cluster structure have been calculated: average bond length and energy, coordination number, and frequencies (probabilities) of their appearance. An increase in the cluster size N is accompanied by increased values of these parameters. It is established that the frequency of appearance of an isomer with a given N value increases with the bond energy. The most probable structures of clusters with N = 10–15 correspond to maximum values of the atomic structure parameters among all isomers of a given size.