The graded Lie algebra structure of Lie superalgebra deformation theory

We show how Lie superalgebra deformation theory can be treated by graded Lie algebras formalism. Rigidity and integrability theorems are obtained.     

A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations

A new eight-dimensional Lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, are derived. Their super-Hamiltonian structures are established by making use of the supertrace identity, and they are integrable in the sense of Liouville.     

Lie groups and gravitation theory

A generalized space with torsion and curvature, defined by a fundamental group, is constructed by starting from the necessity of introducing standards of length and time in gravitation theory. The field variables coincide with the coefficients _i of the infinitesimal operator of the group. It is shown that the structural equations of the group depend on the transformation properties of the object to which they are applied. The simplest equations that the _i can satisfy are given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 40–47, December, 1970.     

A characterization of strict Jacobi-Nijenhuis manifolds through the theory of Lie algebroids

We obtain a characterization of strict Jacobi-Nijenhuis structures using the equivalent notions of generalized Lie bialgebroid and Jacobi bialgebroid.     

Quantum deformation of superalgebra

In this paper we discuss two types ofq-deformations of superalgebra.     

New Ermakov systems from Lie symmetry theory

We derive and discuss new Ermakov systems from the point of view of the Lie symmetry of differential equations.     

Lie transform perturbation theory for Hamiltonian systems

A review of the theory of Lie transform perturbation theory for Hamiltonian systems is presented. The operator theory of Dewar for continuous families of canonical transformations is discussed. It is then used to derive the perturbation method of Deprit. Two examples of the use of this method are provided. In addition, the more efficient perturbation method of Dragt and Finn is discussed.     

漫谈希格斯粒子

希格斯玻色子发现于2012年,是粒子物理学研究中的一件划时代的大事。它在粒子物理的“标准模型”中起关键性作用,通过神秘的对称性破缺机制给基本粒子带来质量,和高深莫测的量子真空息息相关,也被认为在宇宙演化的极早期起重要作用。在希格斯玻色子发现十周年之际,文章将从科普视角出发,描绘希格斯玻色子的理论背景、粒子特性、实验探测、研究现状和展望,揭开希格斯玻色子的神秘面纱,理解它的过去、现在和未来。     

Gauge formulation of a vector-spinor superalgebra

We present a gauge formulation of the Poincaré algebra extended to include fermionic generators belonging to the vector-spinor representation of the Lorentz group. The gauge action of the theory, quadratic in curvature tensors, is derived.     

A Lie theoretic galois theory for the spectral curves of an integrable system: I

In the study of integrable systems of ODE's arising from a Lax pair with a parameter, the constants of the motion occur as spectral curves. The specific curves depend upon the representation of the Lie algebra. In this paper a Galois theory of spectral curves is given that classifies the spectral curves from an integrable system. The spectral curves correspond to conjugacy classes of certain subgroups of the Weyl group for the Lie algebra. The theory is illustrated with the periodic Toda lattice.Partially supported by a Louisiana Education Quality Support Fund grant LEQSF (87-89)-RD-A-8     

Multilevel systems and generalizations of the superalgebra

A new approach to constructing the various generalizations of the one-dimensional supersymmetric quantum mechanics is proposed, including the parasupersymmetric quantum mechanics constructed by Rubakov and Spiridonov as the special case. In particular, we derive the generalized superalgebra, which possesses the features both of the familiar superalgebra and of the parasuperalgebra. Namely, the generalized supercharges Q_i ^± and the Hamiltonian H forms the generalized superalgebra, where Q_i ^±2=0 (as for ordinary superalgebra), but the triple products of generalized supercharges obey the relations Q₁ ⁺Q_j ^–Q_j ⁺=Q_i ⁺H (i, j=1, 2) and Q_i ⁺Q_i ^–Q_j ⁺=(1/4)kQ_i ⁺, Q_i ⁺Q_i ^–Q_j ⁺=(1/4)kQ_i ⁺(i, j=1, 2; ij) (analogous to the parasuperalgebra). Furthermore, the generalized supercharges are conserved, i.e. [H, Q_i ^±]=0.Presented at the International Workshop on Squeezed and Correlated States, Moscow, December 3–7, 1990.     

The Hopf superalgebra of AdS/CFT

We describe the unconventional infinite-dimensional Hopf superalgebra related to the integrable S-matrix of the AdS/CFT correspondence, and discuss its typical and atypical representations.     

A superalgebra morphism of U q [osp(1/2N)] onto the deformed oscillator superalgebra W q (N)

We prove that the deformed oscillator superalgebra W _q (n) (which in the Fock representation is generated essentially byn pairs ofq-bosons) is a factor algebra of the quantized universal enveloping algebra U _q [osp(1/2n)]. We write down aq-analog of the Cartan-Weyl basis for the deformed osp(1/2n) and also give an oscillator realization of all Cartan-Weyl generators.     

Operator-valued connections,Lie connections,and Gauge field theory

Noether's first theorem tells us that the global symmetry groupG _r of an action integral is a Lie group of point transformations that acts on the Cartesian product of the space-time manifold with the space of states and their derivatives. Gauge theory constructs are thus required for symmetry groups that act indiscriminately on the independent and dependent variables where the group structure can not necessarily be realized as a subgroup of the general linear group. Noting that the Lie algebra of a general symmetry groupG _r can be realized as a Lie algebrag _r of Lie derivatives on an appropriately structured manifold,G _r -covariant derivatives are introduced through study of connection 1-forms that take their values in the Lie algebrag _r of Lie derivatives (operator-valued connections). This leads to a general theory of operator-valued curvature 2-forms and to the important special class of Lie connections. The latter are naturally associated with the minimal replacement and minimal coupling constructs of gauge theory when the symmetry groupG _r is allowed to act locally. Lie connections give rise to the gauge fields that compensate for the local action ofG _r in a natural way. All governing field equations and their integrability conditions are derived for an arbitrary finite dimensional Lie group of symmetries. The case whereG _r contains the ten-parameter Poincaré group on a flat space-timeM ₄ is considered. The Lorentz structure ofM ₄ is shown to give a pseudo-Riemannian structure of signature 2 under the minimal replacement associated with the Lie connection of the local action of the Poincaré group. Field equations for the matter fields and the gauge fields are given for any system of matter fields whose action integral is invariant under the global action of the Poincaré group.     

Michael J. Moravcsik: A biographical sketch

A brief biography of Michael J. Moravcsik is presented, concentrating on the chronology of his contributions to theoretical high- and intermediateenergy physics. The evolution of his interest in science development in the third world, scientific methodology, and scientometrics are indicated. A personal reminiscence is included.     

? → Neveu-Schwarz-Ramond superalgebra → Virasoro algebra

There exists a unique object which stands to the Neveu-Schwarz-Ramond (NSR) superalgebra exactly in the same relation as the NSR superalgebra stands to the Virasoro algebra.