We consider the quantum mechanics of a particle on the coset superspace SU(2|1)/[U(1)×U(1)], which is a super-flag manifold with SU(2)/U(1) ∼= S2 ‘body’. By incorporating the Wess-Zumino terms associated with the U(1) × U(1) stability group, we obtain an exactly solvable super-generalization of the Landau model for a charged particle on the sphere. We solve this model using the factorization me...

A linear relation E acting on a Hilbert space is idempotent if E2=E. triplet of subspaces needed to characterize given idempotent: (ranE,ran(I−E),domE), or equivalently, (ker⁡(I−E),ker⁡E,mulE). The relations satisfying the inclusions E2⊆E (sub-idempotent) E⊆E2 (super-idempotent) play an important role. Lastly, adjoint and closure are studied.

Abstract We realize the simple Lie superalgebra G ( 3 ) as supersymmetry of various geometric structures, most importantly super-versions Hilbert–Cartan equation (SHC) and Cartan's involutive PDE system that exhibit 2 symmetry. provide symmetries explicitly compute, via first Spencer cohomology groups, Tanaka–Weisfeiler prolongation negatively graded superalgebras associated with two particular...

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*...

Abstract. Certain facts about frames and generalized frames (g- frames) are extended for the g-frames for Hilbert C*-modules. It is shown that g-frames for Hilbert C*-modules share several useful properties with those for Hilbert spaces. The paper also character- izes the operators which preserve the class of g-frames for Hilbert C*-modules. Moreover, a necessary and suffcient condition is ob- ...

‎In this paper‎, ‎by using the sequence of multipliers‎, ‎we introduce frames with algebraic bounds in Hilbert pro-$ C^* $-modules‎. ‎We investigate the relations between frames and $ ast $-frames‎. ‎Some properties of $ ast $-frames in Hilbert pro-$ C^* $-modules are studied‎. ‎Also‎, ‎we show that there exist two differences between $ ast $-frames in Hilbert pro-$ C^* $-modules and Hilbert $ ...

Frames in Hilbert bimodules are a special case of frames in Hilbert C*-modules. The paper considers A-frames and B-frames and their relationship in a Hilbert A-B-imprimitivity bimodule. Also, it is given that every frame in Hilbert spaces or Hilbert C*-modules is a semi-tight frame. A relation between A-frames and K(H_B)-frames is obtained in a Hilbert A-B-imprimitivity bimodule. Moreover, the ...

We study the transformation law of quantum fields in super Yang-Mills theory quantized in the Wess-Zumino gauge. It can be derived from a local version of generalized Slavnov-Taylor identities for general Green functions. Under suitable normalization conditions the transformations are local. Within the vector multiplet anomalous dimensions become equal. The breaking of susy shows up in Fock but...

We continue the study of centralizers on Kothe function spaces and the commutator estimates they generate (see [29]). Our main result is that if X is a super-reflexive Kothe function space then for every real centralizer Q on X there is a complex interpolation scale of Kothe function spaces through X inducing Q as a derivative, up to equivalence and a scalar multiple. Thus, in a loose sense, al...

abstract. certain facts about frames and generalized frames (g- frames) are extended for the g-frames for hilbert c*-modules. it is shown that g-frames for hilbert c*-modules share several useful properties with those for hilbert spaces. the paper also character- izes the operators which preserve the class of g-frames for hilbert c*-modules. moreover, a necessary and suffcient condition is ob- ...