69 research outputs found
Nonlinear holomorphic supersymmetry, Dolan-Grady relations and Onsager algebra
Recently, it was noticed by us that the nonlinear holomorphic supersymmetry
of order , (-HSUSY) has an algebraic origin. We show that the
Onsager algebra underlies -HSUSY and investigate the structure of the former
in the context of the latter. A new infinite set of mutually commuting charges
is found which, unlike those from the Dolan-Grady set, include the terms
quadratic in the Onsager algebra generators. This allows us to find the general
form of the superalgebra of -HSUSY and fix it explicitly for the cases of
. The similar results are obtained for a new, contracted form of
the Onsager algebra generated via the contracted Dolan-Grady relations. As an
application, the algebraic structure of the known 1D and 2D systems with
-HSUSY is clarified and a generalization of the construction to the case of
nonlinear pseudo-supersymmetry is proposed. Such a generalization is discussed
in application to some integrable spin models and with its help we obtain a
family of quasi-exactly solvable systems appearing in the -symmetric
quantum mechanics.Comment: 18 pages, refs updated; to appear in Nucl. Phys.
Gravitational and higher-derivative interactions of massive spin 5/2 field in (A)dS space
Using on-shell gauge invariant formulation of relativistic dynamics we study
interaction vertices for a massive spin 5/2 Dirac field propagating in (A)dS
space of dimension greater than or equal to four. Gravitational interaction
vertex for the massive spin 5/2 field and all cubic vertices for the massive
spin 5/2 field and massless spin 2 field with two and three derivatives are
obtained. In dimension greater that four, we demonstrate that the gravitational
vertex of the massive spin 5/2 field involves, in addition to the standard
minimal gravitational vertex, contributions with two and three derivatives. We
find that for the massive spin 5/2 and massless spin 2 fields one can build two
higher-derivative vertices with two and three derivatives. Limits of massless
and partial massless spin 5/2 fields in (A)dS space and limits of massive and
massless spin 5/2 fields in flat space are discussed.Comment: 51 pages, LaTeX-2e, v3: Section 1 is divided into Sections 1-6.
Discussion of gravitational and higher-derivative vertices added to Sections
2-6. Tables I, II and Appendices B,C,D,E,F added. Typos correcte
Massive Fields of Arbitrary Integer Spin in Symmetrical Einstein Space
We study the propagation of gauge fields with arbitrary integer spins in the
symmetrical Einstein space of any dimensionality. We reduce the problem of
obtaining a gauge-invariant Lagrangian of integer spin fields in such
background to an purely algebraic problem of finding a set of operators with
certain features using the representation of high-spin fields in the form of
some vectors of pseudo-Hilbert space. We consider such construction in the
linear order in the Riemann tensor and scalar curvature and also present an
explicit form of interaction Lagrangians and gauge transformations for massive
particles with spins 1 and 2 in terms of symmetrical tensor fields.Comment: 15 pages, latex, no figures,minor change
On spin 2 electromagnetic interactions
In this paper we (re)consider the problem of electromagnetic interactions for
massless spin 2 particles and show that in spaces with non-zero
cosmological constant it is indeed possible (at least in linear approximation)
to switch on minimal electromagnetic interactions supplemented by third
derivative non-minimal ones which are necessary to restore gauge invariance.Comment: 5 pages, no figure
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