All possible de Sitter superalgebras and the presence of ghosts (original) (raw)
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Super algebra and Harmonic Oscillator in Anti de Sitter space
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The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape invariance, charge conjugation and other properties of supersymmetric Quantum Mechanics for our equation are discussed. We investigate the dynamical symmetry into definite group. We also obtain the Casimir operator and thermodynamics properties of harmonic oscillator in Anti de sitter space. We have discussed the corresponding algebra for the N=2 Supersymmetry. The energy spectrum of the harmonic oscillator is similar to the flat space but the constant terms of it are different, This constant terms depends to the geometrical parameter of the background. Finally we have obtained the various th...
Fortschritte der Physik, 1986
The hermitean oscillator-like realizations of classical algebras in terms of bosonic and fermionic creation and annihilation operators are given. The hermitean realizations of classical superalgebras using boson-fermion oscillators are explicitely described. The assumption of positive definite metric in a Hilbert space of the oscillators states is exploited. Due to this fact, the realizations of superalgebras in the Hilbert space can be constructed only for: the real orthosymplectic superalgebra osp ( N ; 2 M ; R); the unitary compact superalgebra su ( N ; M ) ; the unitary noncompact one S U ( N ; K , M ) ; and the quaternionic unitary superalgebra uu,(N; M ; H ) . classical Lie superalgebras (i.e. simple Lie superalgebras whose Lie subalgebra is reductive) can be divided into four classes : a) standard classical Lie superalgebras A(%, m), B(n, m ) , C(n) and B(n, m ) ; b) exceptional Lie superalgebras F(4), G(3) ; c ) strange Lie superalgebras P(n), &(n) ; d) one-parameter family of deformations of D(2, 1) denoted by . The standard classical Lie superalgebras are supersymmetric analogues of Cartan classical Lie algebras. The classification of real forms of classical Lie superalgebras are given in [3]. Recently, the realizations of supersymmetry algebras using the oscillator operators was proposed. It is connected with the problem of bosonization of the fermionic systems [4, 51 as well as the description of unitary irreducible representations of noncompact supersymmetries [6--81. By the oscillator method, using bosonic and fermionic oscillators there were constructed unitary irreducible representations of : i) anti-de Sitter superalgebra osp (2; 4 ; R) in [9]; ii) extended anti-de Sitter superalgebra osp ( N ; 4; R) in [lo]; *) On leave of absence from Institute of Teacher's Training-ODN, 50-527 Wroclaw, ul. Dawida la, Poland.
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We consider simple superalgebras which are a supersymmetric extension of the spin algebra in the cases where the number of odd generators does not exceed 64. All of them contain a super Poincaré algebra as a contraction and another as a subalgebra. Because of the contraction property, some of these algebras can be interpreted as de Sitter or anti de Sitter superalgebras. However, the number of odd generators present in the contraction is not always minimal due to the different splitting properties of the spinor representations under a subalgebra. We consider the general case, with arbitrary dimension and signature, and examine in detail particular examples with physical implications in dimensions d = 10 and d = 4.
Positive-energy irreps of the quantum anti de Sitter algebra
Czechoslovak Journal of Physics, 1996
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Modern Physics Letters A, 1992
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Towards a quantum theory of de Sitter space
Journal of High Energy Physics, 2006
We describe progress towards constructing a quantum theory of de Sitter space in four dimensions. In particular we indicate how both particle states and Schwarzschild de Sitter black holes can arise as excitations in a theory of a finite number of fermionic oscillators. The results about particle states depend on a conjecture about algebras of Grassmann variables, which we state, but do not prove.
Quantum (anti)de Sitter algebras and generalizations of the kappa-Minkowski space
2004
We present two different quantum deformations for the (anti)de Sitter algebras and groups. The former is a non-standard (triangular) deformation of SO(4,2) realized as the conformal group of the (3+1)D Minkowskian spacetime, while the latter is a standard (quasitriangular) deformation of both SO(2,2) and SO(3,1) expressed as the kinematical groups of the (2+1)D anti-de Sitter and de Sitter spacetimes, respectively. The Hopf structure of the quantum algebra and a study of the dual quantum group are presented for each deformation. These results enable us to propose new non-commutative spacetimes that can be interpreted as generalizations of the kappa-Minkowski space, either by considering a variable deformation parameter (depending on the boost coordinates) in the conformal deformation, or by introducing an explicit curvature/cosmological constant in the kinematical one; kappa-Minkowski turns out to be the common first-order structure for all of these quantum spaces. Some properties provided by these deformations, such as dimensions of the deformation parameter (related with the Planck length), space isotropy, deformed boost transformations, etc., are also commented.
Nondegenerate super–anti–de Sitter algebra and a superstring action
Physical Review D, 2000
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