1,615 research outputs found

    Hidden supersymmetry and Berezin quantization of N=2, D=3 spinning superparticles

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    The first quantized theory of N=2, D=3 massive superparticles with arbitrary fixed central charge and (half)integer or fractional superspin is constructed. The quantum states are realized on the fields carrying a finite dimensional, or a unitary infinite dimensional representation of the supergroups OSp(2|2) or SU(1,1|2). The construction originates from quantization of a classical model of the superparticle we suggest. The physical phase space of the classical superparticle is embedded in a symplectic superspace T(R1,2)×L12T^\ast({R}^{1,2})\times{L}^{1|2}, where the inner K\"ahler supermanifold L12=OSp(22)/[U(1)×U(1)]=SU(1,12)/[U(22)×U(1)]{L}^{1|2}=OSp(2|2)/[U(1)\times U(1)]=SU(1,1|2)/[U(2|2)\times U(1)] provides the particle with superspin degrees of freedom. We find the relationship between Hamiltonian generators of the global Poincar\'e supersymmetry and the ``internal'' SU(1,1|2) one. Quantization of the superparticle combines the Berezin quantization on L12{L}^{1|2} and the conventional Dirac quantization with respect to space-time degrees of freedom. Surprisingly, to retain the supersymmetry, quantum corrections are required for the classical N=2 supercharges as compared to the conventional Berezin method. These corrections are derived and the Berezin correspondence principle for L12{L}^{1|2} underlying their origin is verified. The model admits a smooth contraction to the N=1 supersymmetry in the BPS limit.Comment: 43 pages, LaTeX Version 2.0

    A Z_3-graded generalization of supermatrices

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    We introduce Z_3-graded objects which are the generalization of the more familiar Z_2-graded objects that are used in supersymmetric theories and in many models of non-commutative geometry. First, we introduce the Z_3-graded Grassmann algebra, and we use this object to construct the Z_3-matrices, which are the generalizations of the supermatrices. Then, we generalize the concepts of supertrace and superdeterminant

    On the Supersymplectic Homogeneous Superspace Underlying the OSp(1/2) Coherent States

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    In this work we extend Onofri and Perelomov's coherent states methods to the recently introduced OSp(1/2)OSp(1/2) coherent states. These latter are shown to be parametrized by points of a supersymplectic supermanifold, namely the homogeneous superspace OSp(1/2)/U(1)OSp(1/2)/U(1), which is clearly identified with a supercoadjoint orbit of OSp(1/2)OSp(1/2) by exhibiting the corresponding equivariant supermoment map. Moreover, this supermanifold is shown to be a nontrivial example of Rothstein's supersymplectic supermanifolds. More precisely, we show that its supersymplectic structure is completely determined in terms of SU(1,1)SU(1,1)-invariant (but unrelated) K\"ahler 22-form and K\"ahler metric on the unit disc. This result allows us to define the notions of a superK\"ahler supermanifold and a superK\"ahler superpotential, the geometric structure of the former being encoded into the latter.Comment: 19 pgs, PlainTeX, Preprint CRM-185

    Higher order relations in Fedosov supermanifolds

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    Higher order relations existing in normal coordinates between affine extensions of the curvature tensor and basic objects for any Fedosov supermanifolds are derived. Representation of these relations in general coordinates is discussed.Comment: 11 LaTex pages, no figure

    Symplectic geometries on supermanifolds

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    Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with a non-degenerate Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is proven that in the odd case there are two different scalar symplectic structures (namely, an odd closed differential 2-form and the antibracket) which can be used for construction of symplectic geometries on supermanifolds.Comment: LaTex, 1o pages, LaTex, changed conten

    Local Differential Geometry as a Representation of the SUSY Oscillator

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    This work proposes a natural extension of the Bargmann-Fock representation to a SUSY system. The main objective is to show that all essential structures of the n-dimensional SUSY oscillator are supplied by basic differential geometrical notions on an analytical R^n, except for the scalar product which is the only additional ingredient. The restriction to real numbers implies only a minor loss of structure but makes the essential features clearer. In particular, euclidean evolution is enforced naturally by identification with the 1-parametric group of dilations.Comment: 10 pages, late

    The wave function of a gravitating shell

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    We have calculated a discrete spectrum and found an exact analytical solution in the form of Meixner polynomials for the wave function of a thin gravitating shell in the Reissner-Nordstrom geometry. We show that there is no extreme state in the quantum spectrum of the gravitating shell, as in the case of extreme black hole.Comment: 7 pages, 1 figur

    A Generalization of the Bargmann-Fock Representation to Supersymmetry by Holomorphic Differential Geometry

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    In the Bargmann-Fock representation the coordinates ziz^i act as bosonic creation operators while the partial derivatives zj\partial_{z^j} act as annihilation operators on holomorphic 00-forms as states of a DD-dimensional bosonic oscillator. Considering also pp-forms and further geometrical objects as the exterior derivative and Lie derivatives on a holomorphic CD{\bf C}^D, we end up with an analogous representation for the DD-dimensional supersymmetric oscillator. In particular, the supersymmetry multiplet structure of the Hilbert space corresponds to the cohomology of the exterior derivative. In addition, a 1-complex parameter group emerges naturally and contains both time evolution and a homotopy related to cohomology. Emphasis is on calculus.Comment: 11 pages, LaTe

    The existence of time

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    Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures - the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has natural symplectic and metric structures. Using this metric and symplectic form, we show that there exist canonically conjugate, orthogonal, metric submanifolds if and only if the original gauged space is Euclidean or signature 0. In the Euclidean cases, the resultant configuration space must be Lorentzian. Therefore, in this context, time may be viewed as a derived property of general relativity.Comment: 21 pages (Reduced to clarify and focus on central argument; some calculations condensed; typos corrected
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