Superfields in higher-dimensional spacetime

We give the constraints in six- and ten-dimensional globally-supersymmetric gauge theories on the superfield covariant derivatives, which reduce to the usual ones for the extended theories in four dimensions. We also compute the six-dimensional action. including the Fayet-Iliopoulos term.     

Representations of (1,0) and (2,0) Superconformal Algebras in Six Dimensions: Massless and Short Superfields

We construct unitary representations of (1,0) and (2,0) superconformal algebras in six dimensions by using superfields defined on harmonic superspaces with coset manifolds USp(2n)/[U(1)]ⁿ, n=1, 2. In the spirit of the AdS₇/CFT₆ correspondence, massless conformal fields correspond to supersingletons in AdS₇. By tensoring them we produce all short representations corresponding to 1/2 and 1/4 BPS anti-de Sitter bulk states of which massless bulk representations are particular cases.     

Superfields with higher spin fermionic coordinates

We consider superspaces with fermionic coordinates belonging to representations of the Lorentz group other than spin 1/2. A general diagrammatic method is introduced which facilitates the identification of the various component fields comprising the superfields. Explicit examples of superfields with fermionic coordinates belonging to (1, 1/2)+(1/2, 1) and (3/2, 0)+(0, 3/2) representations of the Lorentz group are worked out in detail.     

Supersymmetry and Superfields in Three Euclidean Dimensions

The simplest supersymmetry algebra and superspace in three-dimensional Euclidean (3dE) space is examined. Representations of the algebra are considered and the implications of restricting the space of states to states with positive definite norm are determined. A superspace is defined and superfields are introduced. Supersymmetric field theory models in 3dE are described in both superfield and component field forms. The relationship between these models and similar models in four-dimensional Minkowski space is described.     

Matter as Spectrum of Spacetime Representations

Bound and scattering state Schrödinger functions of nonrelativistic quantum mechanics as representation matrix elements of space and time are embedded into residual representations of spacetime as generalizations of Feynman propagators. The representation invariants arise as singularities of rational representation functions in the complex energy and complex momentum plane. The homogeneous space GL(²)U(2) with rank 2, the orientation manifold of the unitary hypercharge-isospin group, is taken as model of nonlinear spacetime. Its representations are characterized by two continuous invariants whose ratio will be related to gauge field coupling constants as residues of the related representation functions. Invariants of product representations define unitary Poincaré group representations with masses for free particles in tangent Minkowski spacetime.     

An Extended Fuzzy Supersphere and¶Twisted Chiral Superfields

A noncommutative associative algebra of the N= 2 fuzzy supersphere is introduced. It turns out to possess a nontrivial automorphism which relates twisted chiral to twisted anti-chiral superfields and hence makes it possible to construct noncommutative nonlinear σ-models with extended supersymmetry. Received: 29 March 1999 / Accepted: 8 April 1999     

Gauge Coupling Constants as Residues of Spacetime Representations

The gauge coupling constants in the electroweak standard model can be written as mass ratios, e.g. the coupling constant for isospin interactions with the mass of the charged weak boson and the mass parameter characterizing the ground state degeneracy. A theory is given which relates the two masses in such a ratio to invariants which characterize the representations of a noncompact nonabelian group with real rank 2. The two noncompact abelian subgroups are operations for time and for a hyperbolic position space in a model for spacetime, homogeneous under dilation and Lorentz group action. The representations of the spacetime model embed the bound state representations of hyperbolic position space as seen in the nonrelativistic hydrogen atom. Interactions like Coulomb or Yukawa interactions are described by Lie algebra representation coefficients. A quantitative determination of the ratio of the invariants for position- and time-related operations, determined by the spacetime representation, gives the right order of magnitude for the gauge coupling constants.     

Regularization as Quantization in Reducible Representations of CCR

A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials (an alternative to the Gupta-Bleuler method) is tested on the example of quantum electromagnetic fields produced by a classical current. The Heisenberg dynamics can be consistently formulated since the fields are given by operators and not operator-valued distributions. The scheme involves a Hamiltonian whose free part is modified but the minimal-coupling interaction is the standard one. Solving Heisenberg equations of motion under the assumption that the fields are free for times t ₀ = ±∞ we arrive at retarded and advanced solutions. Once we have these solutions we can deduce the form of evolution of retarded and advanced fields between two arbitrary finite times. The appropriate unitary evolution operators are found and their generators are computed. Now the generators involve the same free part as before, but the interaction term turns out to be modified. For a pointlike charge localized on a world-line z ^a (t) we find the interaction term of the form where the integration is along those parts of the charge world-line where the charge velocity is nonzero. There is no self-energy contribution. Next we compute photon statistics. Poisson statistics naturally results and infrared divergence can be avoided even for pointlike sources. Classical fields produced by classical sources can be obtained if one computes coherent-state averages of Heisenberg-picture operators. It is shown that the new form of representation automatically smears out pointlike currents. We discuss in detail Poincaré covariance of the theory and the role of Bogoliubov transformations for the issue of gauge invariance. The representation we employ is parametrized by a number that is related to Rényi’s α. It is shown that the “Shannon limit” α→ 1 plays here a role of a correspondence principle with the standard regularized formalism. PACS: 03.70.+k, 41.20.Jb, 42.50.-p.     

Superfields with arbitrary spin spectral representation of the dilatational invariant two-point function

The superfields with arbitrary spin are given as homogeneous functions of one two- component complex commuting spinor and one anticommuting spinor. The spectral representation of the invariant two-point function is found.     

Massless Fields as Unitary Representations of the Poincaré Group

Relativistic zero-mass fields are described as manifestly covariant unitary irreducible representations of the Poincaré group. The wave-equations, which are a necessary condition for unitarity, are constructed for spinor fields of arbitrary spin and for tensor fields of integer spin. Poincaré covariance together with causality and positive energy are used to determine the commutators of quantized fields up to a positive multiple and to prove the spin-statistics theorem. The use of potentials for boson fields is discussed and it is shown that, at the expense of manifest covariance, potentials may be introduced as zero-mass limits of the massive Wigner representations.     

Superfields,auxilliary fields and tensor calculus for N=2 extended supergravity

Starting from the geometry of superspace, we find constraints for torsion and curvatures, which lead to off-shell realizations of N=2 supergravity. We give the action formula, and construct the supergravity lagrangian from it.     

Representations of D-posets

A generalization of an orthoalgebra, which includes the set of all effects (i.e., s.a. operators between 0 and 1 on a Hilbert space) is a D-poset or an effect algebra, equivalently. Two generalizations of test spaces the logics of which are D-posets are investigated and their equivalence is shown.     

Representations of BRS algebra

In the canonical formulation of gauge theories the BRS transformation plays a fundamental rôle. The generator of this transformation along with the ghost number forms an algebra called the BRS algebra. Certain properties of this algebra are essential to the proof of unitarity of the S matrix in the physical sector and also to the discussion of color confinement.In the present paper we present all the possible representations of the BRS algebra in the light of indefinite metric.     

Representations of conformal supersymmetry

The superalgebras of (generalized) conformal supersymmetry have some very interesting unitarizable representations that contain only massless representations of the conformal subalgebra, in spite of contrary claims that have recently been made , .

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Topologizations of Chiral Representations

We analyze and compare two families of topologies that have been proposed for representation spaces of chiral algebras by Huang and Gaberdiel & Goddard respectively. We show, in particular, that for suitable pairs the topology of Gaberdiel & Goddard is coarser. We also give a new proof that the chiral two-point blocks are continuous in the topology of Huang.