Freydoon Mansouri

Geometry of superspaces with Bose and Fermi coordinates and applications to graded Lie bundles and supergravity

The geometry of superspaces with Bose‐ and Fermi‐type coordinates is presented from a coordinate independent point of view. Various geometrical quantities of conventional manifolds are generalized so as to be applicable to superspaces. It is shown that these generalizations can be basically arrived at algebraically by replacing, in the definitions of various geometrical quantities, the Lie derivative of the conventional manifolds with a generalized graded Lie bracket. Explicit expressions for connection coefficients, Riemann curvature tensor, etc., are derived. The general formalism is then applied to graded Lie bundles the relevance of which to supergravity theories is demonstrated.

A new supersymmetric string model and the supergauge constraints in the dual resonance models

Abstract We present a new supersymmetric string model which can carry spin and other quantum numbers and in which the supergauge constraints arise naturally. We obtain the known dual models involving fermions as special cases.

SU(N)-extended conformally invariant actions in superspace☆

Abstract Using the geometrical transformation laws of conformal supergravity, we classify all the available geometrical covariants according to their scale dimensions. We then use these to construct actions for SU(N)-extended conformal supergravity theories.

Geometrical transformation laws of fields in superunified theories

Abstract We present a systematic model-independent method of obtaining off-the-mass-shell transformation laws of fields in superunified theories. The method is applied to pure gravity, gravity coupled to Yang-Mills, conformal gravity, OSp( N ;4) supergravity, and conformal supergravity theories.

Constituent models for basic fields of grand unified theories

Abstract We show how to construct group theoretically basic fields of grand unified models based on SO(4 N + 2) from constituents endowed only with abelian symmetries. Their number and the number of their abelian symmetries equals the rank of SO(4 N + 2). Such constituents can carry definite values not of B - but of ( B − L )-number.

A relativistic quantum dynamical model based on the classical string

Abstract Motivated by geometrical considerations of the string model, we construct a dynamical theory of composite particles that is Poincare invariant in four dimensions, with no tachyons and no ghosts. The resulting physical states lie on indefinitely rising trajectories.

Superunified theories in superspace

The structure of superunified theories in superspace is discussed from the point of view of local gauge invariance. It is shown that the same two requirements which lead to the correct description of gravity determine the structure of these theories. In particular, all the transformation laws of the fields follow from geometry.

Locally supersymmetric theories with model-independent transformation laws

Abstract We construct locally supersymmetric theories based on the inhomogeneous supergroups IOSp(N; 2C), in which supersymmetric gauge fields satisfy model-independent transformation laws. This leads to the construction of actions which are manifestly gauge and coordinate invariants.