Julius Wess

Supergauge Transformations in Four-Dimensions

Abstract Supergauge transformations are defined in four space-time dimensions. Their commutators are shown to generate γ5 transformations and conformal transformations. Various kinds of multiplets are described and examples of their combinations to new representations are given. The relevance of supergauge transformations for Lagrangian field theory is explained. Finally, the abstract group theoretic structure is discussed.

A Lagrangian Model Invariant Under Supergauge Transformations

We study, in the one-loop approximation, a Lagrangian model invariant under supergauge transformations. The model involves a scalar, a pseudoscalar and a spinor field. Supergauge invariance gives rise to relations among the masses and the coupling of these fields and implies the existence of a conserved current. The renormalization procedure is discussed and the relations among masses and couplings are shown to be preserved by renormalization.

Supergauge Invariant Extension of Quantum Electrodynamics

A minimal supergauge invariant extension of quantum electrodynamics is described. It contains a spinor, a scalar and a pseudoscalar field, all charged, plus the photon field and a massless Majorana spinor. A Lagrangian invariant under gauge and supergauge transformations is constructed and shown to be renormalizable in the one-loop approximation.

Extended supersymmetry and gauge theories

Abstract A formulation of gauge theories with an extended supersymmetry for N = 2 is given in terms of superfields. The Lagrangian is expressed in terms of superfields and component fields as well.

Superspace formulation of supergravity

Abstract A geometrical interpretation of supergravity is given in terms of the differential geometry of superspace. Starting from a general affine superspace, the geometry is specified in such a way as to contain as a special case the superspace of a global supersymmetry. Covariant equations are given which are equivalent to those of supergravity in four-space. The question of finding a suitable Lagrangian is discussed.

Supergauge Multiplets and Superfields

Abstract Superfields are defined as functions of the space-time variable x and of anticommuting two-component spinors θ and θ . They have definite transformation properties under supergauge transformations. Their expansion in θ and θ generates a finite number of ordinary fields forming a multiplet. A number of operations are defined which allow the construction of new superfields from given ones. The corresponding set of multiplets is complete, in the sense that the product of any two can be decomposed as a sum of multiplets belonging to the same set.

Superfield Lagrangian for supergravity

Abstract We show that the action for supergravity in superspace is the integral of the determinant of the supervierbein. Our method allows the construction of actions describing the coupling to matter supermultiplets. As an example we give the coupling to the massless vector supermultiplet.

A superfield formulation of the non-linear realization of supersymmetry and its coupling to supergravity

Abstract A thorough investigation of the non-linear realization of supersymmetry is carried out both in flat space and in curved space (supergravity). A manageable superfield formulation is developed which allows one to evaluate the physical effects of the non-linear field when it is coupled to other multiplets. We present several interesting applications (mostly in the context of supergravity) useful in model building.

The two-parameter deformation ofGL(2), its differential calculus, and Lie algebra

The Yang-Baxter equation is solved in two dimensions giving rise to a two-parameter deformation ofGL(2). The transformation properties of quantum planes are briefly discussed. Non-central determinant and inverse are constructed. A right-invariant differential calculus is presented and the role of the different deformation parameters investigated. While the corresponding Lie algebra relations are simply deformed, the comultiplication exhibits both quantization parameters.

The component formalism follows from the superspace formulation of supergravity

Abstract We identify the transformations of local supersymmetry as particular combinations of general coordinate transformations and local Lorentz transformations in superspace. Component fields for supergravity are defined as the values at θ = 0 of the supervielbein and (for the auxiliary fields) of certain components of the supertorsion. For chiral and general multiplets they are defined as the values at θ = 0 of (tangent space) spinorial covariant derivatives. We derive the transformation properties for field multiplets and for chiral density multiplets. The same method can be used for general densities. The lagrangian of supergravity in terms of component fields is obtained.