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The 1.5 formalism played a key role in the discovery of supergravity and it has been used to prove the invariance of essentially all supergravity theories under local supersymmetry. It emerged from the gauging of the super Poincaré group to find supergravity. We review both of these developments as well as the auxiliary fields for simple supergravity and its most general coupling to matter using the tensor calculus. [ABSTRACT FROM AUTHOR]

This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in spacetime (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time. [ABSTRACT FROM AUTHOR]

The idea of applying the gauge principle to formulate the general theory of relativity started with Utiyama in 1956. In this article, various applications of the gauge principle applied to different aspects of the gravitational interactions, are reviewed. [ABSTRACT FROM AUTHOR]