Euclidean linear conformal gravity

Physics

Scientific paper

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Conformal Mapping, Euclidean Geometry, Gauge Invariance, Gravitation Theory, Quantum Theory, Unified Field Theory, Coordinate Transformations, Equivalence, Green'S Functions, Linear Equations, Matter (Physics), Tensor Analysis

Scientific paper

The modern version of quantum gravity is considered, taking into account conformal gravity and, in particular, its supersymmetric extension, conformal supergravity. An analysis of conformal gravity in the group-theoretical framework is conducted. Questions associated with a more general problem related to the formulation of the conformal invariance in gauge theories are explored. Attention is given to the Euclidean formulation of conformal gravitation, a pair of Euclidean conformal fields, transformation laws for the metric tensor and the energy-momentum tensor under conformal inversion, invariant three-point Green functions, and the equivalence of representations and field equations.

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