Conformal Rescalings Applied to Poincare Gauge Theory : Particles and Fields

概要

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Conformal rescalings of spinor are studied, referring to the Penrose approach, in which the factor Z, in H→ZH, is allowed to be complex. There is no gauge field at all associated with the rescalings. This new approach is then applied to Poincare gauge theory whose Lagrange function is linear and quadratic in curvature and torsion. We find that the Lagrange function invariant under complex conformal rescalings is given by the sum of the square of the Weyl tensor, (∂_μυ_ν-∂_νυ_μ)^2 and (∂_μα_ν-∂_να_μ)^2, where υ_μ and α_μ denote, respectively, the vector and axial-vector parts of torsion, and finally additional terms with a complex scalar field. For the two contributions of υ_μ and α_μ, one appears with positive sign and the other with negative sign. This situation is discussed in relation to the zero-energy theorem proved by Boulware et al. in scale invariant theory.
理論物理学刊行会の論文
1985-10-25