Gravity from Poincaré Gauge Theory of the Fundamental Particles. V ---The Extended Bach-Lanczos Identity---

Details Gravity from Poincaré Gauge Theory of the Fundamental Particles. V ---The Extended Bach-Lanczos Identity--- Gravity from Poincaré Gauge Theory of the Fundamental Particles. V ---The Extended Bach-Lanczos Identity---

Feb 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981pthph..65..525h&link_type=abstract

Progress of Theoretical Physics, Vol. 65, No. 2, pp. 525-532

Physics

81

Scientific paper

In the Riemann-Cartan space-time we prove the extended form of the Bach-Lanczos identity,[δ∫ ed^4x(FijmnFmnij-4FijFji+F^2)≡ 0,]where δ denotes that infinitesimal variations in the integral are taken with respect to both the translation gauge field and the Lorentz gauge field, and Fijmn stands for the curvature tensor formed of the Lorentz gauge field; Fij=ηmnFimjn and F=ηijFij. By virtue of this identity, there are five independent invariants quadratic in the Lorentz gauge field strength, when one derives field equations from the action principle.

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