Abstract
Weyl’s theorem is extended making use of the theory of concomitants to obtain a Lagrangian density for the massless bosonic fields without dimensional constants. It turns out to be quadratic in the gravitational field and encompasses all the theories that usually appear in the literature. It is shown that the gauge invariance of the Lagrangian follows from the invariance of the field equations.
Highlights
Weyl's theorem1 establishes that the most general Lagrangian density that may be constructed with the metric and its derivatives up to second order which is linear in second derivatives is a~ - gR + b ~ - g
We have extended Weyt's theorem, making use of the theory of concomitants that comes from it, to obtain a Lagrangian density for the massless bosonic fields, without dimensional constants
It turns out quadratic in the gravitational field even if this order was not prescribed from the outset
Summary
Instituto de Astronomia y Fisica del Espacio (CONICET), Casilla de Correo 67, Suc. 28. Argentina and Departamento de Matematicas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pab. /, Ciudad Universitaria, Buenos Aires, Argentina (Received 8 July 1986; accepted for publication 4 March 1987). Weyl's theorem is extended making use of the theory of concomitants to obtain a Lagrangian density for the massless bosonic fields without dimensional constants. It turns out to be quadratic in the gravitational field and encompasses all the theories that usually appear in the literature. It is shown that the gauge invariance of the Lagrangian follows from the invariance of the field equations
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