Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-02-09
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
7 pages, new idea
Scientific paper
Every field theory, to have some hope of being renormalizable, has to be defined by a lagrangian which terms never exceed the mass dimensions [mass]^4. The dimension of a field is given by one half of four minus the number of derivatives in its kinetic term. This is strictly related to the mass dimensions of the coupling constant in the kinetic term. In particular, a theory has very few chances of being renormalizable if these dimensions are negative. This is what happens in General Relativity, where the coupling of the Hilbert-Einstein action has dimensions [m]^-2. We present here an equivalent formulation of the theory where the Hilbert-Einstein action doesn't contain kinetic terms, but only interaction terms. Moreover, a new kinetic term appears, which coupling has dimensions [m]^0. We suggest that maybe, in this formulation, General Relativity can be renormalized.
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