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2009

Metric Lagrangians with two propagating degrees of freedom

Krasnov, Kirill

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There exists a large class of generally covariant metric Lagrangians that contain only local terms and describe two propagating degrees of freedom.

Trivial examples can be be obtained by applying a local field redefinition to the Lagrangian of general relativity, but we show that the class of two propagating degrees of freedom Lagrangians is much larger.
Thus, we exhibit a large family of non-local field redefinitions that map the Einstein-Hilbert Lagrangian into ones containing only local terms.
These redefinitions have origin in the topological shift symmetry of BF theory, to which GR is related in Plebanski formulation, and can be computed order by order as expansions in powers of the Riemann curvature.

Metric Lagrangians with two propagating degrees of freedom · Around

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G. ’t Hooft and M. J. G. Veltman, Annales Poincare Phys. Theor. A 20
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G. ’t Hooft and M. J. G. Veltman, NATO Adv. Study Inst. Ser. B Phys. 4
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J. F. Plebanski, J. Math. Phys. 18
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H. Urbantke, J. Math. Phys. 25
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Cited in the paper.

Then

R. Capovilla, T. Jacobson and J. Dell, Class. Quant. Grav. 8
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Later among the works it cites.
R. Capovilla, Nucl. Phys. B 373
1992
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I. Bengtsson and P. Peldan, Int. J. Mod. Phys. A 7
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Later among the works it cites.
K. Krasnov, Class. Quant. Grav. 26
Original
2009
Closest in time.

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