https://doi.org/10.1140/epjp/s13360-022-03348-5
Regular Article
Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA)
Saint Petersburg State University, Saint-Petersburg, Russia
Received:
10
April
2022
Accepted:
30
September
2022
Published online:
17
October
2022
The article is devoted to the investigation of the Noether currents and integrals of motion in the special subclass of theories with higher field derivatives — theories under differential field transformations in action (DFTA). Under fairly general assertions, we derive a simple representation for the integrals as sums of “old” integrals of motion, terms that vanish on the “old” equations of motion and surface integrals. We show that for some cosmological theories of that kind with high-order derivatives the last contribution can violate gauge invariance, specifically, diffeomorphisms. Then we investigate ambiguity of the Noether procedure for higher derivative theories and fix it in the way the problem resolves in quite general setting. The obtained results are discussed for the several extensions of the General Relativity, which are obtained by DFTA, in particular, for mimetic, disformal and Regge–Teitelboim theories of gravity. In particular, we calculate Iyer–Wald black hole entropy from the corrected currents and also discuss the derivation of the integral constraints on Sachs–Wolfe effect.
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