MGAT3 - Theoretical Issues in GR |
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Speaker |
Itin, Yakov |
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Talk Title |
Noether procedure and dynamical geometry |
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Abstract |
The Hilbert–Noether theorem states that a current associated with diffeomorphism invariance of a Lagrangian vanishes on shell modulo a divergence of an arbitrary superpotential. Application of the Noether procedure to physical Lagrangians yields, however, meaningful (and measurable) currents. The well-known solution to this ‘paradox’ is to involve the variation of the metric tensor. Such procedure, for the field considered on a fixed (flat) background, is sophisticated logically (one needs to introduce the variation ofa fixed field) and formally. We analyze the Noether procedure for a generic diffeomorphism invariant p-form field model. We show that a consistent description of the canonical energy–momentum current is possible only if the dynamics of the geometry (gravitation) is taken into account. However, even the ordinary used ‘truncated’ consideration yields the proper expression. |
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