Abstract
Noether identities resulting from external symmetries represent “conservation” laws in relativistic field theories and balance laws in 3-dimensional continuum statics, respectively. In a suitably selected 4-dimensional non-Euclidean space-time (3-dimensional stress space), the momentum currents (stresses) entering the conservation (balance) laws can be mapped such that the Noether identities become Bianchi identities, or irreducible pieces thereof. Using a metric-affine space with independent metricg αβ and connection Γ β α , we derive the following types of mapping prescriptions: momentum current → (contraction of) curvature; spin current → torsion; shear current → trace-free nonmetricity; dilation current → Weyl 1-form. The last two mappings constitute the main result. The mapping of the dilation current turns out to be exceptional, since it does not yield a nontrivial Bianchi identity.
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This paper is dedicated to Prof. Ekkehart Kröner, Stuttgart, on the occasion of his 70th birthday.
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McCrea, J.D., Hehl, F.W. & Mielke, E.W. Mapping Noether identities into Bianchi identities in general relativistic theories of gravity and in the field theory of static lattice defects. Int J Theor Phys 29, 1185–1206 (1990). https://doi.org/10.1007/BF00672931
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DOI: https://doi.org/10.1007/BF00672931