Noether and Belinfante stress-energy tensors for theories with arbitrary Lagrangians of tensor fields

Understand

We investigate the connection between stress-energy tensor (SET) arising from Noether's theorem and Belinfante SET which can be obtained as a right-hand side of the Einstein's equation in the flat metric limit.

• This question is studied in the wide class of Poincar\`e-invariant field theories with actions which depend on the tensor fields of arbitrary rank and their derivatives of arbitrary order.
• For this class we derive the relation between these SET and present the exact expression for the difference between them.
• We also show that the difference between corresponding integrals of motion can be expressed as a surface integral over 2-dimensinal infinitely remote surface.