Quantum stress-energy tensors without action functional

42nd LQP Workshop "Foundations and Constructive Aspects of QFT"
Karl-Henning Rehren on June 23, 2018

The stress-energy tensor describes (among other) the coupling of matter
to gravity.

Classical stress-energy tensors are usually derived by variations of the
action. While already for Maxwell, the canonical formula gives an
asymmetric and non-gauge invariant result, the Hilbert prescription (by
variation of the metric) gives the correct symmetric and gauge-invariant
stress-energy tensor.

For higher spins, the problems become more severe because the action has
to take care of manifold constraints. In the quantum case, additional
problems of indefinite metric arise on top, which lead to famous no-go

I present an alternative approach that allows to construct higher-spin
stress-energy tensors intrinsically via the Wigner representation,
without reference to an action functional. The method also applies to
infinite-spin representations.