# Quantum stress-energy tensors without action functional

Karl-Henning Rehren on June 23, 2018

talk-lqp.pdf

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

results.

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.