Trace anomaly and invariance under transformation of units

Abstract

Paying attention to conformal invariance as the invariance under local transformations of units of measure, we take a conformal invariant quantum field as a quantum matter theory in which one has the freedom to choose the values of units of mass, length and time arbitrarily at each point. To be able to have this view, it is necessary that the background on which the quantum field is based be conformal invariant as well. Consequently, defining the unambiguous expectation value of the energy-momentum tensor of such a quantum field through the Wald renormalizing prescription necessitates breaking down the conformal symmetry of the background. Then, noticing the field equations suitable for describing the back-reaction effect, we show that the existence of trace anomaly, known for indicating the brokenness of conformal symmetry in quantum field theory, can also indicate the above gravitational conformal symmetry brokenness