Advantages and Drawbacks Of Effective Theory

The energy momentum tensor for the vacuum field which represents gravity is non-covariant, since the effective gravitational field obeys hydrodynamic equations rather than Einstein equations. However, even for the fully covariant dynamics of gravity, in Einstein theory the corresponding quantity ‘the energy momentum tensor for the gravitational field’ cannot be presented in the covariant form. This is the famous problem of the energy momentum tensor in general relativity. One must sacrifice either covariance of the theory or the true conservation law. From the condensed matter point of view,...

The energy momentum tensor for the vacuum field which represents gravity is non-covariant, since the effective gravitational field obeys hydrodynamic equations rather than Einstein equations. However, even for the fully covariant dynamics of gravity, in Einstein theory the corresponding quantity ‘the energy momentum tensor for the gravitational field’ cannot be presented in the covariant form. This is the famous problem of the energy momentum tensor in general relativity. One must sacrifice either covariance of the theory or the true conservation law. From the condensed matter point of view, the inconsistency between the covariance and the conservation law for the energy and momentum is an aspect of the much larger problem of the non-locality of effective theories. This chapter discusses the advantages and drawbacks of effective theory, non-locality in effective theory, true conservation and covariant conservation, covariance versus conservation, paradoxes of effective theory, Novikov–Wess–Zumino action for ferromagnets as an example of non-locality, effective versus microscopic theory, whether quantum gravity exists, what effective theory can and cannot do, and universality classes of effective theories of superfluidity.