Ward identities for transport of classical waves in disordered media

H. T. Nieh, Liu Chen, Ping Sheng
1998 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Using field-theoretic formalism, we derive Ward identities for the diffusive transport of classical waves in disordered media of a quite general nature. We consider three cases: the scalar wave, the elastic wave, and the electromagnetic wave. For classical waves, it is the energy conservation that underlies the Ward identities, in contrast to the case of electronic systems, for which the Ward identity is a mathematical statement of charge conservation. For the three cases of classical waves,
more » ... classical waves, the Ward identities are of the same general structure, which differs from the electronic Ward identity and reflects the fact that energy transport, instead of charge transport, is accounted for in classical wave systems. The general structure of the Ward identities is seen to be independent of the details of the wave equations. ͓S1063-651X͑97͒06611-7͔ PACS number͑s͒: 03.40. Kf, 41.20.Jb, 62.30.ϩd, 03.70.ϩk LAGRANGIANS FOR CLASSICAL WAVES The starting point of most works on classical waves are based on the wave equations. However, the formalism of Lagrangian field theory provides a more systematic framework for the consideration of many formal aspects of the classical wave systems. The quantum version of this formalism, namely, quantum field theory, is known to have been successfully applied to fundamental theories, such as the *Permanent address: Center for Advanced Study, Tsinghua University,
doi:10.1103/physreve.57.1145 fatcat:hupjpc3kvne7teqrpc4glujfau