Employing induced representations of the Lorentz group (Wigner’s little group construction), formalism for constructing heavy particle effective Lagrangians is developed, and Lagrangian constraints enforcing Lorentz invariance of the $S$ matrix are derived. The relationship between Lorentz invariance and reparametrization invariance is established and it is shown why a standard ansatz for implementing reparametrization invariance in heavy fermion effective Lagrangians breaks down at order $1/M^4$. Formalism for fields of arbitrary spin and for self-conjugate fields is presented, and the extension to effective theories of massless fields is discussed.

• Received 26 August 2012

DOI:https://doi.org/10.1103/PhysRevD.86.094020