Heavy-particle formalism with Foldy-Wouthuysen representation

Understand

Utilizing the Foldy-Wouthuysen representation, we use a bottom-up approach to construct heavy-baryon Lagrangian terms, without employing a relativistic Lagrangian as the starting point.

• The couplings obtained this way feature a straightforward $1/m$ expansion, which ensures Lorentz invariance order by order in effective field theories.
• We illustrate possible applications with two examples in the context of chiral effective field theory: the pion-nucleon coupling, which reproduces the results in the literature, and the pion-nucleon-delta coupling, which does not employ the Rarita-Schwinger field for describing the delta isobar, and hence does not invoke any spurious degrees of freedom.
• In particular, we point out that one of the subleading $\pi N \Delta$ couplings used in the literature is, in fact, redundant, and discuss the implications of this.