Quadratic Lagrangians are obtained by adding surface terms involving the angular momentum to a free particle Lagrangian. Killing–Yano tensors corresponding to the manifold structure induced by the quadratic Lagrangians were calculated and the associated non-generic symmetries were presented.

This paper develops a generalized formulation of Lagrangian mechanics on fibered manifolds, together with a reduction theory for symmetries corresponding to Lie groupoid actions. As special cases, this theory includes not only Lagrangian reduction (including reduction by stages) for Lie group actions, but also classical Routh reduction, which we show is naturally posed in this fibered setting. ...

In earlier publications we have analyzed the strong and radiative decays of heavy hadrons in a formalism which incorporates both heavy-quark and chiral symmetries. In particular, we have derived a heavy-hadron chiral Lagrangian whose coupling constants are related by the heavy-quark flavor-spin symmetry arising from the QCD Lagrangian with infinitely massive quarks. In this paper, we reexamine ...

A system with anholonomic constraints where the trajectories of physical degrees of freedom are autoparallels on a manifold equipped with a general Cartan connection is discussed. A variational principle for the autoparallel trajectories is derived from the d’Alambert-Lagrange principle for anholonomic constrained systems. A geometrical (coordinate-independent) formulation of the variational pr...

In position space the interaction terms of soft-collinear effective theory must be multipole-expanded to obtain interaction terms with homogeneous scaling behaviour. In this note we provide a manifestly gauge-invariant formulation of the theory after this expansion in the presence of non-abelian gauge fields, extending our previous result. We give the effective Lagrangian (including the Yang-Mi...

We consider the low energy limit of three dimensional Quantum Chromodynamics with an even number of flavors. We show that Parity is not spontaneously broken, but the global (flavor) symmetry is spontaneously broken. The low energy effective lagrangian is a nonlinear sigma model on the Grassmannian. Some Chern–Simons terms are necessary in the lagrangian to realize the discrete symmetries correc...

We compute the fully differential rate for the Higgs-boson decay h → Z + −, with Z → ′+ −. For these processes we assume the most general matrix elements within an effective Lagrangian framework. The electroweak chiral Lagrangian we employ assumes minimal particle content and Standard Model gauge symmetries, but it is otherwise completely general. We discuss how information on new physics in th...