Feynman Rules and Factor Ordering in Derivative Coupling and Spin-One Theories

Abstract

Several methods may be employed to derive the Feynman rules for canonical theories. With emphasis on vector particle theories, we recast the theorem of Lee and Yang into functional integral and Hori operator formulations. For the class of Lagrangians considered, equivalent results are obtained. The canonical generating functional is used to relate T and T* products to the Hamiltonian and Lagrangian versions of theories with dependent fields. With the aid of Hori operators, we show that there is a wide class of ordering prescriptions compatible with the Lee-Yang theorem. Of these, the only familiar candidates are normal ordering and symmetrization of momenta and coordinates. It is argued that the latter is preferred, thus confirming a result of Suzuki and Hattori. Finally, the expanded Lee-Yang theorem for general ordering prescriptions is outlined, and ordering for a Yang-Mills theory is discussed.