Yang-Mills fields

Molecular Yang-Mills Fields A. A Nuclear Lagrangean... 

Yang-Mills field is conditioned by the finiteness of the basic Bom-Oppenheimer set. Detailed topics are noted in the introductory Section I. 

XIII. Curl Condition Revisited Introduction of the Yang-Mills Field... 

Like the curl condition is reminiscent of the Yang-Mills field, the quantization just mentioned is reminiscent of a study by Wu and Yang [76] for the quantization of Dirac s magnetic monopole [77-78]. As will be shown, the present quantization conditions just like the Wu and Yang conditions result from a phase factor, namely, the exponential of a phase and not just from a phase. 

The expression in Eq. (137) is reminiscent of the Yang-Mills field, however, it is important to emphasize that the Yang-Mills field was introduced for a different physical situation [58,59]. In fact, what Eq. (137) implies is that for molecular systems the Yang-Mills field is zero if the following two conditions are fulfilled ... 

In what follows, we assume that indeed the group of states foiin an isolated sub-Hilbert space, and therefore have a Yang-Mills field that is zero or not will depend on whether or not the vaiious elements of the t matiix are singular. 

In Section XIII, we made a connection between the curl condition that was found to exist for Bom-Oppenheimer-Huang systems and the Yang-Mills field. Through this connection we found that the non-adiabatic coupling terms can be considered as vector potentials that have their source in pseudomagnetic... 

In Chapter IV, Englman and Yahalom summarize studies of the last 15 years related to the Yang-Mills (YM) field that represents the interaction between a set of nuclear states in a molecular system as have been discussed in a series of articles and reviews by theoretical chemists and particle physicists. They then take as their starting point the theorem that when the electronic set is complete so that the Yang-Mills field intensity tensor vanishes and the field is a pure gauge, and extend it to obtain some new results. These studies throw light on the nature of the Yang-Mills fields in the molecular and other contexts, and on the interplay between diabatic and adiabatic representations. 

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