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** Yang-Mills fields molecular systems **

** Yang-Mills fields non-adiabatic coupling **

Yang-Mills field is conditioned by the finiteness of the basic Bom-Oppenheimer set. Detailed topics are noted in the introductory Section I. [Pg.169]

XIII. Curl Condition Revisited Introduction of the Yang-Mills Field [Pg.635]

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. [Pg.638]

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 [Pg.688]

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. [Pg.688]

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 [Pg.713]

Antisymmetric matrix, non-adiabadc coupling, vector potential, Yang-Mills field, 94-95 Aromaticity, phase-change rule, chemical reaction, 446-453 pericyclic reactions, 447-450 pi-bond reactions, 452-453 sigma bond reactions, 452 Aromatic transition state (ATS), phase-change rule, permutational mechanism, 451-453 [Pg.776]

Yang-Mills fields, pure vi. tensorial gauge [Pg.781]

Entangled states, molecular systems, Yang-Mills fields, 261 [Pg.784]

Gauge fields, molecular systems, Yang-Mills fields, pure w. tensorial gauge fields, 250-253 [Pg.786]

Gauge theories, Yang-Mills field, 204-205 Gauge transformation [Pg.786]

Yang-Mills fields, 249 -250, 255- 257 Lagrangian multiplier, conical intersection location, 488-489, 565 Laguerre polynomials, Renner-Teller effect, triatomic molecules, 589-598 Lanczos reduction [Pg.791]

D + H2 reaction, 164-167 Lie groups, molecular systems, Yang-Mills fields [Pg.792]

Sub-sub-Hilbert space, non-adiabatic coupling construction, 69-70 topological spin, 70-73 Sufficiency criterion, molecular systems, Yang-Mills fields, tensorial field vanishing, 257-259 [Pg.807]

Yang-Mills field, 203-205 Vibrational state analysis [Pg.811]

** Yang-Mills fields molecular systems **

** Yang-Mills fields non-adiabatic coupling **

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