Ontology And Univocity Of Being, Being Is The Ultimate Form For All Of The Forms, Consciousness Is But An Emergent Faculty, Sense Is Found In Subjectivity, Event Is Multiplicity Rather Than Process, Yang-Mills Theory And Pp-Waves And Other Letters Of Cong

K.N.P. Kumar, C.J. Prabhakara, S.K. Narasimha Murthy, B.J. Gireesha


Abstract: Healey considers three possible types of ontology for classical gauge fields (first for electromagnetism in Chapter 2, and then for general Yang-Mills theories in Chapter 4): • "The no gauge potential properties view": the ontology is given by the field strength (which Healey non-standardly calls the gauge field) and not by the gauge potential. • "The localized gauge potential properties view": the gauge potential makes up the ontology, or some other (yet to be determined) quantities that are associated to arbitrarily small neighbourhoods in space-time and that can be derived locally from the gauge potential.• "The non-localized gauge potential properties view": the quantities that make up the ontology can be derived from the gauge potential, but are not necessarily associated to arbitrarily small neighbourhoods in space-time. Healey presents two arguments against the first view. First, this view implies action at a distance. This follows from the Aharonov-Bohm effect, where a magnetic field confined to a localized spatial region still has an effect on the interference pattern of a quantum particle that passes outside that region. Second, in the case of non-Abelian Yang-Mills theories, there exist gauge inequivalent gauge potentials that give rise to the same field strength in a simply connected region. So the field strength at that region would not completely capture the gauge invariant content associated to that region.


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