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Title of Journal: Nuov Cim B

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Abbravation: Il Nuovo Cimento B (1971-1996)

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Società Italiana di Fisica

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10.1002/pc.20693

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1826-9877

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Fourdimensional symmetry from a broad viewpoint

Authors: J P Hsu
Publish Date: 1985/08/01
Volume: 88, Issue: 2, Pages: 140-155
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Abstract

Within the fourdimensional framework of «common relativity» we can introduce a new principle of invariant and universal probability distribution independent of spin property for all quantized field oscillators to formulate finite and unitary field theories Here we consider the gluon field as an exceptional case and postulate that its field oscillators can be pictured as a system of bosons so that the distribution of the gluon oscillators takes the form of the Bose distribution We show thata the perturbative QCD is ultraviolet finiteb the perturbative static potential of quarks is asymptotically linear inr c the force between two quarks vanishes rapidly asr→0 The origin of the asymptotically linear potential due to gluons stems from a quasicondensation of the gluon oscillators which roughly resembles the Einstein condensation But quarks cannot be confined by the perturbative linear potential due to the spinone gluon because of the fourdimensional symmetry feature of the Dirac equation in sharp contrast with the Schrödinger equation However if the asymptotically linear potential between quarks is due to a massless spinzero field then quarks can be confined The fourdimensional framework of special relativity is too restrictive to allow these new concepts and resultsNell’ambito quadridimensionale della «relatività comune» si può introdurre un nuovo principio di distribuzione di probabilità invariante e universale indipendente dalla probabilità di spin per tutti gli oscillatori di campo quantizzati per formulare teorie di campo finite e unitarie Qui si considera il campo gluonico come un caso eccezionale e si ipotizza che i suoi oscillatori di campo possano essere descritti come un sistema di bosoni cosicché la distribuzione di oscillatori gluonici assume la forma della distribuzione di Bose Si mostra chea il QCD perturbativo è ultravioletto finitob il potenziale statico perturbativo dei quark è asintoticamente lineare inr c la forza tra i due quark si annulla rapidamente perr→0 L’origine del potenziale asintoticamente lineare causato dai gluoni deriva da una quasi condensazione degli oscillatori gluonici che somiglia grosso modo alla condensazione di Einstein Ma i quark non possono essere confinati dal potenziale lineare perturbativo a causa del gluone a spin 1 a causa del carattere di simmetria quadridimensionale dell’equazione di Dirac in forte contrasto con l’equazione di Schrödinger Comunque se il potenziale asintoticamente lineare tra quark è dovuto a un campo senza massa e spin 0 allora i quark possono essere confinati Il sistema quadridimensionale della relatività speciale è troppo restrittivo per permettere questi nuovi concetti e risultati


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