Most physicists are very satisfied with this situation («successful» renormalization). They argue that, if one has rules for doing calculations and the results agree with observation, that is all that one requires. But it is not all that one requires. One requires a single comprehensive theory applying to all physical phenomena. Not one theory for dealing with nonrelativistic effects and a separate disjoint theory for dealing with certain relativistic effects. Furthermore, the theory has to be based on sound mathematics.... The renormalization idea would be sensible only if it was applied with finite renormalization factors, not infinite ones.P.A.M. Dirac Mathematical Foundations of Quantum Theory
Summary
We propose a finite and unitary quantum «elecweakdynamics» with the «SU 2×U 1 structure» which may not have the full gauge symmetry. The Higgs scalar fields are not necessary. Gaugeboson massesM W andM Z can be generated by kinematical symmetry-breaking due to the coupling of vacuum fields and gauge fields. It is a local interaction theory formulated on the basis of i) a new principle of universal probability distributionP(p, m) for field oscillators of all fields and ii) the new four-dimensional symmetry framework of «common relativity». We do not employ the four-dimensional framework of special relativity because it is too restrictive to allow the universal probability principle. This principle introduces a radical lengthR into physics and changes drastically the high-energy behaviour of propagators. It makes the theory finite without upsetting unitarity. We show how scattering cross-sections, static electric potential and particle decay in flight are affected by the universal probability principle. These modifications can be tested experimentally.
Riassunto
Si propone una «dinamica elettrodebole» finita e unitaria con strutturaSU 2×U 1 che può non avere simmetria di gauge completa. Si tratta di una teoria di campo locale formulata sulla base di i) un nuovo principio di distribuzione di probabilità universaleP(p, m) per oscillatori di campo di tutti i campi e ii) di un nuovo sistema a simmetria quadridimensionale della «relatività comune». Non si usa il sistema quadridinemsionale della relatività speciale perchè è troppo restrittivo per permettere il principio di probabilità universale. Questo principio introduce una lunghezza radicaleR in fisica e cambia drasticamente il comportamento dei propagatori ad alta energia. Ciò rende la teoria finita senza sconvolgere l'unitarietà. Si mostra come le sezioni d'urto di scattering, il potenziale elettrico statico e il decadimento della particella in volo siano influenzati dal principio di probabilità universale. Queste modifiche possono essere controllate sperimentalmente.
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References
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Moreover, the present formalism (especially the basic relations (9), (10), (2) and (3)) are in harmony with Dirac's viewpoints that the assumption of microcausality in field theories is very likely too stringent and that a less drastic assumption may be adequate,e.g., that there is a fundamental lengthR such that the commutator of two dynamical variables must vanish if they are localized at two points whose separation is spacelike and greater thanR but need not vanish if it is less thanR. SeeP. A. M. Dirac:Rev. Mod. Phys.,21, 392 (1949).
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Supported in part by Southeastern Massachusetts University (permanent address).
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Hsu, J.P. Four-dimensional symmetry from a broad viewpoint.. Nuov Cim B 89, 30–46 (1985). https://doi.org/10.1007/BF02728502
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DOI: https://doi.org/10.1007/BF02728502