Summary
The relation of conformal symmetry to the existence of zero energy-momentum (improved) solutions is investigated in four-dimensional space for a class of Lagrangian models. It is pointed out that in Minkowski space such solutions are either constant (or trivial) or the theory is conformally invariant. In Euclidean space such solutions may be constructed if solutions to the conformally invariant theories are known.
Riassunto
Si discute la connessione fra simmetria conforme e l’esistenza, per una classe di modelli Lagrangiani, di soluzioni per cui il tensore «migliorato» energia-impulso sia nullo. Si nota che, nel caso dello spazio di Minkowski a quattro dimensioni, tali soluzioni sono costanti (o banali) oppure il modello è conformemente invariante. Nello spazio Euclideo tali soluzioni possono essere costruite una volta note le soluzioni dei modelli conformemente invarianti.
Реэюме
Исследуется свяэь конформной симметрии с сушествованием рещений с нулевым эначением знергии-импульса в четырехмерном пространстве для класса моделей с Лагранжианами. Отмечается, что в пространстве Минко-вского такие рещения либо являются постоянными (или тривиальными), либо теория является конформно инвариантной. В звклидовом пространстве такие рещения могут быть сконструированы, если иэвестны рещения в конформно инвариантных теориях.
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References
S. Fubini:Nuovo Cimento,34 A, 521 (1976).
A. A. Belavin, A. M. Polyakov, A. S. Schwartz andYu. S. Tyuphin:Phys. Lett.,59 B, 85 (1975).
R. Jackiw andC. Rebbi:Phys. Rev. D,14, 517 (1976).
V. de Alfaro, S. Fubini andG. Furlan:A new classical solution of the Yang-Mills field equations, Ref. TH 2232-CERN.
R. Jackiw andC. Rebbi:Phys. Rev. Lett.,37, 172 (1976).
C. Callan, R. Dashen andD. Gross:Phys. Lett.,63 B, 334 (1976).
R. Jackiw:Semi-classical analysis of quantum field theory, inLectures at XVI Escuela Latino Americana, 1976, Caracas, Venezuela.
This is the same requirement as that for finite-energy solutions. For such solutions,Φ tends asymptotically to a null point of the potential. (See,e.g., ref. (8)).
S. Coleman:Classical lumps and their quantum descendants, inLectures at the 1975 School «Ettore Majorana», Erice, Italy.
An analogous solution to an Abelian Yang-Mills theory was discussed byFurlan in context with Fubini’s program (9).
G. Furlan: private communication.
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Girardello, L., Pallua, S. Pseudoparticles and conformal symmetry. Nuov Cim A 41, 377–387 (1977). https://doi.org/10.1007/BF02730114
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DOI: https://doi.org/10.1007/BF02730114