Il Nuovo Cimento A (1965-1970)

, Volume 52, Issue 1, pp 173–191 | Cite as

Consequences of an unreasonable mass spectrum on a relativistic field theory

  • D. Korff
  • Z. Fried


The effects of an unreasonable mass spectrum on a relativistically invariant field theory are examined. It is found that a field operator which transforms according to a representation of the homogeneous Lorentz group cannot be given an unreasonable-mass-spectrum particle interpretation without violating Lorentz invariance. Conversely, it is found that the existence of an unreasonable mass spectrum for a field operator precludes it from transforming according to a representation of the homogeneous Lorentz group. However, a relativisticallyinvariant theory is still possible. That is, a field theory may be constructed which maintains its form under a general Lorentz transformation. For the case of a discrete contribution to the unreasonable mass spectrum, the standard field-theoretical formulation is obtained as the square of the mass is allowed to approach zero from below.


Matrix Element Lorentz Transformation Free Field Real Mass Commutation Rule 
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Следствия нецелесообразного спектра масс в релятивистской теории поля


Исследуются эффекты нецелесообразного спектра масс в релятивистско инвариантной теории поля. Получается, что оператор поля, который преобразуется в соответствии с представлением однородной группы Лорентца не может быть найден из рассмотрения нецелесообразного спектра масс частиц, без нарушения Лорентц-инвариантности. И наоборот, найдено, что существование нецелесообразного спектра масс для оператора поля мешает ему преобразовываться в соответствии с представлением однородной группы Лорентца. Однако, релятивистски инвариатная теория все же является возможной. Т.е. может быть сконструирована теория поля, которая сохраняет свою форму при общем преобразовании Лорентца. Для случая дискретного вклада в нецелесообразный спектр масс, получается стандартная теоретическая формулировка, когда квадрат массы имеет возможность стремиться к нулю снизу.


Si esaminano gli effetti di uno spettro di massa incongruo su una teoria dei campi relativisticamente invariante. Si trova che ad un operatore di campo che si trasforma secondo una rappresentazione del gruppo di Lorentz omogeneo non si può dare un’interpretazione di particella con spettro di massa incongruo senza violare l’invarianza di Lorentz. Per converso si trova che l’esistenza di uno spettro di massa incongruo per un operatore di campo gli impedisce di trasformarsi secondo una rappresentazione del gruppo di Lorentz omogeneo. Tuttavia è ancora possibile una teoria relativisticamenteinvariante. Cioè si può costruire una teoria dei campi che mantiene la sua forma a seguito di una trasformazione di Lorentz generale. Nel caso di un contributo discreto allo spettro di massa incongruo, si ottiene la consueta formulazione della teoria dei campi quando si fa tendere il quadrato della massa a zero dal basso.


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Copyright information

© Società Italiana di Fisica 1967

Authors and Affiliations

  • D. Korff
    • 1
  • Z. Fried
    • 1
  1. 1.Lowell Technological InstituteLowellUSA

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