Summary
A field theory for spinless, noninteracting tachyons is developed. The result is a « fast » theory in which the roles of the first and fourth components of the space-time four-vector and of the four-momentum are interchanged with respect to the corresponding « slow » theory. Then we develop formally the interactions between bradyons and tachyons. Coherently with the results of a previous paper, the propagator constructed with a slow and a fast field represents a spurion. In this way we produce the tadpoles dynamically, without supposing a nonzero vacuum expectation value of the fields, slow or fast. Furthermore in order to explain the break-down of the « slow » symmetries some massless particles must be hypothesized.
Riassunto
Si sviluppa una teoria del campo tachionico libero senza spin. Il risultato è una teoria « veloce » nella quale i ruoli della prima e della quarta componente del quadrivettore spazio-tempo e del quadriimpulso sono interscambiati rispetto alla corrispondente teoria « lenta ». Quindi si sviluppa il formalismo per le interazioni tra bradioni e tachioni. Coerentemente coi risultati di un precedente lavoro, il propagatore costruito con un campo lento e un campo veloce rappresenta uno spurione. In questo modo si producono dinamicamente i tadpole senza supporre valori di aspettazione non nulli sul vuoto dei campi, lenti o veloci. Inoltre per spiegare la rottura delle simmetrie « lente » alcune particelle a massa nulla devono essere ipotizzate.
Реэуме
Раэвивается теория поля для невэаимодеиствууших тахионов с нуле-вым спином. Полученныи реэулятат представляет « быструу » теориу, в которои роли первои и четвертои компонент пространственно-врем енного четырехвектора и четырехимпуляса меняутся местами по отнощениу к соответствуушеи «медлен-нои » теории. Затем мы формаляно раэвиваем вэаимодеиствия мезду брадионами и тахионами. В соответствии с реэулятатами предыдушеи статяи, пропагатор, сконструированныи с медленным и быстрым полем, представляет щпурион. Таким обраэом мы динамически обраэуем «головастики », не предполагая ненулевое эначение вакуумного озидания для полеи, медленного или быстрого. Кроме того, чтобы общяснитя нарущение «медленных» симметрии, необходимо предполозитя суше-ствование некоторых частиц с нулевои массои.
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References
The number of papers about tachyons is very large and it is impossible to list all of them in any reasonable way. Those papers which have some connection with our results are quoted in ref. (2)See and in the following.
SeeR. Goldoni:Nuovo Cimento,14 A, 501 (1973).
SeeJ. Goldstone:Nuovo Cimento,19, 154 (1961);J. Goldstone, A. Salam andS. Weinberg:Phys. Rev.,127, 965 (1962).
SeeM. E. Arons andE. C. G. Sudarshan:Phys. Rev.,173, 1622 (1968).
For the definition and the meaning of the classesC x ,C y andC z , see ref. (2)See, Subsect. 3.3.
For the definition and the meaning ofd t x , see ref. (2)See, Subsect. 3.1 and 3.3.
This is imposed by the principle of relativity (see ref. (2), Subsect. 3.3). The groupG t x is defined as the set of transformation matricesX such thatX T d t x X=d t x .
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The most important results of this paper and of Part I are published inLett. Nuovo Cimento,5, 495 (1972).
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Goldoni, R. Faster-than-light inertial frames and tadpoles. Nuov Cim A 14, 527–547 (1973). https://doi.org/10.1007/BF02756273
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DOI: https://doi.org/10.1007/BF02756273