Self-consistent derivation of multiple mass values in renormalized field theories View Full Text


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Article Info

DATE

1971-05

AUTHORS

E. R. Caianiello, M. Marinaro, G. Scarpetta

ABSTRACT

It is shown that the study of self-consistent renormalized models of thegϕ4 theory, obtained by truncating it without destroying renormalizability, yields a nonlinear equation for the physical massmf. Already in the lowest possible approximation one finds two possible and mutually exclusive values formf, The method is quite general, not limited to thegϕ4 theory and seems well suited to a rigorous computation of mass spectra from field theories. A remarkable consequence of the multivaluedness ofmf is that, although the field equations stay invariant under arbitrary renormalization prescriptions, their solutionsdo not: renormalization parameters lose their indeterminacy and must be fixed from experiment. Si mostra che lo studio di modelli rinormalizzati autocoerenti della teoriagϕ4, ottenuti troncando la teoria sensa distruggere la rinormalizzabilità, dà un’equazione non lineare per la massa fisicamf, Già all’approssimazione più bassa possibile troviamo permf due possibili valori che si escludono a vicenda. I1 metodo è del tutto generale, non limitato alla teoriagϕ4 e sembra adatto per un calcolo rigoroso degli spettri di massa dalle teorie di campo. Una conseguenza notevole della molteplicità dei valori dimf è che, sebbene le equazioni di campo siano invarianti per arbitrari e prescrizioni di rinormalizzazione, le loro so;uzioni non lo siano: i parametri di rinormalizzazione perdono la loro indeterminatezza e debbono essere fissati dagli esperimenti. Показывается, что исследование само-согасованных перенормиро-ванных моделей теорииgφ4, полученной в результате обРезания, но без уничто-жения перенорнируемости, приводит к нелинейному уравнению для физической массыmf. Уже в низшем возможном приближении получ аются две в⊸зможных и взаимно исключающихся величины дляmf. Этот метод является довольно общим, а ие ограничивается теориейgφ4. По-видимому, этот ⇐етод очень удобен для строгого вычисления спектров масс из других теорий. Важным следствием мио-лозначностиmf является тот факт, что, хотя уравнения поля оказываытся инвариант-ными относительно произвольиых процедур перенорми ровок, но их решения не-инвариантны: т.е. параметры перенормировки теряют свою неопределенность и должны быть риксированы из экзперимента. More... »

PAGES

195-219

References to SciGraph publications

  • 1970-06. On the renormalizable approximations in field theory in IL NUOVO CIMENTO B (1965-1970)
  • 1971-02. On analytic regularization in quantum field theory in IL NUOVO CIMENTO A (1965-1970)
  • 1969-04. Form-invariant renormalization in IL NUOVO CIMENTO A (1965-1970)
  • 1969-04. A class of finite-part integration rules for quantum field theory defined by a method of analytic continuation in IL NUOVO CIMENTO A (1965-1970)
  • Journal

    TITLE

    Il Nuovo Cimento A (1971-1996)

    ISSUE

    1

    VOLUME

    3

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf02912617

    DOI

    http://dx.doi.org/10.1007/bf02912617

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1001320486


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