Skip to main content
SpringerLink
Log in

Commutators near the light-cone

II: Scaling functions and their analytic continuation to the annihilation region

Коммутаторы вблиэи светового конуса

II: Масщтабные функции и их аналитическое продолжение в аннигиляционную область

  • Published:
Il Nuovo Cimento A (1971-1996)

Summary

A concrete dynamical model is studied to obtain information on scaling and related problems. The role ofO 4 expansion is pointed out, and the relation of scaling to small-distance behaviour of interactions is made evident. Problems connected with gauge invariance are analysed. The Schwinger-term sum rule forF L(ω) is discussed in the presence of Regge subtractions. The problem of analytic continuation of scaling functions into the annihilation channel is examined in a simple approximation.

Riassunto

Si studia un modello dinamico concreto per ottenere dei risultati sul comportamento di scala e problemi connessi. Si mette in luce il ruolo di uno sviluppoO 4 e si mette in evidenza la relazione tra il comportamento di scala e il tipo di interazione a piccole distanze. Si analizzano problemi connessi con la invarianza di gauge. Si discute la regola di somma del termine di Schwinger perF L(ω) in presenza di sottrazioni di Regge. Si esamina in una semplice approssimazione il problema della continuazione analitica delle funzioni di scala nel canale di annichilazione.

Реэюме

Исследуется конкретная динамическая модель, чтобы получить информацию о подобии и смежных проблемах. Отмечается роль расщиренияO 4 и свяэь подобия с поведением вэаимодействий на малых расстояниях делается очевидной. Аналиэируются проблемы, свяэанные с калибровочной инвариантностью. Обсуждается правило сумм дляF L(gw) при наличии вычитаний Редже. В простом приближении исследуется проблема аналитического продолжения масщтабных функций в аннигиляционный канал.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Gatto andP. Menotti:Nuovo Cimento,2 A, 881 (1971), hereafter referred to as I.

    Article  ADS  MathSciNet  Google Scholar 

  2. J. D. Bjorken:Phys. Rev.,179, 1547 (1969).

    Article  ADS  Google Scholar 

  3. R. Jackiw, R. P. Van Royen andG. B. West:Phys. Rev. D,2, 2473 (1970);H. Leutwyler andJ. Stern:Nucl. Phys.,20 B, 77 (1970).

    Article  ADS  Google Scholar 

  4. J. D. Bjorken:Phys. Rev.,148, 1467 (1966);K. Johnson andF. Low:Progr. Theor. Phys.,37–38, 74 (1966).

    Article  ADS  Google Scholar 

  5. See,e.g.,G. Altarelli andH. R. Rubinstein:Phys. Rev.,187, 2111 (1969);T. K. Gaisser andJ. C. Polkinghorne:Nuovo Cimento,1 A, 501 (1971);S. J. Chang andP. M. Fishbane:Phys. Rev. D,2, 1084 (1970).

    Article  ADS  Google Scholar 

  6. G. K. Wilson:Phys. Rev.,179, 1499 (1969);R. Brandt andG. Preparata:Nucl. Phys.,27 B, 541 (1971);Y. Frishman:Phys. Rev. Lett.,25, 966 (1970).

    Article  ADS  MathSciNet  Google Scholar 

  7. H. Fritsch andM. Gell-Mann: to be published;J. M. Cornwall andR. Jackiw:Phys. Rev. D,4, 367 (1971);D. A. Dicus, R. Jackiw andV. L. Teplitz: MIT preprint CTP 207 (1971).

  8. J. D. Bjorken andE. A. Paschos:Phys. Rev.,185, 1975 (1969);P. V. Landshoff, J. C. Polkinghorne andR. D. Short:Nucl. Phys.,28 B, 225 (1971).

    Article  ADS  Google Scholar 

  9. S. D. Drell, D. J. Levy andT. M. Yan:Phys. Rev.,187, 2159 (1969);J. Pestieau andP. Roy:Phys. Lett.,30 B, 483 (1969).

    Article  ADS  Google Scholar 

  10. H. Leutwyler andJ. Stern:Nucl. Phys.,20 B, 77 (1970).

    Article  ADS  MathSciNet  Google Scholar 

  11. An analogous subtraction is performed byJ. M. Cornwall, D. Corrigan andE. R. Norton:Phys. Rev. D,3, 536 (1971).

    Article  ADS  Google Scholar 

  12. A. Zee:Phys. Rev. D,3, 2432 (1971).

    Article  ADS  MathSciNet  Google Scholar 

  13. For alternative ways for evaluating the scaling function for the box diagram see:S. D. Drell andT. M. Yan: SLAC-PUB 808 (1970).

  14. F. Zachariasen:Phys. Rev.,121, 1851 (1961);M. Gell-Mann andF. Zachariasen:Phys. Rev.,124, 953 (1961);W. Thirring:Nuovo Cimento,23, 1064 (1962);Theoretical Physics (Vienna, 1963), p. 451.

    Article  ADS  MathSciNet  Google Scholar 

  15. S. Ferrara, R. Gatto andA. Grillo: to appear inNucl. Phys.

Download references

Author information

Authors and Affiliations

  1. Istituto di Fisica dell’Università, Padova, Italy

    R. Gatto

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Italy

    R. Gatto & P. Menotti

  3. Scuola Normale Superiore, Pisa, Italy

    P. Menotti

Authors
  1. R. Gatto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Menotti
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gatto, R., Menotti, P. Commutators near the light-cone. Nuov Cim A 7, 118–143 (1972). https://doi.org/10.1007/BF02728682

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02728682

Search

Navigation