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Il Nuovo Cimento (1955-1965)

, Volume 18, Issue 3, pp 482–504 | Cite as

Cellular space-time and quantum field theory

Article

Summary

A simple cellular model of space-time is introduced which incorporates a fundamental length in a natural way. The usual concept of field quantities as functions of geometrical points is rejected in favour of the concept of field quantities as functionals of elementary cells. Consequently the usual field equations in the form of partial differential equations are replaced by corresponding partial difference equations. Subsequent quantization yields anS-matrix which is not vitiated by the presence of serious divergences. The basic space-time structure and theS-Matrix (which does not involve derivative coupling) are shown to be integral Lorentz covariant. The semi-convergence or asymptotic behaviour of theS-matrix series is established, and a meaningful Borel-sum of the « gross »S-matrix series is presented.

Riassunto

Si introduce un semplice modello cellulare dello spazio-tempo, comprendente in modo naturale una lunghezza fondamentale. Il concetto usuale delle quantità di campo come funzioni dei punti geometrici viene respinto a favore del concetto delle quantità di campo come funzionali delle celle elementari. Conseguentemente le usuali equazioni di campo sotto forma di equazioni differenziali parziali sono sostituite dalle corrispondenti equazioni alle differenze parziali. La successiva quantizzazione fornisce una matriceS che non è inficiata dalla presenza di divergenze notevoli. Si dimostra che la struttura fondamentale dello spazio-tempo e la matriceS (che non comporta accoppiamenti derivati) sono covarianti per trasformazioni « discrete » di Lorentz, si determina la semi-convergenza o il comportamento asintotico della serie della matriceS, e si presenta una significativa somma di Borel della « maggiorante » della serie della matriceS.

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Copyright information

© Società Italiana di Fisica 1960

Authors and Affiliations

  • A. Das
    • 1
  1. 1.Dublin Institute for Advanced StudiesDublin

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