Il Nuovo Cimento (1955-1965)

, Volume 17, Issue 3, pp 375–383 | Cite as

Quantum electrodynamics in an expanding universe

  • F. L. Scarf


The equations of quantum electrodynamics are investigated in an expanding universe characterized by a de Sitter metric. It is assumed that the expansion occurs on a microscopic level and that ħ, the bare electron mass and the bare charge are all constant. For a particular coordinate system the operators may be expressed in terms of coupled flat-space fields which havem replaced bymR(t). The equivalent quantized field problem is soluble using standard perturbation theory with modified commutators and Green’s functions. As a first approxmation, adiabatic changes caused by the expansion are evaluated by imaking the replacementm→mR in all final formulae. Renormalization effects are examined using asymptotic expressions which contain ultraviolet cut-offs. Assuming that the cutoff procedures are meaningful and are related to the structure of the physical electron, it is noted that the renormalized mass and charge could vary with time for a particular kind of cut-off process.


Si esaminano le equazioni dell’elettrodinamica quantistica in un universo in espansione caratterizzato da una metrica di de Sitter. Si suppone che l’espansione avvenga a livello microscopico e che ħ, la massa nuda dell’elettrone e la carica nuda siano tutte costanti. Per un particolare sistema di coordinate gli operatori possono essere espressi in termini di campi accoppiati dello spazio piano che hannom sostituito damR(t). Il problema equivalente del campo quantizzato si risolve usando la teoria standard della perturbazione con commutatori e funzioni di Green modificati. In prima approssimazione i cambiamenti adiabatici prodotti dall’espansione vengono valutati facendo la sostituzionem→mR in tutte le formule finali. Gli effetti di rinormalizzazione vengono esaminati usando espressioni asintotiche che contengono tagli ultravioletti. Supponendo che i procedimenti di taglio siano significativi e siano in rapporto alla struttura dell’elettrone fisico, si nota che la massa e la carica rinormalizzate possono variare col tempo per un tipo particolare di procedimenti di taglio.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. (2).
    H. Bondi:Cosmology (Cambridge, 1952), chap. 9;W. H. McCrea:Rep. Progr. Phys.,16, 331 (1953).Google Scholar
  2. (3).
    D. R. Brill andJ. A. Wheeler:Rev. Mod. Phys.,29, 465 (1957).MathSciNetADSCrossRefMATHGoogle Scholar
  3. (4).
    Schrödinger has mapped the source-free electromagneticfield strengths into flat space quantities for conformally flat spaces (E. Schrödinger:Proc. Irish Acad.,46, 25 (1940); see alsoM. von Laue:Helv. Phys. Acta, Suppl.,4, 42 (1956)).MATHGoogle Scholar
  4. (5).
    Gutzwiller has examined these equations in terms of a potentialĀ defined by (M. Gutzwiller:Helv. Phys. Acta,29, 313 (1956)). HisĀ isnot related to ourA by any simple equation such as Furthermore, in this work the condition was used so that the final equation forĀ involves in an explicit and complex manner.MathSciNetMATHGoogle Scholar
  5. (6).
    W. Thirring:Principles of Ouantum Electrodynamics (New York, 1958), p. 177.Google Scholar
  6. (7).
    For many forms ofR(t) the out-state has unusual properties in at least one of the two frames. A discussion of this point shall appear in theProceedings of the Royaumont Conference on Gravitation (C.N.R.S., Paris, 1960).Google Scholar
  7. (8).
    L. D. Landau:Niels Bohs and the Development of Physics (New York, 1955), pp. 52–69. A somewhat different form forZ is given in this reference.Google Scholar

Copyright information

© Società Italiana di Fisica 1960

Authors and Affiliations

  • F. L. Scarf
    • 1
  1. 1.University of WashingtonSeattle

Personalised recommendations