## Abstract

Quantum field theory (QFT) was developed during the late 1920s to describe the interaction of charged particles with the electromagnetic field. During the 1930s the formalism was extended by Fermi to model *β*-decay phenomena and by Yukawa to explain nuclear forces. All these field theories have one feature in common: the interaction between the fields takes place at a single point in space-time. Such local quantum field theories seem to be the most efficient way to obtain a synthesis of quantum mechanics and special relativity consistent with the principle of causality. However, local quantum field theories are flawed: their perturbative solutions are divergent, the infinities that are encountered being a consequence of the locality of the interaction. Stimulated by important experimental advances after World War II (the measurement of the Lamb shift and of the hyperfine structure of hydrogen), renormalization theory was formulated to circumvent the divergence difficulties encountered in higher order calculations in quantum electrodynamics (QED). In this approach QED is defined by a limiting procedure. A cutoff is introduced into the theory so that the physics at momenta higher than some momentum—or equivalently the physics at distances shorter than some cut-off length—is altered and all calculated quantities thereby rendered finite but cut-off dependent. The parameters of the cut-off theory are then expressed in terms of physically measurable quantities (such as the mass and charge of the particles which are described by the theory).

### Keywords

Microwave Helium Deuterium Sorb Metaphor## Preview

Unable to display preview. Download preview PDF.

### References

- Appelquist, T. and J. Carazzone (1975), “Infrared singularities and massive fields,”
*Phys. Rev. D***11**, pp. 2856–2861.ADSCrossRefGoogle Scholar - Born, M., W. Heisenberg, and P. Jordan (1926), “Zur quantemmechnik. II,”
*Z. Phys.***35**, pp. 557–615.ADSCrossRefGoogle Scholar - Bromberg, Joan (1976), “The concept of particle creation before and after quantum mechanics,”
*Hist. Stud. Phys. Sci.***7**, pp. 161–191.Google Scholar - Bromberg, Joan (1977), “Dirac’s quantum electrodynamics and the wave particle equivalence,” in
*History of Twentieth Century Physics. Proc. Int. School of Physics*, “Enrico Fermi” Course LVII, C. Weiner, ed., New York: Academic.Google Scholar - Brown, L. M. (1981), “Yukawa’s prediction of the meson,”
*Centaurus***25**, pp. 71– 132.MathSciNetADSCrossRefGoogle Scholar - Brown, L. M. (1985), “How Yukawa arrived at the meson theory,”
*Progr. Theor. Phys.***85**, pp. 13–19.CrossRefGoogle Scholar - Cao, T. Y. (1991), “The Reggeization program 1962–1982: Attempts at reconciling quantum field theory with S-matrix theory,”
*Arch. Hist. Exact Sci.***41**, 239–283.MathSciNetMATHGoogle Scholar - Cassidy, D. C., “Cosmic ray showers, high-energy physics, and quantum field theories,”
*Hist. Stud. Phys. Sci.***12**, pp. 1–39.Google Scholar - Coleman, S. and E. Weinberg (1973), “Radiative corrections as the origin of symmetry breaking,”
*Phys. Rev. D***7**, pp. 1888–1910.ADSCrossRefGoogle Scholar - Coleman, S. (1986),
*Secret Symmetry*, Cambridge: Cambridge University Press.Google Scholar - Cushing, J. (1982), “Models and methodologies in current theoretical high-energy physics,”
*Synthèse***50**, pp. 5–101.MathSciNetCrossRefGoogle Scholar - Cushing, J. T. (1990),
*Theory Construction and Selection in Modern Physics: The S-Matrix Theory*, Cambridge: Cambridge University Press.MATHGoogle Scholar - Darrigol, O. (1988), “The quantum electrodynamical analogy in early nuclear theory or the roots of Yukawa’s theory,”
*Rev. Hist. Sci.***41**, pp. 226–297.Google Scholar - Dirac, P. A. M. (1927a), “The quantum theory of the emission and absorption of radiation,”
*Proc. R. Soc. London Ser. A***114**, pp. 243–265.ADSMATHCrossRefGoogle Scholar - Dirac, P. A. M. (1927b), “The quantum theory of dispersion,”
*Proc. R. Soc. London Ser. A***114**, pp. 710–728.ADSMATHCrossRefGoogle Scholar - Dirac, P. A. M. (1929), “Quantum mechanics of many-electron systems,”
*Proc. R. Soc. London Ser. A***126**, pp. 714–723.ADSGoogle Scholar - Dirac, P. A. M. (1930a), “A theory of electrons and protons,”
*Proc. R. Soc. London Ser. A***126**, pp. 360–365.ADSMATHCrossRefGoogle Scholar - Dirac, P. A. M. (1930b),
*Quantum Mechanics*, 1st ed., ( Oxford: Oxford University Press).MATHGoogle Scholar - Dresden, M. (1985), “Reflections on ‘Fundamentally and Complexity’,” in
*Physical Reality and Mathematical Description*, C. P. Enz and J. Mehra, eds., Dordrecht: Reidel, pp. 133–166.Google Scholar - Dyson, F. J. (1949a), “The radiation theories of Tomonaga, Schwinger, and Feynman,”
*Phys. Rev.***75**, pp. 486–502.MathSciNetADSMATHCrossRefGoogle Scholar - Dyson, F. J. (1949b), “The
*S*matrix in quantum electrodynamics,”*Phys. Rev.***75**, pp. 1736–1755.MathSciNetADSMATHCrossRefGoogle Scholar - Dyson, F. J. (1951), “The renormalization method in quantum electrodynamics,”
*Proc. R. Soc. London Ser. A***207**, pp. 395–401.MathSciNetADSMATHCrossRefGoogle Scholar - Dyson, F. J. (1952), “Divergence of perturbation theory in quantum electrodynamics,”
*Phys. Rev.***85**, pp. 631–632.MathSciNetADSMATHCrossRefGoogle Scholar - Einstein, A. (1949), “Autobiographical notes,” in
*Albert Einstein: Philosopher— Scientist*, P. A. Schilpp, ed., Evanston: The Library of Living Philosophers.Google Scholar - Fermi, E. (1934), “Versuch einer theorie der
*β*-strahlen. I,” Z.*Phys*.**88**, pp. 161–171.MATHCrossRefGoogle Scholar - Feynman, R. P. (1966), The development of the space-time view of quantum mechanics. Nobel lecture,
*Science***1966**, pp. 699–708.ADSCrossRefGoogle Scholar - Feynman, R. P. (1948b), “A relativistic cutoff for classical electrodynamics,”
*Phys. Rev.***74**, pp. 939–946.MathSciNetADSMATHCrossRefGoogle Scholar - Feynman, R. P. (1948c), “Relativistic cutoff for quantum electrodynamics,”
*Phys. Rev.***74**, pp. 1430–1438.MathSciNetADSMATHCrossRefGoogle Scholar - Feynman, R. P. (1949a), “The theory of positrons,”
*Phys. Rev*.**76**, pp. 749– 768.MathSciNetADSMATHCrossRefGoogle Scholar - Feynman, R. P. (1949b), “The space-time approach to quantum electrodynamics,”
*Phys. Rev.***76**, pp. 769–789.MathSciNetADSMATHCrossRefGoogle Scholar - Feynman, R. P. (1966), “The development of the space-time view of quantum mechanics. Nobel lecture,”
*Science***1966**, pp. 699–708.ADSCrossRefGoogle Scholar - Galison, P. (1983), “The discovery of the muon and the failed revolution against quantum electrodynamics,”
*Centaurus***26**, pp. 262–316.MathSciNetADSCrossRefGoogle Scholar - Gell-Mann, M. and F. Low (1954), “Quantum electrodynamics at small distances,”
*Phys. Rev.***95**, pp. 1300–1312.MathSciNetADSMATHCrossRefGoogle Scholar - Gell-Mann, M. (1985), “From renormalizability to calculability?” in
*Shelter Island II*, R. Jackiw, N. N. Khuri, S. Weinberg, and E. Witten, eds., Cambridge, MA: MIT Press.Google Scholar - Georgi, H. (1989), “Effective quantum field theories,” in
*The New Physics*, Paul Davies, ed., Cambridge: Cambridge University Press, pp. 4446–4457.Google Scholar - Gross, D. (1985a), “Beyond quantum field theory,” in
*Recent Developments in Quantum Field Theory*, J. Ambjorn, B. J. Durhuus, and J. L. Petersen, eds., New York: Elsevier.Google Scholar - Gross, D. (1985b), “On the uniqueness of physical theories,” in
*A Passion for Physics*, C. DeTar, J. Finkelstein, and Chugi. Tan, eds., Singapore: World Scientific.Google Scholar - Kinoshita, Toichiro (1990),
*Quantum Electrodynamics*, Singapore: World Scientific.MATHGoogle Scholar - Lamb, W. E. Jr. and R. C. Retherford (1947), “Fine structure of the hydrogen atom by a microwave method,”
*Phys. Rev.***72**, pp. 241–243.ADSCrossRefGoogle Scholar - Lepage, G. Peter (1989), “What is renormalization?” preprint, CLNS, 89/970. Newman Laboratory of Nuclear Studies, Cornell University.Google Scholar
- Lewis, H. W. (1948), “On the reactive terms in quantum electrodynamics,”
*Phys. Rev*., pp. 173–176.ADSCrossRefGoogle Scholar**13** - Nafe, J. E., E. B. Nelson, and I.I. Rabi (1947), “The hyperfine structure of atomic hydrogen and deuterium,”
*Phys. Rev.***71**, pp. 914–915.ADSCrossRefGoogle Scholar - Ovrut, B. and H. Schnitzer (1981a), “The decoupling theorem and minimal subtractions,”
*Phys. Lett. B***100/5**, pp. 403–406.ADSCrossRefGoogle Scholar - Ovrut, B. (1981b), “Effective field theories and higher dimension operators,”
*Phys. Rev. D***24**, pp. 1695–1698.ADSCrossRefGoogle Scholar - Pais, A. (1986),
*Inward Bound*, New York: Oxford University Press.Google Scholar - Polchinski, P. (1984), “Renormalization and effective Lagrangian,”
*Nucl. Phys. B***231**, pp. 269–295.ADSCrossRefGoogle Scholar - Schweber, S. S. (1986a), “Shelter Island, Pocono, and Oldstone: The emergence of American quantum electrodynamics after World War II,”
*Osiris*(Second Series)**2**, pp. 265–302.MathSciNetCrossRefGoogle Scholar - Schweber, S. S. (1986b), “Feynman and the visualization of space-time processes,”
*Rev. Mod. Phys.***58**, pp. 449–508.MathSciNetADSCrossRefGoogle Scholar - Schwinger, J. (1948a), “On quantum electrodynamics and the magnetic moment of the electron,”
*Phys. Rev.***73**, pp. 416–417.MathSciNetADSMATHCrossRefGoogle Scholar - Schwinger, J. (1948b), “Quantum electrodynamics. I. A covariant formulation,”
*Phys. Rev.***74**, pp. 1439–1461.MathSciNetADSMATHCrossRefGoogle Scholar - Schwinger, J. (1951), “On the Green’s functions of quantized field. I,”
*Proc. Natl. Acad. Sei. U.S.A.***37**, pp. 452–459.MathSciNetADSCrossRefGoogle Scholar - Schwinger, J. (1973), “A report on quantum electrodynamics,” in
*The Physicist’s Conception of Nature*, ( J. Mehra, ed., Reidel, Dordrecht ), pp. 413–429.Google Scholar - Schwinger, J. (1983), “Renormalization theory of quantum electrodynamics: An individual view,” in
*The Birth of Particle Physics*, L. M. Brown and L. Hoddeson, eds., Cambridge: Cambridge University Press, pp. 329–353.Google Scholar - Stückelberg, E. C. G. and A. Peterman (1953), “La normalisation des constantes dans la theorie des quanta,”
*Helv. Phys. Acta***26**, pp. 499–520.MathSciNetMATHGoogle Scholar - Symanzik, K. (1970), “Small distance behavior in field theory and power counting,”
*Commun. Math. Phys.***18**, pp. 227–246.MathSciNetADSMATHCrossRefGoogle Scholar - Tomonaga, S. (1946), “On a relativistically invariant formulation of the quantum theory of wave fields,”
*Progr. Theor. Phys.***1**, pp. 27–42.MathSciNetADSMATHCrossRefGoogle Scholar - Tomonaga, S. (1965), “Development of quantum electrodynamics,” in
*Nobel Lectures (Physics) : 1963–1970*, Amsterdam: Elsevier, pp. 126–136.Google Scholar - Weinberg, S. (1960), “High energy behavior in quantum field theory,”
*Phys. Rev*.**118, pp**. 838–849.MathSciNetADSMATHCrossRefGoogle Scholar - Weinberg, S. (1967), “A model of leptons,”
*Phys. Rev. Lett.***19**, pp. 1264–1266.ADSCrossRefGoogle Scholar - Weinberg, S. (1977), “The search for unity: Notes for a history of quantum field theory,”
*Deadalus*, Fall 1977, Vol. II of*Discoveries and Interpretations in Contemporary Scholarship*.Google Scholar - Weinberg, S. (1979), “Phenomenological Lagrangian,”
*Physica A***96**, pp. 327– 340.ADSCrossRefGoogle Scholar - Weinberg, S. (1980a), “Conceptual foundations of the unified theory of weak and electromagnetic interactions,”
*Rev. Mod. Phys.***52**, pp. 515–524.MathSciNetADSCrossRefGoogle Scholar - Weinberg, S. (1980b), “Effective gauge theories,”
*Phys. Lett. B***91**, pp. 51–55.ADSCrossRefGoogle Scholar - Weinberg, Steven (1983), “Why the renormalization group is a good thing,” in
*Asymptotic Realms of Physics: Essays in Honor of Francis E. Low*, A. H. Guth, K. Huang, and R. L. Jaffe, eds., Cambridge, MA: MIT Press.Google Scholar - Weinberg, Steven (1985a), “The ultimate structure of matter,” in
*A Passion for Physics: Essays in Honor of Geoffrey Chew*, C. DeTar, J. Finkelstein, and C. I. Tan, eds., Singapore: World Scientific.Google Scholar - Weinberg, Steven (1985b), “Calculation of fine structure constants,” in
*Shelter Island II*, Cambridge, MA: MIT Press.Google Scholar - Weinberg, Steven (1986a), “Particle physics: Past and future,”
*Int. J. Mod. Phys. A***1/1**pp. 135–145.MathSciNetADSCrossRefGoogle Scholar - Weinberg, Steven (1986b), “Towards the final laws of physics,” in
*Elementary Particles and the Laws of Physics. The 1986 Dirac Memorial Lectures*, Cambridge: Cambridge University Press.Google Scholar - Weinberg, Steven (1987), Steven (1987), “Newtonianism, reductionism and the art of congressional testimony,” Talk at the Tercentenary Celebration of Newton’s
*Principia*. University of Cambridge, 30 June 1987.Google Scholar - Wentzel, G. (1943),
*Einführung in der Quantentheorie der Wellenfelder*, Wein: Franz Deuticke.MATHGoogle Scholar - Wilson, K. G. (1965), “Model Hamiltonians for local quantum field theory,”
*Phys. Rev. B***140**, pp. 445–457.ADSCrossRefGoogle Scholar - Wilson, K. G. (1969), “Non-Lagrangian models of current algebra,”
*Phys. Rev.***179**, pp. 1499–1512.MathSciNetADSCrossRefGoogle Scholar - Wilson, K. G. (1970a), “Operator-product expansions and anomalous dimensions in the Thirring model,”
*Phys. Rev. D***2**, pp. 1473–1477.ADSCrossRefGoogle Scholar - Wilson, K. G. (1970b), “Anomalous dimensions and the breakdown of scale invariance in perturbation theory,”
*Phys. Rev. D***2**, pp. 1478–1493.ADSCrossRefGoogle Scholar - Wilson, K. G. and J. Kogut (1974), “The renormalization group and the ε expansion,”
*Phys. Rep. C***12**, p. 131.CrossRefGoogle Scholar - Wilson, K. G. (1975), “The renormalization group: Critical phenomena and the Kondo problem,”
*Rev. Mod. Phys.***47**, pp. 773–840.ADSCrossRefGoogle Scholar - Wilson, K. B. (1979), “Problems in physics with many scales of length,”
*Sci. Am.***241**, pp. 158–179.CrossRefGoogle Scholar - Wilson, K. G. (1983), “The renormalization group and critical phenomena,”
*Rev. Mod. Phys*.**55**, pp. 583–600.ADSCrossRefGoogle Scholar