# Quantum

## Quantum Field Theory And Renormalization

Although the quantum theory began with the study of radiation, it took more than two decades before the electromagnetic field itself was quantized. The results obtained before 1928 used semiclassical approaches such as Bohr's correspondence principle. Dirac first made a fully quantum theory of electrons interacting with photons in 1927. Heisenberg, Pauli, and later Fermi, extended the theory, but although it produced valuable results not otherwise obtainable, it was found to be mathematically unsound at very high energy, and predicted infinite results for the obviously finite charge and mass of the electron. The problem was solved only in the late 1940s by the renormalization theories of the American theorists Richard Feynman, Julian Schwinger, Freeman Dyson, and the Japanese theorist Sin-itiro Tomonaga. Elementary particle physics in the twenty-first century is dominated by a so-called Standard Model, which is based entirely on the use of renormalized quantum fields.

*See also* **Physics**; **Relativity**; **Science**.

## BIBLIOGRAPHY

Bell, J. S. *Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy.* 2nd ed. Cambridge, U.K., and New York: Cambridge University Press, 1993. On hidden variables, the measurement problem, and so on.

Cassidy, David C. *Uncertainty: The Life and Science of Werner Heisenberg.* New York: W. H. Freeman, 1991.

Cushing, James T. *Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony.* Chicago: University of Chicago Press, 1994.

Feynman, Richard P., Robert P. Leighton, and Matthew Sands. *The Feynman Lectures on Physics.* Vol. 3. Reading, Mass.: Addison-Wesley, 1965.

Fine, Arthur. *The Shaky Game: Einstein, Realism, and the Quantum Theory.* Chicago: University of Chicago Press, 1986.

Heilbron, J. L. *The Dilemmas of an Upright Man, Max Planck as Spokesman for German Science.* Berkeley: University of California Press, 1986.

Jammer, Max. *The Conceptual Development of Quantum Mechanics.* New York: McGraw-Hill, 1966.

Kragh, Helge. *Dirac: A Scientific Biography.* Cambridge, U.K., and New York: Cambridge University Press, 1990.

——. *Quantum Generations, A History of Physics in the Twentieth Century,* Princeton, N.J.: Princeton University Press, 1999.

Kuhn, Thomas S. *Black-Body Theory and the Quantum Discontinuity, 1894–1912.* Oxford: Oxford University Press, 1978. Reprint. Chicago: University of Chicago Press, with a new afterword. Kuhn's view that Planck did not introduce a quantum discontinuity until 1911 is controversial.

Mehra, Jagdish, and Helmut Rechenberg. *The Historical Development of Quantum Theory.* 6 vols. New York: Springer-Verlag, 1982–2001. The most complete history available.

Moore, Walter. *Schrödinger: Life and Thought.* Cambridge, U.K., and New York: Cambridge University Press, 1989.

*Nobel Lectures in Physics.* Vol. 2: 1922–1941. New York: Elsevier, 1965.

Pais, Abraham. *Niels Bohr's Times: In Physics, Philosophy, and Polity.* Oxford: Clarendon 1991.

——. "*Subtle Is the Lord—": The Science and the Life of Albert Einstein,* Oxford, U.K., and New York: Oxford University Press, 1982.

Schweber, Silvan S. *QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga.* Princeton, N.J.: Princeton University Press, 1994.

van der Waerden, B. L., ed. *Sources of Quantum Mechanics.* Amsterdam: North-Holland Publishing, 1967. Reprint. New York: Dover Publications, 1968.

Wheaton, Bruce R. *The Tiger and the Shark: Empirical Roots of Wave-Particle Dualism.* Cambridge, U.K., and New York: Cambridge University Press, 1983.

*Laurie* *M.* *Brown*

## Additional topics

- Quantum - Bibliography
- Quantum - Relativistic Quantum Theory And Antimatter
- Other Free Encyclopedias

Science EncyclopediaScience & Philosophy: *Propagation* to *Quantum electrodynamics (QED)*Quantum - Planck's Paper Of 1900, Einstein's Light Quantum, Neils Bohr And The "old Quantum Theory"