Definitions

Dirac

Dirac

[dih-rak]
Dirac, Paul Adrien Maurice, 1902-84, English physicist. He was educated at the Univ. of Bristol and St. John's College, Cambridge, and became professor of mathematics at Cambridge in 1932. In 1928, Dirac published a version of quantum mechanics that took into account the theory of relativity (see quantum theory). One consequence of his theory was the prediction of negative energy states for the electron, implying the existence of an antiparticle to the electron; this antiparticle, the positron, was discovered in 1932 by C. D. Anderson. Dirac's equation for the motion of a particle is a relativistic modification of the Schrödinger wave equation, the basic equation of quantum mechanics. For their work Dirac and Erwin Schrödinger shared the 1933 Nobel Prize in Physics. Dirac also received the Copley Medal of the Royal Society in 1952 for this and other contributions to the quantum theory, including his formulation (with Enrico Fermi) of the Fermi-Dirac statistics and his work on the quantum theory of electromagnetic radiation. He wrote The Principles of Quantum Mechanics (1930, 4th ed. 1958).

See biographies by H. Kragh (1990) and G. Farmelo (2009).

(born Aug. 8, 1902, Bristol, Gloucestershire, Eng.—died Oct. 20, 1984, Tallahassee, Fla., U.S.) English mathematician and theoretical physicist. His first major contribution (1925–26) was a general and logically simple form of quantum mechanics. About the same time, he developed ideas of Enrico Fermi, which led to the Fermi-Dirac statistics. He then applied Albert Einstein's special theory of relativity to the quantum mechanics of the electron and showed that the electron must have spin of 12. Dirac's theory also revealed new states later identified with the positron. He shared the 1933 Nobel Prize for Physics with Erwin Schrödinger. In 1932 Dirac was appointed Lucasian Professor of Mathematics at the University of Cambridge, a chair once occupied by Isaac Newton. Dirac retired from Cambridge in 1969 and held a professorship at Florida State University from 1971 until his death.

Learn more about Dirac, P(aul) A(drien) M(aurice) with a free trial on Britannica.com.

In quantum mechanics, one of two possible ways (the other being Bose-Einstein statistics) in which a system of indistinguishable particles can be distributed among a set of energy states. Each available discrete state can be occupied by only one particle. This exclusiveness accounts for the structure of atoms, in which electrons remain in separate states rather than collapsing into a common state. It also accounts for some aspects of electrical conductivity. This theory of statistical behaviour was developed first by Enrico Fermi and then by P.A.M. Dirac (1926–27). The statistics apply only to particles such as electrons that have half-integer values of spin; the particles are called fermions.

Learn more about Fermi-Dirac statistics with a free trial on Britannica.com.

(born Aug. 8, 1902, Bristol, Gloucestershire, Eng.—died Oct. 20, 1984, Tallahassee, Fla., U.S.) English mathematician and theoretical physicist. His first major contribution (1925–26) was a general and logically simple form of quantum mechanics. About the same time, he developed ideas of Enrico Fermi, which led to the Fermi-Dirac statistics. He then applied Albert Einstein's special theory of relativity to the quantum mechanics of the electron and showed that the electron must have spin of 12. Dirac's theory also revealed new states later identified with the positron. He shared the 1933 Nobel Prize for Physics with Erwin Schrödinger. In 1932 Dirac was appointed Lucasian Professor of Mathematics at the University of Cambridge, a chair once occupied by Isaac Newton. Dirac retired from Cambridge in 1969 and held a professorship at Florida State University from 1971 until his death.

Learn more about Dirac, P(aul) A(drien) M(aurice) with a free trial on Britannica.com.

In graph theory, there are two theorems that are commonly referred to as Dirac's theorem, both named after the mathematician Gabriel Andrew Dirac:

  1. Let G be a k-connected graph. Then for any set of k vertices in G, there exists a cycle in G that passes through all k vertices.
  2. Let G be a graph on n ≥ 3 vertices. If each vertex has degree at least n/2 then G is hamiltonian.

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