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APS » Journals » Phys. Rev. Lett. » Volume 53 » Issue 5
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Phys. Rev. Lett. 53, 419–422 (1984)

Relativistic Extension of the Analogy between Quantum Mechanics and Brownian Motion

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B. Gaveau
Institut de Mathematiques, Université de Paris VI, Paris, France

T. Jacobson
Physics Department, University of Texas, Austin, Texas 78712

M. Kac
Mathematics Department, University of Southern California, Los Angeles, California 90089

L. S. Schulman
Physics Department, Technion, Haifa, Israel

Received 5 March 1984; published in the issue dated 30 July 1984

Schrödinger's equation and the heat equation are connected to one another by analytic continuation, as are the Feynman integral and the Wiener integral. We extend this form of correspondence to the relativistic domain by identifying Poisson processes whose real version gives rise to the telegrapher's equation and which when analytically continued produce the Dirac equation.

© 1984 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.53.419
DOI:
10.1103/PhysRevLett.53.419
PACS:
03.65.Ca, 02.30.+g, 05.40.+j, 11.10.Qr
 
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