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Physics Letters A

A Lorentz covariant stochastic wave function dynamics for open systems

Heinz‐Peter Breuer, Francesco Petruccione

Published Jun 1, 1998• 7 citations
Publisher
DOI
10.1016/s0375-9601(98)00202-3

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We show that the Schr\"odinger equation can be derived assuming the Galilean covariance of a generic wave equation and the validity of the de Broglie's wave-particle duality hypothesis. We also obtain from this set of assumptions the transformation law for the wave function under a Galilean boost and prove that complex wave functions are unavoidable for a consistent description of a physical system. The extension to the relativistic domain of the above analysis is also provided. We show that Lorentz covariance and wave-particle duality are consistent with two different transformation laws for the wave function under a Lorentz boost. This leads to two different wave equations, namely, the Klein-Gordon equation and the Lorentz covariant Schr\"odinger equation.
Lorentz-covariant harmonic oscillator wave functions are constructed from the Lorentz-invariant oscillator differential equation of Feynman, Kislinger, and Ravndal for a two-body bound state. The wave functions are not invariant but covariant. As the differential equation contains the time-separation variable, the wave functions contain the same time-separation variable which does not exist in Schrödinger wave functions. This time-separation variable can be shown to belong to Feynman's rest of the universe, and can thus be eliminated from the density matrix. The covariant probability interpretation is given. This oscillator formalism explains Feynman's decoherence mechanism which is exhibited in Feynman's parton picture.