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Physical Review A

Relativistic theory for continuous measurement of quantum fields

Lajos Diósi

Published Nov 1, 1990• 81 citations
Publisher

Abstract

We have proposed a formal theory for the continuous measurement of relativistic quantum fields. We have also derived the corresponding scattering equations. The proposed formalism reduces to known equations in the Markovian case. Two recent models for spontaneous quantum state reduction have been recovered in the framework of our theory. A possible example of the relativistic continuous measurement has been outlined in standard quantum electrodynamics. The continuous measurement theory possesses an alternative formulation in terms of interacting quantum and stochastic fields.

DOI
10.1103/physreva.42.5086

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We have proposed a formal theory for the continuous measurement of relativistic quantum fields. We have also derived the corresponding scattering equations. The proposed formalism reduces to known equations in the Markovian case. Two recent models for spontaneous quantum state reduction have been recovered in the framework of our theory. A possible example of the relativistic continuous measurement has been outlined in standard quantum electrodynamics. The continuous measurement theory possesses an alternative formulation in terms of interacting quantum and stochastic fields.
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In order to address the measurement problem of quantum theory we make the assumption that quantum state reduction should be regarded as a genuine physical process deserving of a dynamical description. Generalizing the nonrelativistic spontaneous localization models of Ghirardi, Rimini, Weber, and Pearle, a relativistic state reduction mechanism is proposed. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a mediating field to facilitate smearing of quantum field interactions.
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We have considered the dynamics of simple measuring devices coupled to quantized relativistic Heisenberg fields. We have defined localized observables and derived covariant equations for the joint probability distribution of the measured outcomes. The proposed formalism is based on standard field-theoretical terms. We have shown that our formalism yields the expected anticoincidence when two devices detect two wave packets of a single electron. Applications in the measurement theory of vacuum fluctuations have been suggested.