Quantum Measurement of Space-Time Events

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Brody, D C and Hughston, L P. 2021. Quantum Measurement of Space-Time Events. Journal of Physics A: Mathematical and Theoretical, 54(23), 235304. ISSN 1751-8113 [Article]

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Official URL: https://iopscience.iop.org/article/10.1088/1751-81...

Abstract or Description

Abstract. The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space. As well as a complex structure and a symplectic structure, the future tube, seen as an eight-dimensional real manifold, is endowed with a natural positive- definite Riemannian metric that accommodates the underlying geometry of the indefinite Minkowski space metric, together with its symmetry group. A unitary representation of the 15-parameter group of conformal transformations can then be constructed that acts upon the Hilbert space of square-integrable holomorphic functions on the future tube. These structures are enough to allow one to put forward a quantum theory of phase-space events. In particular, a theory of quantum measurement can be formulated in a relativistic setting, based on the use of positive operator valued measures, for the detection of phase-space events, hence allowing one to assign probabilities to the outcomes of joint space-time and four- momentum measurements in a manifestly covariant framework. This leads to a localization theorem for phase-space events in relativistic quantum theory, determined by the associated Compton wavelength.

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Article

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https://doi.org/10.1088/1751-8121/abfac6