Quantum Measurement of Space-Time Events
- URL: http://arxiv.org/abs/2011.11541v3
- Date: Thu, 1 Apr 2021 07:28:57 GMT
- Title: Quantum Measurement of Space-Time Events
- Authors: Dorje C. Brody, Lane P. Hughston
- Abstract summary: The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space.
The structures are enough to allow one to put forward a quantum theory of phase-space events.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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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