Bundle Theoretic Descriptions of Massive Single-Particle State Spaces;
With a view toward Relativistic Quantum Information Theory
- URL: http://arxiv.org/abs/2201.04324v2
- Date: Mon, 18 Sep 2023 04:00:59 GMT
- Title: Bundle Theoretic Descriptions of Massive Single-Particle State Spaces;
With a view toward Relativistic Quantum Information Theory
- Authors: Heon Lee
- Abstract summary: We suggest bundle theoretic descriptions of massive single-particle state spaces, which are basic building blocks of Relativistic Quantum Information Theory.
A link between the usual Hilbert space description is provided by a generalized induced representation construction on the $L2$-section space of the bundle.
Some of the theoretical implications of the formalism will be explored at the end of the paper.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Relativistic Quantum Information Theory (RQI) is a flourishing research area
of physics, yet, there has been no systematic mathematical treatment of the
field. In this paper, we suggest bundle theoretic descriptions of massive
single-particle state spaces, which are basic building blocks of RQI. In the
language of bundle theory, one can construct a vector bundle over the set of
all possible motion states of a massive particle, in whose fibers the moving
particle's internal quantum state as perceived by a fixed inertial observer is
encoded. A link between the usual Hilbert space description is provided by a
generalized induced representation construction on the $L^2$-section space of
the bundle. The aim of this paper is two-fold. One is to communicate the basic
ideas of RQI to mathematicians and the other is to suggest an improved
formalism for single-particle state spaces that encompasses all known massive
particles including those which have never been dealt with in the RQI
literature. Some of the theoretical implications of the formalism will be
explored at the end of the paper.
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