Speaker
Description
We explore the interplay among noncommutativity, noncanonicality, and observability
in quantum mechanics based on an extended Heisenberg algebra. Using the Bopp
shift technique, we develop a unified framework in which noncommutative and
noncanonical effects are systematically incorporated into quantum operators. The
resulting framework leads to modified Schrödinger, Klein–Gordon, Dirac, and Pauli
equations and provides a systematic description of their observable consequences. We
introduce an energy-dependent parameterization scheme to explore possible
connections between noncommutative quantum effects and several fundamental
problems, including dark energy and quantum decoherence. We also show that the
extended algebra can generate anomalous velocity and acceleration for free particles,
offering a possible quantum-mechanical perspective on the accelerated expansion of
the Universe. Furthermore, noncommutativity gives rise to novel quantum
fluctuations and generalized uncertainty relations beyond the standard Heisenberg
form. Our results indicate that noncommutativity and noncanonicality may have
genuine observable consequences, suggesting new connections between extended
quantum mechanics and cosmology.
| Topic | Noncommutativity, Quantum Mechanics |
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