NON-UNITARY AND UNITARY TRANSITIONS IN GENERALIZED QUANTUM MECHANICS, NEW SMALL PARAMETER AND INFORMATION PROBLEM SOLVING

2003/11/25 by Alexander Shalyt-Margolin, A. E. Shalyt-Margolin · 2 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #hep-th

paper · pdf · doi:10.1142/s0217732304013155

published as Mod.Phys.Lett. A19 (2004) 391 · 18 pages

arxiv created 2003/11/25 · openalex publication_date 2004/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quantum Mechanics of the Early Universe is considered as deformation of a well-known Quantum Mechanics. Similar to previous works of the author, the principal approach is based on deformation of the density matrix with concurrent development of the wave function deformation in the respective Schrödinger picture, the associated deformation parameter being interpreted as a new small parameter. It is demonstrated that the existence of black holes in the suggested approach in the end twice causes non-unitary transitions resulting in the unitarity. In parallel this problem is considered in other terms: entropy density, Heisenberg algebra deformation terms, respective deformations of Statistical Mechanics — all showing the identity of the basic results. From this an explicit solution for Hawking's information paradox has been derived.

Citations

• Quantum Mechanics of the Early Universe and its Limiting Transition
• Generalized uncertainty relations in a quantum theory and thermodynamics from the uniform point of view
• The Generalized Uncertainty Principle and Black Hole Remnants
• Non-Unitary and Unitary Transitions in Generalized Quantum Mechanics and Information Problem Solving
• Density matrix and dynamical aspects of Quantum Mechanics with Fundamental Length
• The black hole information paradox
• Generalized Uncertainty Relations,Fundamental Length and Density Matrix
• Deformed density matrix, Density of entropy and Information problem
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle

Cited by

• Minimal Length, Measurability and Gravity
• The Quantum and Statistical Theory of Early Universe and Its Possible Applications to Cosmology