326 research outputs found
Background Independent Quantum Mechanics, Metric of Quantum States, and Gravity: A Comprehensive Perspective
This paper presents a comprehensive perspective of the metric of quantum
states with a focus on the background independent metric structures. We also
explore the possibilities of geometrical formulations of quantum mechanics
beyond the quantum state space and Kahler manifold. The metric of quantum
states in the classical configuration space with the pseudo-Riemannian
signature and its possible applications are explored. On contrary to the common
perception that a metric for quantum state can yield a natural metric in the
configuration space with the limit when Planck constant vanishes, we obtain the
metric of quantum states in the configuration space without imposing this
limiting condition. Here, Planck constant is absorbed in the quantity like Bohr
radii. While exploring the metric structure associated with Hydrogen like atom,
we witness another interesting finding that the invariant lengths appear in the
multiple of Bohr radii.Comment: 25 Pages;journal reference added:Published in- Int. J. Theor. Phys.
46 (2007) 3216-3229. References revise
Toward a Background Independent Quantum Theory of Gravity
Any canonical quantum theory can be understood to arise from the
compatibility of the statistical geometry of distinguishable observations with
the canonical Poisson structure of Hamiltonian dynamics. This geometric
perspective offers a novel, background independent non-perturbative formulation
of quantum gravity. We invoke a quantum version of the equivalence principle,
which requires both the statistical and symplectic geometries of canonical
quantum theory to be fully dynamical quantities. Our approach sheds new light
on such basic issues of quantum gravity as the nature of observables, the
problem of time, and the physics of the vacuum. In particular, the observed
numerical smallness of the cosmological constant can be rationalized in this
approach.Comment: Awarded Honorable Mention, 2004 Gravity Research Foundation Essay
Competition; 8 pages, LaTe
Spin and Rotations in Galois Field Quantum Mechanics
We discuss the properties of Galois Field Quantum Mechanics constructed on a
vector space over the finite Galois field GF(q). In particular, we look at
2-level systems analogous to spin, and discuss how SO(3) rotations could be
embodied in such a system. We also consider two-particle `spin' correlations
and show that the Clauser-Horne-Shimony-Holt (CHSH) inequality is nonetheless
not violated in this model.Comment: 21 pages, 11 pdf figures, LaTeX. Uses iopart.cls. Revised
introduction. Additional reference
Transient Astrophysical Pulses and Quantum Gravity
Searches for transient astrophysical pulses could open an exciting new window
into the fundamental physics of quantum gravity. In particular, an evaporating
primordial black hole in the presence of an extra dimension can produce a
detectable transient pulse. Observations of such a phenomenon can in principle
explore the electroweak energy scale, indicating that astrophysical probes of
quantum gravity can successfully complement the exciting new physics expected
to be discovered in the near future at the Large Hadron Collider.Comment: 7 pages, This essay received an honorable mention in the Gravity
Research Foundation Essay Competition, 200
- …