2014/01/31 by Jeremy Adelman, Franz Hinterleitner, Seth Major
Physics and Astronomy · #Black Holes and Theoretical Physics #Constraint (computer-aided design) #Gravitation #Hamiltonian (control theory) #Hamiltonian constraint #Hilbert space #Kinematics #Minkowski space #Noncommutative and Quantum Gravity Theories #Operator (biology) #Pulsars and Gravitational Waves Research #Regularization (linguistics) #gr-qc
paper · pdf · doi:10.1088/0264-9381/32/5/055009
published in Classical and Quantum Gravity 32(5), 055009 (IOP Publishing) · 43 pages
openalex publication_date 2015/02/10 · arxiv created 2016/04/28 · arxiv updated 2016/04/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In a (1+1)-dimensional midi-superspace model for gravitational plane waves, a flat space–time condition is imposed with constraints derived from null Killing vectors. Solutions to a straightforward regularization of these constraints have diverging length and volume expectation values. Physically acceptable solutions in the kinematic Hilbert space are obtained from the original constraint by multiplying with a power of the volume operator and by a similar modification of the Hamiltonian constraint, which is used in a regularization of the constraints. The solutions of the modified Killing constraint have finite expectation values of geometric quantities. Further, the expectation value of the original Killing constraint vanishes, but its moment is non-vanishing. As the power of the volume grows, the moment of the original constraint grows, while the moments of volume and length both decrease. Thus, these states provide possible kinematic states for flat space, with fluctuations. As a consequence of the regularization of operators, the quantum uncertainty relations between geometric quantities such as length and its conjugate momentum do not reflect naive expectations from the classical Poisson bracket relations.