TY - JOUR
AU - Kuzmichev, V. E.
AU - Kuzmichev, V. V.
PY - 2019/02/21
Y2 - 2024/05/30
TI - Generalized Uncertainty Principle in Quantum Cosmology for the Maximally Symmetric Space
JF - Ukrainian Journal of Physics
JA - Ukr. J. Phys.
VL - 64
IS - 2
SE - Fields and elementary particles
DO - 10.15407/ujpe64.2.100
UR - https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2018586
SP - 100
AB - <p>The new uncertainty relation is derived in the context of the canonical quantum theory with gravity in the case of the maximally symmetric space. This relation establishes a connection between fluctuations of the quantities, which determine the intrinsic and extrinsic curvatures of the spacelike hypersurface in spacetime and introduces the uncertainty principle for quantum gravitational systems. The generalized time-energy uncertainty relation taking gravity into account gravity is proposed. It is shown that known Unruhâ€™s uncertainty relation follows, as a particular case, from the new uncertainty relation. As an example, the sizes of fluctuations of the scale factor and its conjugate momentum are calculated within an exactly solvable model. All known modifications of the uncertainty principle deduced previously from different approaches in the theory of gravity and the string theory are obtained as particular cases of the proposed general expression.</p>
ER -