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Loop quantum gravity - Wikipedia LQG is formally background independent, meaning the equations of LQG are not embedded in, or dependent on, space and time (except for its invariant topology) Instead, they are expected to give rise to space and time at distances which are 10 times the Planck length
Introduction to loop quantum gravity - Imperial College London Loop quantum gravity is an attempt to formulate a quantum theory of general rel-ativity The quantisation is performed in a mathematically rigorous, non-perturbative and background independent manner and standard matter couplings are considered
Lecture notes on LQR LQG controller design - staff. uz. zgora. pl Notation 2: Equation (1 7) To make sure that J0 is a feedback invariant, we ask that Pbe chosen so that is called an Algebraic Riccati Equation (ARE) A 0P+PA+Q (PB+N)R 1(B0P+N) = 0: (1 7) In this case, we conclude from (1 6) that the optimal control is given by u(t) = u0(t) = R 1(B0P+N0)x(t); 8t 0; which results in the following closed-loop
Lecture 20: Linear Dynamics and LQG - University of Washington Equation (3) is known as the system state equation Going back to our example, the states of the helicopter dynamics can therefore be chosen as the position h and the velocity vbecause the motion of the helicopter can be completely described in terms of these two
LQG inspired spacetimes as solutions of the Einstein equations - arXiv. org Although LQG does not yet constitute a complete quantum theory of spacetime, particularly near classical singularities,itsapplicationshavebeenpredominantlyconcentratedinsemiclassicalregimes Substantialprogresshas beenmadeinmodelingsingularityresolutionandbuildingeffectivequantum-correctedgeometries[69–74],including
1 LQG Problem Formulation - Laurent Lessard we go back to the stochastic system with noise, and consider Linear–Quadratic–Gaussian (LQG) control Wewanttofindtheoptimalcontrolpolicyforastochasticsystemwheretheobservation
Loop Quantum Gravity - SpringerLink Because of the technical and conceptual difficulties with the Hamiltonian constraint equation, proponents of LQG have sought alternative ways of understanding the dynamics of LQG
Path Integral Formulation of LQG, Semiclassical Limit, • The path integral formulation is rigorously derived from the canonical LQG (in reduced phase space) • The path integral computes the LQG amplitude between boundary states • The path integral is manifestly finite, and manifestly unitary
LQG, Strings and all that - homes. psd. uchicago. edu 1 The use of the set of canonical variables involving a complex connection leads to a simplification of the Hamiltonian constraint With the use of a real connection, the constraint loses its simple polynomial form Initially this was considered as a serious obstacle for quantization