Dark Energy, Background Independent Quantum Mechanics and the Origin of Cosmological Constant

We explore the extended framework of the generalized quantum mechanics and discuss various aspects of neighborhood in the construction of space in search of origin of cosmological constant. We propose to expand definition of the volume of the phase space in eight dimensions with an overall constraint in the form of uncertainty relation as: $(\Delta p_{x}\Delta p_{y}\Delta p_{z}\Delta E)(\Delta x\Delta y\Delta z\Delta t)\sim h^{4}$. We argue that the phase space volume in the eight dimensions is an appropriate representation that it should be, and the relation $(\Delta \Lambda)(\Delta V)\sim h$ again brings it down to the reduced phase space.