Linear operators can also be called directional operators. In the sense that they are well-behaved sticklers, obeying and following rules of vector calculus. On the other hand, if these rules cannot be followed properly for most cases then they become nervous operators.
Nervous operators can be downright unpredictable. Their physical nature approaches the catastrophic edges of complexity and chaos. At the least, they vacillate in a state of perpetual random fluctuation, making every orientation indecisively possible, but never quite decided on a strongly preferred direction. Officially, these modus operandi function best perfectly in an infinitesimal region of quantum spacetime. Therefore, all quantum vacuum operators are necessarily nervous physical operators of the 1st, 2nd, and 3rd kind.
Many can be found in the science halls of thermodynamics, in the central regions of stars and galaxies, having heated discussions, trying to decide or to select the greatest temperature dependent operator among them. But lack of electrical resistance often creates Cooper pairs of superconductors, not reluctant Pauli’s reclusive resistors. But still the best outcomes are simply a bunch of average indicators. Nonetheless, all these average economic indicators are described by the most sophisticated techniques of quantum statistical mechanics. The results are two major separators: the easy-go-lucky friendly bosons and the firmed-dogged dogmatic fermions.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
It sounds like the separators are having a major identity crisis of their minor coordinate field functions. Just make them into stings and all will be well; just ask Dr. Greene.
David
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