Constraints
A system represented by a complete graph contains many invariant quantities. For large graphs, however, not all these quantities are independent and we must specify dimensional and gauge constraints. Why the particular number of dimensions or particular gauge group is chosen is still not known. The constraints and whether they are satisfied exactly or approximately is the key to invariance mechanics and the difference between it and conventional field theory. Work is being done to see whether the breaking of these constraints is a consequence of the gravitational field. If the constraints are satisfied only approximately, i.e. if there is a quantum uncertainty in the constraints then they are best thought of as local maxima of the amplitudes of a system which occur due to the specific Feynman rules used.
Read more about this topic: Invariance Mechanics
Famous quotes containing the word constraints:
“Play is a major avenue for learning to manage anxiety. It gives the child a safe space where she can experiment at will, suspending the rules and constraints of physical and social reality. In play, the child becomes master rather than subject.... Play allows the child to transcend passivity and to become the active doer of what happens around her.”
—Alicia F. Lieberman (20th century)
“The analogy between the mind and a computer fails for many reasons. The brain is constructed by principles that assure diversity and degeneracy. Unlike a computer, it has no replicative memory. It is historical and value driven. It forms categories by internal criteria and by constraints acting at many scales, not by means of a syntactically constructed program. The world with which the brain interacts is not unequivocally made up of classical categories.”
—Gerald M. Edelman (b. 1928)