In physics, invariance mechanics, in its simplest form, is the rewriting of the laws of quantum field theory in terms of invariant quantities only. For example, the positions of a set of particles in a particular coordinate system is not invariant under translations of the system. However, the (4-dimensional) distances between the particles is invariant under translations, rotations and Lorentz transformations of the system.
The invariant quantities made from the input and output states of a system are the only quantities needed to give a probability amplitude to a given system. This is what is meant by the system obeying a symmetry. Since all the quantities involved are relative quantities, invariance mechanics can be thought of as taking relativity theory to its natural limit.
Invariance mechanics has strong links with loop quantum gravity in which the invariant quantities are based on angular momentum. In invariance mechanics, space and time come secondary to the invariants and are seen as useful concepts that emerge only in the large scale limit.
Read more about Invariance Mechanics: Feynman Rules, Constraints
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