Superselections

Superselections are a concept in quantum mechanics that refers to a particular way of formulating the theory. Instead of considering all possible states of a system, superselections focus on a special class of states that are physically observable. These observable states are often called "physical states" or "superselected sectors."

The idea behind superselections is that not all states that can be mathematically constructed are actually realizable or measurable in an experiment. Certain properties of a quantum system, such as its electric charge or baryon number, are conserved. This means that a system cannot spontaneously transition from a state with one charge to a state with a different charge. Superselections formalize this idea by partitioning the Hilbert space of all possible states into subspaces, where transitions between states in different subspaces are forbidden.

Within each superselected sector, the usual rules of quantum mechanics apply, and time evolution is described by the Schrödinger equation. However, a system is confined to its particular sector and cannot escape it. This implies that if a system starts in a state with a specific charge, it will always remain in a state with that same charge.

Superselection rules have implications for measurement in quantum mechanics. When a measurement is performed, the outcome must correspond to one of the observable states within the system's superselected sector. The existence of superselection rules helps to explain why certain quantities are always observed to have definite values, even in the presence of quantum superposition. It provides a framework for understanding the relationship between the mathematical formalism of quantum mechanics and the physical reality of observable phenomena.