TABLE OF CONTENTS As we saw in the previous chapter, although several quantum numbers appear to be conserved in strong high-energy processes, some are violated in weak and electromagnetic interactions. This must reflect the inherent character of the underlying forces. Consequently, understanding the origin of conservation principles, and under what conditions they are violated, would appear to be an important element in the formulation of a quantitative description of particle interactions. We will therefore first address the question of how conservation laws arise in physical theories. As we will see shortly, the surprisingly simple answer is that whenever there is an underlying symmetry in a physical system, namely if our system is not affected by a change in some coordinate or other dynamical variable, then we can define a conserved charge (quantum number) associated with that symmetry. Conversely, if there is a conserved quantity associated with a physical system, then there exists an underlying invariance or symmetry principle responsible for its conservation. This observation, known as Noethers Theorem (after Emmy Noether), gives rise to powerful restrictions on the structure of physical theories. We now turn to issues related to symmetries in physical systems.
In simple terms, any set of transformations that leaves the equations of motion of a system unchanged or invariant, defines what is known as a symmetry of that physical system. Symmetries can be discussed using either the Lagrangian or the Hamiltonian formalism, for both classical as well as quantum theories. We...
