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Symmetries and conservation laws are a constant theme in physics, and nowhere more so than in particle physics.To understand the connection between these we consider firstly a simple example, that of translational invariance, and show that it leads directly to the conservation of linear momentum.In atomic physics, spectroscopy is a vital ingredient in understanding the structure of atoms in terms of nuclei and electrons, and it plays an analogous role in elucidating the internal structure of hadrons in terms of their constituent quarks.In both cases, each state in the spectrum has not only a specific energy but also well-defined values of 'good' quantum numbers associated with conserved observables, like angular momentum, whose quantum mechanical operators commute with the Hamiltonian of the system.Conservation laws have an equally important place in hadron spectroscopy, and the first task in studying hadrons is to determine which are the appropriate conserved quantities and to measure their values for observed states.

Symmetries and conservation laws are a constant theme in physics, and nowhere
more so than in particle physics. In this chapter we concentrate on those laws
that are associated with space–time symmetries and their applications in strong
and electromagnetic interactions. Such conservation laws are particularly important
in spectroscopy. In atomic physics, spectroscopy is a vital ingredient in understanding the structure of atoms in terms of nuclei and electrons, and it plays an
analogous role in elucidating the internal structure of hadrons in terms of their constituent quarks. In both cases, each state in the spectrum has not only a specific
energy but also well-defined values of ‘good’ quantum numbers associated with
conserved observables, like angular momentum, whose quantum mechanical operators commute with the Hamiltonian of the system. In atomic physics these quantum
numbers are crucial to understanding the degeneracies of the energy levels, their
behaviours in the presence of electric and magnetic fields, and the selection rules
that govern transitions between them. Conservation laws have an equally important
place in hadron spectroscopy, and the first task in studying hadrons is to determine which are the appropriate conserved quantities and to measure their values for
observed states.
Some of the conservation laws discussed in this chapter – those for linear and
angular momentum – are universal laws of nature, valid for all interactions. Others we
shall meet, like parity, are only conserved in the approximation that weak interactions
are neglected. Their violation will be discussed in Chapter 10. Here we shall neglect
weak interactions and concentrate on the strong and electromagnetic interactions with
which we will be primarily concerned in the next two chapters.
The conservation laws we discuss have their origin in the symmetries and invariance properties of the underlying interactions. To understand the connection between
these we consider firstly a simple example, that of translational invariance, and show
that it leads directly to the conservation of linear momentum.