ABSTRACT
In this chapter we discuss discrete symmetries in quantum field theories, i.e. the transformations:
• inversion of the spatial coordinate axes at a given time: x → −x, t → t (12.1)
or parity, which we denote with P , • substitution of every particle by its antiparticle, and vice versa, or charge conjugation, C,
• inversion of time, or time reversal t → −t, x → x (12.2)
which we denote as T . The first two transformations are represented in the Hilbert space of states
by unitary operators while time inversion must act as an anti-unitary operator. In this chapter we will refer principally to the QED Lagrangian which, as we
symmetries of QED. At the end of the chapter we will consider the Fermi Lagrangian, the prototype description of the weak interactions, in which the symmetries are individually violated, beginning with parity, and the only exact symmetry is the product of all three, the TCP transformation.
