each pair has spin zero and even parity, and the last nucleon is in the 1d5/2 shell, which has even parity since ℓ = 2 for a d orbital. Quantum field theory If one can show that the vacuum state is invariant under parity, , the Hamiltonian is parity invariant and the quantization conditions remain unchanged under parity, then it follows that every state has good parity, and this parity is conserved in any reaction. To show that quantum electrodynamics is invariant under parity, we have to prove that the action is invariant and the quantization is also invariant. For simplicity we will assume that canonical quantization is used; the vacuum state is then invariant under parity by construction. The invariance of the action follows from the classical invariance of Maxwell's equations. The invariance of the canonical quantization procedure can be worked out, and turns out to depend on the transformation of the annihilation operator: where denotes the momentum of a photon and refers to its polarization state. This is equivalent to the statement that the photon has odd intrinsic parity. Similarly all vector bosons can be shown to have odd intrinsic parity, and all axial-vectors to have even intrinsic parity. A straightforward extension of these arguments to scalar field theories shows that scalars have even parity, since This is true even for a complex scalar field. (Details of spinors are dealt with in the article on the Dirac equation, where it is shown that fermions and antifermions have opposite intrinsic parity.) With fermions, there is a slight complication because there is more than one spin group. Parity in the Standard Model Fixing the global symmetries Applying the parity operator twice leaves the coordinates unchanged, meaning that must act as one of the internal symmetries of the theory, at most changing the phase of a state. For example, the Standard Model has three global U(1) symmetries with charges equal to the baryon number , the lepton number , and the electric charge . Therefore, the parity operator satisfies for some choice of , , and . This operator is also not unique in that a new parity operator can always be constructed by multiplying it by an internal symmetry such as for some . To see if the parity operator can always be defined to satisfy , consider the general case when for some internal symmetry present in the theory.