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Take a real unit vector in spin space $\hat{\mathbf{d}}$ and choose orthogonal orbital axes. The model hasIt vanishes at the two polar directions and is largest at the equator. The orbital factor changes sign when $\hat{\mathbf{k}}$ is reversed, as required for the odd orbital part of spin-triplet p-wave pairing. Calling the phase A does not mean its order parameter is one real number.

For a simple spin-triplet p-wave pairing description, let the $3\times 3$ matrix $A$, with complex number entries, map an orbital direction $\hat{\mathbf{k}}$ on the Fermi surface into a triplet gap vector $\mathbf{d}=A\hat{\mathbf{k}}$. The indices refer to spin and orbital components. A scalar amplitude cannot retain all these relative orientations. Anthony James Leggett's account connects that extra structure to the magnetic responses of the different phases.^[ref]

Here are two explicit idealizations, with a common positive scale $\Delta$ and an overall quantum phase omitted. They show how odd orbital pairing can have either nodes or an isotropic gap. They do not calculate which state has the lower Helmholtz free energy.

Spin-triplet p-wave pairing has pair spin $S=1$ and orbital angular momentum $L=1$, allowing multiple order parameters beyond conventional BCS theory with zero orbital angular momentum. ^[ref]

Specifying this symmetry does not determine its microscopic attraction mechanism. A short exchange-symmetry check explains why these quantum numbers fit fermions. The spin-one-half triplet states $|\uparrow \uparrow ⟩$, $(|\uparrow \downarrow ⟩+|\downarrow \uparrow ⟩)/\sqrt{2}$ and $|\downarrow \downarrow ⟩$ are symmetric under exchange. A stipulated orbital factor proportional to relative momentum $k_x$ changes sign under $\mathbf{k}\mapsto -\mathbf{k}$. Multiplying any symmetric spin function by that odd orbital factor gives an antisymmetric pair wave function, as required by Fermi-Dirac statistics. By comparison, an even s-wave orbital factor needs the antisymmetric spin singlet state. This checks compatibility with exchange statistics; it neither selects a stable phase nor derives its transition temperature.