Restriction of the basis to two-dimensions

It is convenient to introduce polar coordinates, k and p, as in Fig. 1. The expansion becomes then, for k independent gaps, i.e. dropping the factor k2 

The dependence of p(CO) as CO 0 is reflected in the behavior of several physical quantities as a function of temperature. 

Since the density of states depends on the symmetry of the gap, any measurement sensitive to p(CO) will give information on the symmetry of the gap. An example is ARPES measurements [15]. The photoemission intensity can be written as 

The arguments of Ambegaokar et al. are based on the introduction of a coordinate dependent gap 

In the method of interacting bosons, one introduces boson creation, T t, and annihilation, [ operators satisfying boson commutation relations 

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