  The two-dimensional d-wave superconducting state of the high temperature
superconductors has a number of different elementary excitations: the
spin-singlet Cooper pairs, the spin S=1/2 fermionic quasiparticles, and a
bosonic S=1 resonant collective mode, phi_{alpha}, at the antiferromagnetic
wavevector. Although the phi_{alpha} quanta are strongly coupled to the gapped
quasiparticles near the (pi,0), (0,pi) wavevectors (the "hot spots"), they are
essentially decoupled from the low energy quasiparticles near the nodes of the
superconducting gap. Consequently, distinct and independent low energy quantum
field theories can be constructed for the phi_{alpha} and nodal quasiparticle
excitations. We review recent work introducing a 2+1 dimensional boundary
conformal field theory for the damping of the phi_{alpha} excitations by
non-magnetic impurities, which is built on the proximity to a magnetic ordering
transition at which the phi_{alpha} condense; the results are compared with
neutron scattering experiments. Photoemission and THz conductivity measurements
indicate that the nodal quasiparticles undergo strong inelastic scattering at
low temperatures; we propose that this is due to fluctuations near a quantum
phase transition, and critically analyze candidate order parameters and field
theories.
