  Motivated by recent measurements of the lifetime (decay width) of paramagnons
in quantum antiferromagnet TlCuCl3, we investigate paramagnon decay in a heat
bath and formulate an appropriate quantum theory. Our formulation can be split
into two regimes: (i) a non-perturbative, 'hot quantum soup' regime where
paramagnon width is comparable to its energy; (ii) usual perturbative regime
where paramagnon width is significantly lower than its energy. Close to the
Neel tempera- ture the paramagnon width becomes comparable to its energy and
falls into the hot quantum soup regime. To describe this regime we develop a
new finite frequency, finite temperature technique for a nonlinear quantum
field theory; the 'golden rule of quantum kinetics'. The formulation is generic
and applicable to any three dimensional quantum antiferromagnet in the vicinity
of a quantum critical point. Specifically we apply our results to TlCuCl3 and
find agreement with experimental data. Additionally, we show that logarithmic
running of the coupling constant in the upper critical dimension changes the
commonly accepted picture of the quantum disordered and quantum critical
regimes.
