Critical dynamics as a field theory

Critical dynamics [1-3] is considered systematically from the point of view of quantum field theory. The connection between dynamics and statics and its consequences for the renormalization constants is discussed in detail. The main technical result is the 3 calculation of the $\varepsilon^3$ contribution in the $4-2\varepsilon$ expansion of the dynamical exponent $\Delta_\omega$ (critical dimension of frequency) for the $O_n$-symmetrie $\varphi^4$ model. Instead of the value $\Delta_\omega=2+0,726(1-2\varepsilon\cdot 1,687)\eta$ obtained previously [4], the value $\Delta_\omega=2+0,726(1-2\varepsilon\cdot 0,1885)\eta$ is obtained.