4-7 August 2020
Asia/Tokyo timezone

QCD at nonzero temperature and density

7 Aug 2020, 17:40


QCD at nonzero Temperature and Density QCD at nonzero Temperature and Density


Akira Ohnishi (Yukawa Institute for Theoretical Physics, Kyoto University)


Replica evolution of classical field is proposed as an approximate simulator of real-time quantum field dynamics at finite temperatures. We consider $N$ classical field configurations $(\phi_{\tx},\pi_{\tx} (\tau=0,1,\cdots N-1)$, dubbed as replicas, which interact with each other via the $\tau$-derivative terms and evolve with the classical equation of motion. The $\tau$-derivative terms in the Hamiltonian, $\xi^2 \sum_x (\phi_{x+\hat{\tau}}-\phi_x)^2/2$, correspond to the kinetic part of the Euclidean action in the imaginary time formalism of the finite temperature quantum field theory by regarding the replica index $\tau$ as the imaginary time index.Thus the replica evolution is technically the same as the molecular dynamics part of the hybrid Monte-Carlo sampling. The partition function of replicas at temperature $\xi$ is proven to be proportional to that in quantum field theory at temperature $T=\xi/N$. At the same time, the time dependence of the replica-index average of field variables is described by the classical equation of motion when the fluctuations are small. We examine the statistical and dynamical properties of the $\phi^4$ theory in the 4+1 spacetime dimensions. We note that the Rayleigh-Jeans divergence in the classical field can be removed in replica evolution with $N \geq 2$ by including the mass counterterm. We also find that the thermal mass obtained from the unequal time correlation function at zero momentum grows as a function of the coupling as in the perturbative estimate in the small coupling region. Hence the replica evolution, the classical field theory with improved quantum statistical property, would be a candidate to represent the real-time evolution of quantum field.

Primary author

Akira Ohnishi (Yukawa Institute for Theoretical Physics, Kyoto University)


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