Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-07-26
J.Math.Phys.47:082101,2006
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, no figures
Scientific paper
We study the time evolution of the expectation value of the anharmonic oscillator coordinate in a coherent state as a toy model for understanding the semiclassical solutions in quantum field theory. By using the deformation quantization techniques, we show that the coherent state expectation value can be expanded in powers of $\hbar$ such that the zeroth-order term is a classical solution while the first-order correction is given as a phase-space Laplacian acting on the classical solution. This is then compared to the effective action solution for the one-dimensional $\f^4$ perturbative quantum field theory. We find an agreement up to the order $\l\hbar$, where $\l$ is the coupling constant, while at the order $\l^2 \hbar$ there is a disagreement. Hence the coherent state expectation values define an alternative semiclassical dynamics to that of the effective action. The coherent state semiclassical trajectories are exactly computable and they can coincide with the effective action trajectories in the case of two-dimensional integrable field theories.
Dias Nuno Costa
Mikovic Aleksandar
Prata Joao Nuno
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