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Physica A Statistical Mechanics and its Applications

Functional mean field expansion for the many-body initial condition problem

S. Cruz Barrios, A. F. R. de Toledo Piza

Published Sep 1, 1989• 0 citations
Publisher
DOI
10.1016/0378-4371(89)90407-x

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A time-dependent projection technique is used to treat the initial-value problem for self-interacting fermionic fields. On the basis of the general dynamics of the fields, we derive formal equations of kinetic-type for the set of one-body dynamical variables. A nonperturbative mean-field expansion can be written for these equations. We treat this expansion in lowest order, which corresponds to the Gaussian mean-field approximation, for a uniform system described by the chiral Gross-Neveu Hamiltonian. Standard stationary features of the model, such as dynamical mass generation due to chiral symmetry breaking and a phenomenon analogous to dimensional transmutation, are reobtained in this context. The mean-field time evolution of nonequilibrium initial states is discussed.
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