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Acta Physica Sinica

TRANSFORMATION PROPERTIES OF THREE SETS OF CLOSED TIME PATH GREEN'S FUNCTIONS

ZHOU GUANG-ZHAO, Yu Shan Lu, Bailin Hao, 中国科学院理论物理研究所

Published Jan 1, 1980• 5 citations
Publisher

Abstract

In this article, we derived the transformations among three sets of elosed time path Green's functions and some calculation rules, from which a general definition of arbitrary multipoint retarded and advanced Green's functions follows naturally. Some algebraic identities among multipoint functions have shown to be the consequences of the property W[J+,J-](J+=J-=J)=0 for the generating functional on the closed time path.

DOI
10.7498/aps.29.878

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In this article, we derived the transformations among three sets of elosed time path Green's functions and some calculation rules, from which a general definition of arbitrary multipoint retarded and advanced Green's functions follows naturally. Some algebraic identities among multipoint functions have shown to be the consequences of the property WJ+,J-=0 for the generating functional on the closed time path.
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The closed time path Green's function (CTPGF) formalism is applied to the critical dynamics. The related results for the CTPGF approach are briefly reviewed. Three different forms of CTPGF's are defined, transformations from one to another form and other useful computation rules are given. The path integral presentation of the generating functional for CTPGF's is used to derive the Ward-Takahashi identities under both linear and nonlinear transformations of field variables. The generalized Langevin equations for the order parameters and conserved variables are derived from the vertex functional on the closed time path. The proper form of the equations for the conserved variables, including automatically the mode coupling terms, is determined according to the Ward-Takahashi identities and the linear response theory. All existing dynamic models are reobtained by assuming the corresponding symmetry properties for the system. The effective action for the order parameters is deduced by averaging over the random external field. The Lagrangian formulation of the statistical field theory is obtained if the random field one-loop approximation and the second-order approximation of order-parameter fluctuations on different time branches are both taken. The various possibilities of improving the current theory of critical dynamics within the framework of CTPGF's are discussed. The problem of renormalization for the finite-temperature field theory is considered. The whole theoretical framework is also applicable to systems near the stationary states far from equilibrium, whenever there exists an analog of the potential function ("free energy").
We present an extension of the analysis previously applied to the retarded part of the coupled cluster (CC) Green's function to its advanced part. In analogy to our earlier studies for the retarded part, we demonstrate that the advanced CC Green's function is expressed in terms of connected diagrams only, which is a direct consequence of algebraic form of equations satisfied by CC amplitudes. We also demonstrate that ω-derivatives of the advanced CC Green's function can be calculated analytically and can be expressed in terms of connected diagrams only. We analyse the structure of connected diagrams and the role of intermediate operators which satisfy electron affinity equation-of-motion CC-type conditions.