TY - JOUR

T1 - Projection operator approach to Langevin equations in φ4 theory

AU - Koide, Tomoi

AU - Maruyama, Masahiro

AU - Takagi, Fujio

N1 - Copyright:
Copyright 2005 Elsevier B.V., All rights reserved.

PY - 2002/5

Y1 - 2002/5

N2 - We apply the projection operator method (POM) to φ4 theory and derive both quantum and semiclassical equations of motion for the soft modes. These equations have no time-convolution integral term, in sharp contrast with other well-known results obtained using the influence functional method (IFM) and the closed time path method (CTP). However, except for the fluctuation force field terms, these equations are similar to the corresponding equations obtained using IFM with the linear harmonic approximation, which was introduced to remove the time-convolution integral. The quantum equation of motion in POM can be regarded as a kind of quantum Langevin equation in which the fluctuation force field is given in terms of the operators of the hard modes. These operators are then replaced with c-numbers using a certain procedure to obtain a semiclassical Langevin equation. It is pointed out that there are significant differences between the fluctuation force fields introduced in this paper and those introduced in IFM. The arbitrariness of the definition of the fluctuation force field in IFM is also discussed.

AB - We apply the projection operator method (POM) to φ4 theory and derive both quantum and semiclassical equations of motion for the soft modes. These equations have no time-convolution integral term, in sharp contrast with other well-known results obtained using the influence functional method (IFM) and the closed time path method (CTP). However, except for the fluctuation force field terms, these equations are similar to the corresponding equations obtained using IFM with the linear harmonic approximation, which was introduced to remove the time-convolution integral. The quantum equation of motion in POM can be regarded as a kind of quantum Langevin equation in which the fluctuation force field is given in terms of the operators of the hard modes. These operators are then replaced with c-numbers using a certain procedure to obtain a semiclassical Langevin equation. It is pointed out that there are significant differences between the fluctuation force fields introduced in this paper and those introduced in IFM. The arbitrariness of the definition of the fluctuation force field in IFM is also discussed.

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U2 - 10.1143/PTP.107.1001

DO - 10.1143/PTP.107.1001

M3 - Article

AN - SCOPUS:0036562896

VL - 107

SP - 1001

EP - 1035

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 5

ER -