### Abstract

The canonical formalism of thermally dissipative semifree fields in the time-dependent situation is presented. The use of thermal covenant derivatives simplifies the formulation considerably. With this formalism one can unambiguously obtain the interaction Hamiltonian under any thermal situation which together with the free propagator enables perturbative calculations to be performed. The "on-shell" renormalization condition in the time-dependent case is also discussed. The model of a system with a thermal reservoir illustrates how the present formalism works in time-dependent situations.

Original language | English |
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Pages (from-to) | 2925-2938 |

Number of pages | 14 |

Journal | Journal of Mathematical Physics |

Volume | 28 |

Issue number | 12 |

Publication status | Published - 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*28*(12), 2925-2938.

**Time-dependent canonical formalism of thermally dissipative fields and renormalization scheme.** / Hardman, I.; Umezawa, H.; Yamanaka, Yoshiya.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 28, no. 12, pp. 2925-2938.

}

TY - JOUR

T1 - Time-dependent canonical formalism of thermally dissipative fields and renormalization scheme

AU - Hardman, I.

AU - Umezawa, H.

AU - Yamanaka, Yoshiya

PY - 1987

Y1 - 1987

N2 - The canonical formalism of thermally dissipative semifree fields in the time-dependent situation is presented. The use of thermal covenant derivatives simplifies the formulation considerably. With this formalism one can unambiguously obtain the interaction Hamiltonian under any thermal situation which together with the free propagator enables perturbative calculations to be performed. The "on-shell" renormalization condition in the time-dependent case is also discussed. The model of a system with a thermal reservoir illustrates how the present formalism works in time-dependent situations.

AB - The canonical formalism of thermally dissipative semifree fields in the time-dependent situation is presented. The use of thermal covenant derivatives simplifies the formulation considerably. With this formalism one can unambiguously obtain the interaction Hamiltonian under any thermal situation which together with the free propagator enables perturbative calculations to be performed. The "on-shell" renormalization condition in the time-dependent case is also discussed. The model of a system with a thermal reservoir illustrates how the present formalism works in time-dependent situations.

UR - http://www.scopus.com/inward/record.url?scp=0011281139&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011281139&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0011281139

VL - 28

SP - 2925

EP - 2938

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 12

ER -