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Prog. Theor. Phys. Supplement No.15 (1960) pp. 3-60

[ Full Text PDF : FREE ACCESS (2893K) ]

Formal Theory of Green Functions

Tomokazu Kato,* Tetsuro Kobayashi** and Mikio Namiki*,**

*Department of Applied Physics, Waseda University, Tokyo
**Science and Engineering Research Laboratory, Waseda University, Tokyo

(Received September 21, 1960)

Abstract:

The formal theory of Green functions is reviewed for many particle problems in nuclear physics or in solid state physics. In particular, one- and two-particle Green functions are discussed in detail. The Feynman amplitudes are also explained together with the effective potential and its applications. This article contains the following sections:
§1. Preliminary remarks
§2. Definition of Green functions
§3. Structure of equations satisfied by Green functions
3.1 One-particle Green function
3.2 Two-particle Green function
§4. Perturbation theory and its foundation
§5. Spectral representation and its application
§6. Connection with reaction matrix
§7. Amplitudes and their matrix
7.1 Definitions of amplitudes and effective potential
7.2 Nuclear optical model
7.3 One electron in insulators and semi-conductors
Appendix I. Functional differentiation
Appendix II. Schwinger's dynamical principle
Appendix III. Polaron problem


URL : http://ptp.ipap.jp/link?PTPS/15/3/
DOI : 10.1143/PTPS.15.3

[ Full Text PDF : FREE ACCESS (2893K) ] Citation:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 59 (1990) pp. 3750-3764 :
    Theory of Angle-Resolved X-Ray Photoemission by Multiple Scattering Cluster Method. II. Damped One-Electron Formulas Derived from Many-Body Theory and Application to Si(111)-(√3×√3) Ag 3d Spectra
    Takashi Fujikawa and Morio Hosoya
  2. Progress of Theoretical Physics Vol. 56 No. 5 (1976) pp. 1383-1395 :
    The Inadequacy of the Impulse Approximation for a Hard Core Potential
    Hichang Kang

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