DOI: 10.1063/1.1664616. Perturbation Expansion for Real-Time Green's Functions

Perturbation Expansion for Real-Time Green's Functions

10.1063/1.1664616

Crossref journal-article

AIP Publishing

Journal of Mathematical Physics (317)

Abstract

The development of the time-translation operators in a matrix element of an arbitrary operator is examined. It is noted that we may interpret time as evolving from some remotely early time (t0) to a time in the far future (t∝) and then back to (t0). Using this interpretation, a perturbation expansion is developed for Green's functions defined along this path and a separation of the two-particle interaction terms into self-energy parts and single-particle Green's function terms is justified for quantities on this path. A connection is established between the real-time Green's functions and the Green's function defined along the path, thereby yielding a perturbation expansion for the real-time functions and a justification of the separation of the interaction terms in the equations of motion for the real-time quantities. The transport equations of Kadanoff and Baym are derived without resorting to an analytic continuation from imaginary times and without the correction terms of Fujita.

Bibliography

Craig, R. A. (1968). Perturbation Expansion for Real-Time Greenâs Functions. Journal of Mathematical Physics, 9(4), 605â611.

Authors 1

R. A. Craig (first)

References 17 Referenced 162

{'key': '2024021104051256000_r1'}
10.1063/1.1703704 / J. Math. Phys. (1961)
10.1016/0003-4916(66)90143-6 / Ann. Phys. (N.Y.) (1966)
10.1063/1.1704736 / J. Math. Phys. (1965)
{'key': '2024021104051256000_r5', 'first-page': '1515', 'volume': '47', 'year': '1964', 'journal-title': 'Zh. Eksp. Teor. Fiz.'} / Zh. Eksp. Teor. Fiz. (1964)
{'key': '2024021104051256000_r5a', 'first-page': '1018', 'volume': '20', 'year': '1965', 'journal-title': 'Sov. Phys.—JETP'} / Sov. Phys.—JETP (1965)
{'key': '2024021104051256000_r6'}
10.1016/0003-4916(66)90137-0 / Ann. Phys. (N.Y.) (1966)
10.1103/PhysRev.154.1233 / Phys. Rev. (1967)
{'key': '2024021104051256000_r7'}
{'key': '2024021104051256000_r8'}
{'key': '2024021104051256000_r9'}
10.1063/1.1703727 / J. Math. Phys. (1961)
{'key': '2024021104051256000_r11'}
{'key': '2024021104051256000_r12'}
{'key': '2024021104051256000_r13'}
{'key': '2024021104051256000_r14'}

Dates

Type	When
Created	21 years, 6 months ago (Feb. 10, 2004, 12:14 p.m.)
Deposited	1 year, 6 months ago (Feb. 10, 2024, 11:05 p.m.)
Indexed	1 month, 3 weeks ago (July 2, 2025, 3:27 p.m.)
Issued	57 years, 4 months ago (April 1, 1968)
Published	57 years, 4 months ago (April 1, 1968)
Published Print	57 years, 4 months ago (April 1, 1968)

Funders 0

None

BibTeX

@article{Craig_1968, title={Perturbation Expansion for Real-Time Green’s Functions}, volume={9}, ISSN={1089-7658}, url={http://dx.doi.org/10.1063/1.1664616}, DOI={10.1063/1.1664616}, number={4}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Craig, R. A.}, year={1968}, month=apr, pages={605–611} }

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