The perturbation theory of Hille and Phillips for semigroups of bounded linear operators on a Banach space is modified to apply to the semigroups of positive traceclass operators encountered in quantum statistical mechanics.
REFERENCES
1.
2.
T. Kato, Perturbation Theory for Linear Operators (Springer, New York, 1966).
3.
D. Ruelle in Applications of Mathematics to Problems in Theoretical Physics, Summer School 1965 Cargèse, Corsica, edited by F. Lurçat (Gordon‐Breach, New York, 1967).
4.
5.
S.
Miracle‐Sole
and D. W.
Robinson
, Commun. Math. Phys.
14
, 235
(1969
).6.
The basic reference for semigroups of interest is E. Hille and R. S. Phillips, Functional Analysis and Semigroups, revised edition (Am. Math. Soc., Providence, R.I., 1957). Our detailed references will generally be given as HP a.b. which will refer to Sec. a.b. of this treatise.
7.
8.
Some relevant publications are
T.
Matsubara
, Progr. Theoret. Phys.
14
, 351
, 1955
;L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962);
A. A. Abrikosov, L. P. Gor’kov and J. E. Dzyaloshinsky, Methods of Quantum Field Theory in Statistical Physics (Prentice‐Hall, Englewood Cliffs, N.J., 1963);
C. Bloch, Diagram Expansions in Quantum Statistical Mechanics in Studies in Statistical Mechanics (Wiley, New York, 1965), Vol. III. A more detailed list is to be found in Ref. 9.
9.
C. W. Gruber, thesis (Princeton University, 1968).
10.
R. T. Powers, thesis (Princeton University, 1967).
11.
12.
13.
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© 1971 The American Institute of Physics.
1971
The American Institute of Physics
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