We give a general expression for the normally ordered form of a function where is a function of boson creation and annihilation operators satisfying . The expectation value of this expression in a coherent state becomes an exact generating function of Feynman-type graphs associated with the zero-dimensional quantum field theory defined by . This enables one to enumerate explicitly the graphs of given order in the realm of combinatorially defined sequences. We give several examples of the use of this technique, including the applications to Kerr-type and superfluidity-type Hamiltonians.
REFERENCES
1.
J. D.
Bjorken
and S. D.
Drell
, Relativistic Quantum Fields
(McGraw-Hill
, St. Louis, 1965
).2.
A. N.
Vasiliev
, Functional Methods in Quantum Field Theory and Statistical Physics
(Gordon and Breach
, Amsterdam, 1998
).3.
J. R.
Klauder
and E. C. G.
Sudarshan
, Fundamentals of Quantum Optics
(Benjamin
, New York, 1968
).4.
5.
W. M.
Zhang
, D. F.
Feng
, and R.
Gilmore
, Rev. Mod. Phys.
62
, 867
(1990
).6.
R. M.
Wilcox
, J. Math. Phys.
8
, 962
(1967
).7.
P.
Blasiak
, K. A.
Penson
, and A. I.
Solomon
, Phys. Lett. A
309
, 198
(2003
).8.
M. A.
Méndez
, P.
Blasiak
, K. A.
Penson
(unpublished).9.
C. M.
Bender
, D. C.
Brody
, and B. K.
Meister
, J. Math. Phys.
40
, 3239
(1999
);10.
11.
R.
Aldrovandi
, Special Matrices of Mathematical Physics
(World Scientific
, Singapore, 2001
).12.
A. D.
Wilson-Gordon
, V.
Bužek
, and P. L.
Knight
, Phys. Rev. A
44
, 7647
(1991
).13.
G.
Dattoli
, S.
Lorenzutta
, C.
Cesarano
, and P. E.
Ricci
, Integral Transforms Spec. Funct.
13
, 521
(2002
).14.
A. I.
Solomon
, J. Math. Phys.
12
, 390
(1971
).15.
16.
N. J. A.
Sloane
, Encyclopedia of Integer Sequences, 2005
, http:∕∕www.research.att.com∕∼njas∕sequences© 2005 American Institute of Physics.
2005
American Institute of Physics
You do not currently have access to this content.
