Some papers with similar ideas
Some papers with similar ideas, which however do not
yet implement, that the generator of the transformation is continuous and
depends on the running Hamiltonian itself are listed here.
There are at least two lines of similar ideas which preceeded the flow
equations
 The idea to diagonalize a quantum Hamiltonian by considering it at
different discretely chosen energy and length scales and thus performing a
renormalization group analysis dates back to the seventies. Two main streams
were
 on the one hand side the solution of the Kondo
problem by
 K.G. Wilson, The Renormalization Group: Critical Phenomena
and the Kondo Problem, Rev. Mod. Phys. 47 (1975) 773
 and on the other hand side the investigation of the Anderson localization
by
 D.C. Licciardello and D.J. Thouless,
Constancy of Minimum Metallic Conductivity in Two Dimensions,
Phys. Rev. Lett. 35 (1975) 1475,
 F.J. Wegner, Electrons in Disordered Systems.
Scaling near the Mobility Edge,
Z. Phys. B25 (1976) 327,
 P.A. Lee, RealSpace Scaling Studies of Localization,
Phys. Rev. Lett. 42 (1979) 1492,
Scaling Studies of Localization, J. Noncr. Solids 35+36 (1980) 21,
 and E. Domany and S. Sarker, Renormalization Group Study of
Anderson Localization, Phys. Rev B20 (1979) 945,
A Scaling Theory of Anderson Localization, J. Phys. C13 (1980) L273.
 A second line came from two Russian groups, which eventually informed us
about their work: They performed continuous transformations for spin systems
with a constant generator of the unitary transformation,

one around D.A. Garanin and V.S. Lutinov,
 Hightemperature spin wave dynamics of the uniaxial
antiferromagnets,
Solid State Communications 44 (1982) 1359;
 Normal modes and relaxation processes in magnetically ordered materials
with singlesite anisotropy,
Teor. mat. Fiz. 60 (1984) 133;
 Spin waves in the easyplane ferromagnets,
Physica A 126 (1984) 133;
 and with L.V. Panina,
The magnonmagnon interactions in easyplane antiferromagnets,
Physica A 184 (1992) 523557.
 The other one is around V.L. Safonov,
 Method of the Spin Hamiltonian Diagonalization,
Phys. Lett. A 97 (1983) 164;
 with A.V. Andrienko, V.I. Ozhogin, A. Yu. Yakubovskii,
Study of mechanisms of nuclearspinwave relaxation in the weakly anisotropic
antiferromagnet CsMnF_{3},
Zh. Eksp. Teor. Fiz. 84 (1983) 1158 [Sov. Phys. JETP 57 (1983)673];
 with R.M. Farzetdinova,
On a possibility of magnon pumping in crystals with twolevel defects,
J. Magn. Magn. Mater. 98 (1991) L235;
 Theory of superconductivity for quasiparticles with parastatistics,
Phys. Stat. Solidi (b) 174 (1992) 223;
 with Q. Shi, M. Mino, H. Yamazaki,
Unitary transformations in weakly nonideal Bose gases,
Phys. Lett. A238 (1998) 258;

Continuous Unitary Transformations, quantph/0202095.

If this second approach is applied to the elimination of the electronphonon
interaction, then it yields the singular result by Fröhlich and not the
smooth effective interaction as obtained with the flow equations, where
the generator is varied with the corresponding effective Hamiltonian.
Back to main page Flow equations.
November 2002