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Generalized normal ordering

GENERALIZED NORMAL ORDERING, IRREDUCIBLE BRILLOUIN CONDITIONS, AND CONTRACTED SCHRODINGER EQUATIONS... [Pg.293]

Formulating conditions for the energy to be stationary with respect to variations of the wavefunction P in this generalized normal ordering, one is led to the irreducible Brillouin conditions and irreducible contracted Schrodinger equations, which are conditions on the one-particle density matrix and the fe-particle cumulants k, and which differ from their traditional counterparts (even after reconstruction [4]) in being strictly separable (size consistent) and describable in terms of connected diagrams only. [Pg.294]

GENERALIZED NORMAL ORDERING and partial trace relations... [Pg.303]

We introduce the generalized normal ordering in various steps, starting with the traditional particle-hole formalism. [Pg.309]

The results of the last section, which are essentially a reformulation of the traditional particle-hole formalism for excitation operators, were first presented in 1984 [8]. At that time it was not realized that only two very small steps are necessary to generalize this formalism to arbitrary reference states. Only after Mukherjee approached the formulation of a generalized normal ordering on a rather different route [2], did it come to our attention how easy this generalization actually is, when one starts from the results of the last section. [Pg.311]

Then the excitation operators in generalized normal ordering are in a compact form ... [Pg.313]

For the formulation of the generalized Wick theorem corresponding to the generalized normal ordering, we need the matrix element rf, Eq. (65), of the one-hole density matrix and the cumulants kjc, Eqs. (39)-(47), of the fc-particle density matrices. [Pg.314]

Eor products of operators a in the generalized normal order we then get... [Pg.314]

Let us point out, without going into detail, that the generalized normal ordering can, of course, also be formulated in a spin-free form [30]. [Pg.319]

The condition for E to be stationary with respect to unitary one-particle transformations in generalized normal order is... [Pg.320]

The concept of generalized normal ordering is very powerful, but still waiting to become a standard tool in many-body physics. It is the natural generalization of... [Pg.328]

Generalized normal ordering is intimately linked to the cumulants Xk of the k-particle density matrices (for short, density cumulants). The contractions in the sense of the generalized Wick theorem involve the... [Pg.329]

If one formulates the conditions for stationarity of the energy expectation value in terms of generalized normal ordering, one is led to either the irreducible fc-particle Brillouin conditions IBCj or the irreducible A -particle contracted Schrodinger equations (IBC ), which are conditions to be satisfied by y = yj and the k. One gets a hierarchy of k-particle approximations that can be truncated at any desired order, without any need for a reconstruction, as is required for the reducible counterparts. [Pg.329]


See other pages where Generalized normal ordering is mentioned: [Pg.293]    [Pg.293]    [Pg.295]    [Pg.297]    [Pg.299]    [Pg.301]    [Pg.305]    [Pg.307]    [Pg.309]    [Pg.309]    [Pg.311]    [Pg.313]    [Pg.315]    [Pg.316]    [Pg.317]    [Pg.319]    [Pg.321]    [Pg.323]    [Pg.325]    [Pg.327]    [Pg.329]    [Pg.329]    [Pg.44]    [Pg.47]   


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Generalized normal ordering Hamiltonian

Generalized normal ordering Wick theorem

Generalized normal ordering particle-hole formalism

Spin orbitals generalized normal ordering

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