Annihilation/creation operators

The following angle-action representations [14] are available for the classical equivalents of the right-hand and left-hand creation-annihilation operators [46] ... 

Or is the frequency of the harmonic oscilator and b) are boson (phonon) creation (annihilation) operators. In order to use the perturbation theory we have to split the Hamiltonian (16) onto the unperturbed part Hq and the perturbation H ... 

Positive semidefinite Hamiltonians can be constructed by taking an operator that depends on g creation/annihilation operators and multiplying the operator... 

Bose birth-death (creation-annihilation) operators a-, at, 6-, fet ... 

The E operators are the elementary operators, the generators, in unitary group theory. Below we give some commutator relations between E operators, e operators, creation and annihilation operators that are important for developing a good strategy for evaluating many of the quantities that show up in the later derivation. 

For one shell of equivalent electrons representation (14.65) has been found in which the irreducible tensorial products are constructed separately for creation operators and annihilation operators. Likewise, such a representation can also be found for two-shell configurations. In that case,... 

The three curves shown in Fig. 3 are the ones calculated by using this Hamiltonian. Here, f J1 is the electronic transfer T between the fiu orbital a of the mth C60 molecule and the fiu orbital b of the nth C o molecule, where a and b denote x, y, and z f is chosen so as to reproduce the result of the electronic structure calculations. We also use spin electron in the flu orbital a of the mth C60 molecule. Furthermore, is the band energy of the flu electron of the band index a (a = 1,2, and 3) and the wavenumber k the band energies are obtained by diagonalizing the Hamiltonian H0 and we use ak(J(akli) to denote the corresponding creation (annihilation) operators. 

In terms of the creation-annihilation electron and phonon operators the Hamiltonian can be cast as follows ... 

As usual, the index k includes the wave vector k and the polarizations e [ and e2 perpendicular to k, and al (at) is the creation (annihilation) operator for photons of energy h(ok = he k 1. We must write in this formalism the operators, vector potential, and electric field which are involved in our calculations ... 

The basic elements of the second-quantization formalism are the annihilation and creation operators (Linderberg and (3hrn, 1973). The annihilation operator ap annihilates an electron in orbital creation operator ap (the conjugate of ap) creates an electron in orbital p. These operators satisfy the anticommutation relations... 

For the analysis of the various formalisms, manipulation of the equations, generating normal product of terms via Wick s theorem, and particularly for indicating how the proofs of the several different linked cluster theorems are achieved, we shall make frequent use of diagrams. For the sake of uniformity, we shall mostly adhere to the Hugenholtz convention/1/. All the constituents of the diagrams will be operators in normal order with respect to suitable closed-shell determinant taken as the vacuum. We shall refer to the creation/annihilation operators with respect to this vacuum after the h-p transformation.The hamiltonian H will also be taken to be in normal order with respect to... 

The creation operators in Eqs. [22] and [23] are restricted to act only on the virtual orbitals, and the annihilation operators may act only on the occupied orbitals. Therefore, by Eq. [21], the creation-annihilation operator pairs exactly anticommute ... 

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