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Questions tagged [second-quantization]

Second quantization or canonical quantization in quantum field theory and many-body systems is the collective organizing and accounting of an infinity of quantum excitations and their interactions through quantum field operators.

Second quantization or canonical quantization in quantum field theory and many-body systems is the collective organizing and accounting of an infinity of quantum excitations and their interactions through quantum field operators. The quantum many-body states are represented in Fock space, consisting of an infinity of single-particle states filled up with a certain number of identical particles.

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Kinetic energy operator in second quantization formalism

If we want to express a quantum mechanical oeprator $ \hat{A}$ in second quantization formalism, it is $$ \hat{A} = \sum_{\alpha, \beta} \langle \alpha | \hat{A}|\beta \rangle c^{\dagger}_{\alpha}c_{\beta} $$ So if we represent the kinetic operator…
user42298
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Representation of operators in Fock space

In first quantization, the operator $J$ assumes the form $J=\sum_{i}j(x_i)$. In Fock space, it is instead written as $J=\int dx \psi^\dagger(x)j(x)\psi(x)$, where $\psi^\dagger, \psi$ are the field operators. Is $j(x)$ an operator in Fock space or…
Annie
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Diagonalizing quadratic Hamiltonian in second quantization

I have a Hamiltonian of the form $H = \Sigma_{ij} H_{ij}a^\dagger_ia_j$, and I want to diagonlize it: Let $ H_{ij} = \Sigma_{\alpha}U_{i\alpha}\epsilon_\alpha U^*_{j\alpha} $, where U is a unitary matrix. Then I proceed by inserting this in the…
Dimitri
  • 161