# 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.

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### Canonical quantization - can't form creation or annilhation operators?

This question is related to this PSE question I asked yesterday. From this question and what I have read, the general procedure for canonical quantization is as follows (correct me if I am wrong): ...
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### Diagonalization of a Hamiltonian in Second Quantization

I have the following Hamiltonian of a fermionic two particle system. $H =2 \epsilon_m f^\dagger f + \epsilon_d d^\dagger d + t df +t f^\dagger d^\dagger + t f^\dagger d + td^\dagger f$ t $\in I R$ ...
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### What's the right Fourier transformation definition of creation or annihilation operators in lattice model?

Very often one can view the solid as lattice model and then use the the language of second quantization,namely taking the occupation number representation, to express the Hamiltonian of the system. In ...
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### Classical and quantum field in beam-splitter

Why is the annihilation operator $\hat a$ the quantum analog of a classical field amplitude $\mathcal{E}$? Is the quantized electromagnetic field not a sum of the annihilation and creator operator?...
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### Second quantization using matlab [closed]

I am attempting to create creation and annihilation operator used in 2nd quantisation in quantum mechanics. I want to do this both numerically and symbolically. Here is the idea: $n= {c^\dagger}c$ ...
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### Terms $\hat{c}^{\dagger}_{i\uparrow} \hat{c}^\phantom{\dagger}_{i+1\downarrow}+\text{h.c.}$ in tight-binding hamiltonians

The basic tight-binding hamiltonian consists of terms of the form $$\hat{c}^{\dagger}_{i\uparrow} \hat{c}^\phantom{\dagger}_{i+1\uparrow}+\text{h.c.}$$ (where $\text{h.c.}$ denotes the adjoint of the ...
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### Majorana Operators

My question concerns a comment made on this post: Because one needs two Majorana modes $\gamma_1$ and $\gamma_2$ to each regular fermionic $c^\dagger c$ one, any two associated Majorana modes ...
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### Second quantization field derivative commutator

For the symmetrized quantum field theory Lagrangian of the free dirac field $$\mathcal{L} = i[\overline{\psi}_a,({\partial_\mu}\gamma^\mu \psi)^a] -m[\overline{\psi}_a,\psi^a ]$$ the terms are ...
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### Schrödinger wavefunctional quantum-field eigenstates

The reason that I have this problem is that I'm trying to solve problem 14.4 of Schwartz's QFT book, which've confused me for a long time. The problem is to construct the eigenstates of a quantum ...
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### Tight-binding model of diatomic solid

I am working on a problem based on Problem 1.6 in Gerald D. Mahan - Many Particle Physics, 3rd edition. The problem: Consider a tight-binding solid which has alternating atoms of type A and B. The ...
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### Many body physics - changing to $k$ space

I have an example in my notes starting with Linear Chain: $$H=-t\sum_{\langle i i' \rangle} c_i^\dagger c_{i'} = -2t \sum_k c_k^\dagger c_k \cos{k}$$ I don't know where the $2 \cos{k}$ comes ...
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### Time reversal symmetry of fock states

How does the time reversal symmetry work in the second quantization frame of non-relativistic quantum mechanics? In particular what is the time-reversed of a given Fock-state? As an example let's ...
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### Does E commute with B (in second quantization)?

In second quantization, there's a standard procedure where we first find solutions to Maxwell's Equations. After doing so we apply quantum mechanical properties to these solutions. So for some ...
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