Here we have used an example, where the operators are bosonic operators, while for fermionic operators, the retarded functions are defined with anti-communtators instead of the usual ( see Second quantization)
22.
This is of great use in quantum field theory : each separate Fourier component of a wave can be treated as a separate harmonic oscillator and then quantized, a procedure known as " second quantization ".
23.
The analogous uncertainty principle for photons forbids the simultaneous measurement of the number n of photons ( see Fock state and the Second quantization section below ) in an electromagnetic wave and the phase \ phi of that wave
24.
Since \ Psi ( \ bold { r } ) and \ Psi ^ { \ dagger } ( \ bold { r } ) are second quantization operators defined in every point in space they are called quantum field operators.
25.
He was involved in the development of operator form of perturbation theory, approximate second quantization, adiabatic approximation for systems with translational invariance, and other theoretical physics methods which play an important role in the theory of many-particle systems.
26.
In the other case, one may start with a finite number of generators, but in the course of second quantization, a need for an infinite number of generators arises : one each for every possible momentum that a fermion might carry.
27.
I now notice that Second Quantization / IRWolfie who posted this'complaint'only yesterday is now " "'taking a short wikibreak and will be back on Wikipedia in August or so "'" according to his talk page!
28.
One could say, " study wave equations, study Fourier transforms, study the hydrogen atom, study the simple harmonic oscillator, study Hilbert spaces, and study second quantization and how the uncertainty principle is just Pontryagin duality then you will " get it " ".
29.
This meant that quantizing a field " appeared " to be similar to quantizing a theory that was already quantized, leading to the fanciful term "'second quantization "'in the early literature, which is still used to describe field quantization, even though the modern interpretation detailed is different.
30.
The first step in second quantization is to express such quantum states in terms of "'occupation numbers "', by listing the number of particles occupying each of the single-particle states | \ phi _ 1 \ rang, | \ phi _ 2 \ rang, etc . This is simply another way of labelling the states.
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