The term "second quantization" can be a bit misleading because it does not refer to a literal second round of quantization. Instead, it is a mathematical framework used in quantum field theory to describe systems with an arbitrary number of particles.
To understand why it is called "second quantization," let's consider the historical context. The development of quantum mechanics in the early 20th century primarily focused on describing the behavior of individual particles, such as electrons or photons. This formulation is often referred to as "first quantization." It deals with wave functions, operators, and observables for single particles.
However, when dealing with systems that involve a large number of identical particles, such as gases, solids, or fields, the first quantization approach becomes impractical. It is more convenient to describe these systems in terms of creation and annihilation operators, which represent the creation and destruction of particles.
The "second quantization" formalism introduces a new perspective by treating particles as excitations or quanta of quantum fields. The fields are defined at every point in space and time and can have varying numbers of particles present at different locations. This framework provides a more natural description of systems with varying particle numbers and allows for the creation and annihilation of particles.
So, in summary, the term "second quantization" arose because it introduced a new mathematical formalism to describe systems with many particles in terms of field operators, building upon the foundation of "first quantization" that focused on individual particles. It does not imply a repetition or a literal second round of quantization, but rather a different approach to understanding quantum systems with many particles.