So the symmetrization (or anti-symmetrization) must be introduced to eliminate this redundancy in the first quantization description.

Unlike first quantization, conventional second quantization is completely unambiguous, in effect a functor.

Using a technique introduced by Rhorlich for the ordinary free string, we perform a first quantization of this spinning string.

In the field theory context, it is also called second quantization, in contrast to the semi-classical first quantization for single particles.

In the first quantization language, the many-body state is described by answering a series of questions like "which particle is on which state".

In quantum theory (see first quantization) the energy of the photons is thus directly proportional to the frequency of the EMR wave.

First quantized wave functions involve complicated symmetrization procedures to describe physically realizable many-body states because the language of first quantization is redundant for indistinguishable particles.

Thus, by convention, the original form of particle quantum mechanics is denoted first quantization, while quantum field theory is formulated in the language of second quantization.

In the first quantization formalism, this constraint is guaranteed by representing the wave function as linear combination of permanents (for bosons) or determinants (for fermions) of single-particle states.

First quantization is appropriate for studying a single quantum-mechanical system being controlled by a laboratory apparatus that is itself large enough that classical mechanics is applicable to most of the apparatus.

A first quantization of a physical system is a semi-classical treatment of quantum mechanics, in which particles or physical objects are treated using quantum wave functions but the surrounding environment (for example a potential well or a bulk electromagnetic field or gravitational field) is treated classically.

It is also known as canonical quantization in quantum field theory, in which the fields (typically as the wave functions of matters) are thought of as field operators, in a similar manner to how the physical quantities (position, momentum etc.) are thought of as operators in first quantization.