field quantization
Field quantization is the procedure that turns a classical field — like the electromagnetic field of Maxwell — into a quantum field whose energy comes in discrete packets. You start with the classical field, decompose it into a set of independent vibrating modes, and then treat each mode exactly like a quantum harmonic oscillator. The energy of each mode can then only climb the ladder in whole steps, and each step corresponds to adding one quantum, that is, one particle.
Done this way, the photon is not assumed at the outset; it falls out as a result. Quantizing the electromagnetic field automatically produces quanta of light, each carrying energy proportional to its frequency, recovering Planck's and Einstein's early insights from a deeper principle. The same recipe applied to other fields yields their particles, which is why it is sometimes called canonical quantization.
Field quantization is what makes the leap from waves to particles precise rather than poetic. It explains why electromagnetic energy is absorbed and emitted in lumps, gives a firm meaning to creation and annihilation of particles, and even forces the vacuum to carry a residual zero-point energy. It is the technical heart of how a continuous classical field becomes a countable swarm of quanta.
Treat every mode as an oscillator: its rungs are particle counts, and the ½ is the mode's zero-point energy.
Calling this 'second quantization' is traditional but a bit of a misnomer: you are quantizing the classical field once. The deceptive name comes from historically quantizing the matter wave a second time after de Broglie's first quantization.