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There are basics questions that bugging me so much.

1. The road from classical partical to QF.

So particle in classical mech is discrete right, and we take a continuous

aproach to make it into classical field. But what does it mean by "quantizing" the field? Do we make it into a discrete entity again, but with certain rules (commutation rule)? So why is it called a field and not particle? Does it means that we can say that particle is field and field is particle just like we see the duality of wave-particle?

So what does it mean by "single particle wave equation then?

2. Fields, Particle and Antiparticle

In the beginning of ch 2, peskin wrote that single particle relativistic wave equation give rise to +ve and -ve energy. That's why we have no right to assume that any relativistic process can be explained in terms of single particle only but rather particle and antiparticle.

But then near the end of ch 2, we get equation of pi in terms of creation and annihilation operator. Can I then interpret the field as consist of particle and antiparticle which is represented by creation and anihilation operator?

Thanks