In quantum field theory, particle state is a ray that provides poincare group irreducible representation in Hilbert state space of quantum mechanics.

That's basically it. As far as mathematical description is concerned, it sounds profound! Electrons, photons, gravitons and Higgs bosons are all different variants of the above objects: they only exist in poincare group in different forms and may carry internal charges (such as charges).

The result of this description is completely consistent with the fact that the behaviors of these entities are exactly the same, at least qualitatively, and they may be more familiar with the examples of quantum dot particles in single particle theory (such as giant particles in potential wells, or similar things).

Therefore, all the usual intuition about particles from the simple quantum mechanical model can be applied to the examples of quantum field theory. Particles are abstract states in Hilbert space, carrying physical quantities (mass, spin, charge, etc. They have no specific position, no size, no waves at all, and no point objects. Once you understand that they are not necessarily either of these two things, you will understand that wave-particle duality is not a "problem", it just reflects our ignorance; The result of trying to confuse our classical intuition with the quantum world is obviously flawed and unnecessary.

They are quantum.

"What is quantum?" 1900 In one hundred years, Max Planck put forward the idea that the electromagnetic field is not a continuous "classical" field, but is composed of fragments or blocks, which he called "quantum" (from Latin quantum, meaning "how much"). Although Maxwell's classical electromagnetic field can be arbitrarily small, the quantum field is composed of blocks that cannot be reduced any more. Quantum can overlap each other, but each quantum keeps its own characteristics; It has its own life and its own death. In this sense, and only in this sense, a field quantum is similar to a particle.

Particles are quantum computers. In the 1920s, it was found that the particles that make up matter showed the characteristics of waves. This leads to the development of quantum mechanics, which has the characteristics of wave-particle duality. When QFT appeared, this annoying problem (see Northam's quotation) was solved. QFT has no particles; Only fields. 1954, Julian Schwinger completed the QFT formula, and finally treated the force field and the material field equally.