# What is a particle in QFT framework? [duplicate]

I've heard that in QFT a particle is a local excitation of a quantized field, but I can't understand how can I imagine this. For example in the second quantization of the Klein-Gordon field we get an operator like this $$\Phi = \int d^3pN_p(a_p^{\dagger}e^{i(\omega_pt-px)}+a_pe^{-i(\omega_pt-px)})$$ What does this physically mean? Where do the particles come from? Is it correct to imagine a particle like a perturbation of this field, whatever it means?

• Welcome to Physics! I have made a couple of edits to your question to make the language sound more natural. Please feel free to revert these edits (or make further edits) if I have changed the meaning of your question. Commented Feb 7, 2022 at 14:17
• Possible duplicates: physics.stackexchange.com/q/163691/50583, physics.stackexchange.com/q/127141/50583 Commented Feb 7, 2022 at 14:30

When you quantize a free Klein-Gordon field, you find the spectrum is described by a Fock space. Each Fourier mode obeys the equation for a harmonic oscillator. Therefore, each of the $$a_p^\dagger$$ operators acts like a creation operator, creating an excitation in mode $$p$$, much like in the harmonic oscillator in quantum mechanics, the creation operator creates an excitation. For each value of $$p$$, you can create an infinite tower of states, labeled by $$n_p$$, the number of excitations with momentum $$p$$. We interpret $$n_p$$ as the number of particles with momentum $$p$$.