# Is every particle sustained ripple in its respective field?

This is neither a homework nor a calculational question, but more of a conceptual one.

I was wondering can every particle; that is, the ones indivisible (because divisible ones can be broken down into constituents quarks, etc.); be characterized as just a "ripple" in its respective field. In essence, what I am asking is can we formulate quantum and macro physics just in-terms of field without ontologizing particles?

For instance,

1. a photon being a "ripple," or excitation to be exact, in the electromagnetic field.
2. Higgs particle being an excitation of higgs field...

And so forth!

Also, feel free to correct any misunderstandings evident in the question!

• I removed a comment thread that was getting unnecessarily heated. Please remember to assume good faith on the part of other users and to not respond in kind when you feel attacked. Please also remember that comments are for criticizing and improving the question, not for giving partial answers or your own opinions on a topic. Commented Feb 21, 2019 at 18:02

The field theory of elementary particles is based on quantum mechanics. For each particle in the elementary particle table

of the standard model of particle physics, it is posited that a field exists covering all space-time, in the following mathematical model:

The field is represented by the free particle wave function solution of the corresponding equation, dirac for fermions,klein gordon for bosons, quantized maxwell for photons.

Wave functions are complex functions and in this sense not "real", i.e. not into one to one correspondence with real numbers. Creation and annihilation operators acting sequentially on the electron field, for example, will propagate the electron in space time, and Feyman diagrams have been developed in order to be able to calculate interactions between particles to be compared with experiment, real numbers.

A free traveling electron cannot be represented by the plane wave solutions,which cover from minus-infinity to plus-infinity in energy and momentum and spacetime, because it is localized, and wave packet solutions are used in this case, that should satisfy the Heisenberg Uncertainty principle for that energy and momentum and location, though there is just the conceptual need for such a description. For any comparison with experiments it is interactions of particles that are checked by the Feynman diagram calculations, and the creation/annihilation operators on the plane waves are adequate for that, afaik.

a photon being a "ripple," or excitation to be exact, in the electromagnetic field.

A single non interacting photon has to be a wavepacket on the photon field, propagating the energy/momentum of the photon with creation and annihilation operators over a wavepacket of plain waves.

> Higgs particle being an excitation of higgs field..

Ditto for Higgs.

One could conceptually think of the wavepackets as solitons travelling on the underlying complex fields , but one should always remember all these models are based on quantum mechanics, a basically probabilistic theory, connecting calculations to real numbers .

• Hi, thank you for the answer. Please correct me it I am missing something, but what I am understanding so far is that almost all particles except an electron can be conceptualized as just an excitation. As for photon being a wave packet, I agree with that. Since it is not stationary, and its self propagating, but what I am wondering: can we still think of a photon as just that, a self propagating energy fluctuation, right? Commented Feb 21, 2019 at 19:07
• @BertrandWittgenstein'sGhost Electrons are no special--they are also the so-called excitations in the electron-field. We usually don't talk much about the field corresponding to the matter particles such as electrons, quarks, muons, etc. but nonetheless, they are, in the framework of QFT, excitations in their respective fields.
– user87745
Commented Feb 21, 2019 at 19:17
• @BertrandWittgenstein'sGhost There is some nice accessible discussion on the field-particle issue in the introductory chapter of Ryder's QFT book. Have fun! :)
– user87745
Commented Feb 21, 2019 at 19:24