I am confused about the word "particle" being used in academic contexts. Some professors at my university are adamant on the fact that particles do not exist, and only fields, as per QFT. One of them even showed me a citation from one of Julian Schwinger's QM books where he himself states this supposed fact. I've been going around to different professors asking for explanations, but I'm still a bit confused, so I thought I could make a consultation here. Some of the profs I've asked say there are only simulations of particles, yet "particle physics" is still a valid area of research, and even the Wikipedia page (I know) for QFT defines it as "...the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics." So I am just confused about the usage of the word "particle" being used today, if QFT is the widely accepted theory, and QFT says that there are no particles, only excitations of fields.
People who claim that there are only fields of the particles given in the particle table of elementary particles and particles are an emergent phenomenon are platonists. I.e. they believe that mathematical functions exist as molds and nature fill up the mold with the appropriate behavior. These tend to be theoretical physicists.
Experimental physicists follow the beliefs that Nature exists, and mathematics is a tool that allows to model nature, to describe it and predict future behaviors, but there is no ultimate theory or point of view, at the moment.
Back when I was in graduate studies in 1961, I learned field theory in a nuclear physics course, with the creation and annihilation operators working on nuclei ( I have forgotten most of the stuff) and nuclear physicists are still working on this.. Thus I view field theory as a beautiful calculational tool for many-particle systems, but for me, as an experimental physicist, particles exist.
The confusion goes away if one defines what is a particle in classical physics, how the name went to cosmic rays and particle physics became a term, and what is a quantum field theory.
A particle in classical mechanics can be kinematically described by its mass and the motion of its center-of-mass system is a unique and specific trajectory and characterizes its motion. An impact point of the classical particle is a specific (x,y,z) at time t. A ball hits a wall at a point.
Look at this bubble chamber picture and tell me that those are not particles as defined in classical physics turning in a magnetic field perpendicular to the plane of the picture:
The quantum mechanical framework, complete with its tools of field theoretical calculations has to enter to mathematically model the decays and their angular distribution, and it is trite to state that these distributions are probabilistic obeying quantum mechanical rules.
So depending on the boundary conditions the pion, for example, displays classical particle identity, and at the decay point, it displays its quantum mechanical nature which needs the whole quantum mechanics background to be described and predictable statements made.
It is really the "wave-particle" duality that is displayed in this simple picture, where for "wave" substitute "quantum field theory".
If experiments in the future validate a "Theory of Everything" I would be willing to adopt the platonic idea, because it means any measurement will be predictable by the TOE. But as each generation of physicists thinks they have solved all physics questions and only engineering problems remain most probably the platonists fall in the hubris of thinking we have reached the end of our observations of nature and we need no new or even radical mathematical tools to describe it.
The modern viewpoint is that there are no particles, only fields. However, excitations of these fields behave like particles, and you can interpret many states in a given field theory in a particle picture where you consider them as particles. Nothing about this is inherently wrong as long as you know the underlying physics.
As far as I can tell, other than the fact that when we detect field excitations, they behave like particles, the reason we call it "particle physics" is because it's easier to say and explain, and it maps well onto older terminology that isn't incorrect for the experiments most people are doing.
Currently I'm having trouble trying to think of a name that would be more technically accurate that isn't too overly long and complicated. "Field physics" wouldn't work because fields are too general a concept and it doesn't often get at the core of what people are doing; "field excitation physics" is just a mouthful and in general would require giving too much explanation. "Particle physics" cuts right to the important matters in a way that practitioners understand and can be easily understood without getting a truly wrong idea of whats going on.
Well, the "modern viewpoint" in @Jared Dziurgot's answer is not shared by everyone. It is equally possible to say that there are only particles and fields are merely helpful mathematical tools to describe them. For example, one famous promoter of this perspective this is Nima Arkani-Hamed. He likes to say:
"particles are physical, fields are not - just ask your experimental colleagues what they measure... "
This also applies to @Darkseid's answer. The magnetic and electric fields that we measure consist of many many particles if we take a closer look.
This is an ontological question. Different people may express different point of views on the subject. There is some truth to both particles and field being fundamental.
In a sense all our experiments involve particles. We accelerate and collide hadrons, leptons, and are generally interested in the particles that they produce. If viewed this way - one could say that the fields are just a convenient instrument to describe this.
On the other hand, magnetic and electric fields are observable (e.g. through particle tracks in a cloud chamber. Which may suggest that the fields are fundamental.
All in all, both views are correct as long as you know how it works from underlying principles.
The concept of "particle" comes from our need to explain nature in terms that we can understand. It doesn't necessarily mean that there is such a thing as a particle. It just means that we can observe certain phenomena and we find it convenient to say that they correspond to a particle.
Whatever definition you wish to use, it always needs to depend on the context you are using it in. And that is also where it is valid. The concept of particle is very useful in classical mechanics, and some aspects of quantum mechanics. As we probe deeper into microscopic world it loses its validity.
The current and best description we have of that subatomic world is described by quantum field theory and the underlying "building blocks" are the fields. This is a different context than classical mechanics. The fields in quantum field theory create phenomena that we find convenient to say are created by particles if we wish to explain them using terms we are more familiar with.
In summary, whether "particles" exist is indeed an ontological/epistomological question and it shouldn't be worrying a physicist. Leave it to philosophers.
It is worth remembering, as others have indicated, "All models are wrong but some are useful". The choice of a wave or particle model fits in right there. People often take up very particular positions on these sort of things when procastinating in public, even though they may see some sense in the alternates in private.
The Wave - Particle discussion has two different aspects.
The first is the Classical - Quantum distinction, and often it is this case that is being put. The classical Newtonian approach beings to fail at some point and and a broader method becomes useful. In this case the distictions are made artificially gross and over-done, using attention grabbing phraseology that tries to squeeze out any thought.
The second is the concept of it being wave-particle duality wherby there is a mathematical equivalence between the two approaches. Usually here both sides drop some alledgedly minor factor for their approach which then breaks the duality. Particle have no width. Waves have no centre. Most wave approaches pretend the wave is plane and infinite, thus has infinite energy (or it has negligible existance). Or it is polarised and spherical (Mott), hence without poles.
Once one gains a wave origin and direction, one has a 'particle'. Just as 'particles' need to gain a width to their fuzz ball existance. They are then quantum realistic, while the plane wave / perfect impulse view was a non-physical mathematical ideal.
The extra bit of information is that most of Physics appears to have missed the developments in Wavelets which provide a set of wave functions 'wavelets' that have compact support for their finite energy and form a full set of bases for these 'particle's. In particular "The Friendly Guide to Wavelets" by Gerald Kaiser (mathematician) covers how they solve the EM wave equation and Schrodingers equation, and where the uncertainty principle came from (Fourier), and that Heiseberg linked it to the quantum system.
Neither plain waves nor point particles are good represenations of physical reality.
The key to solving your confusion, is to remember that SM, QM, QFT, etc., are only models, who's purpose is to help us understand our world. Also, you need to understand that each of these models, has its own vocabulary, jargon, and expressions, which are used to describe their theories. So, if QFT wants to use "excitation fields" for something that SM calls "particles," it should cause you no trouble. You just have to learn the "jargon" of each model, so that you can understand it.