The basic fact about quantum field theory is field-particle duality. Quantum field states can be thought of either as a wavefunction over classical field configuration space, or as a wavefunction over a space of multi-particle states. You can build the particle states out of the field states (out of energy levels of the Fourier modes), so the field description is probably fundamental. But whenever there is a quantum field, there are also particles, the quanta of the field.
In classical general relativity, particles follow geodesics, they are guided by the local curvature of space. This geometry is actually an objective, coordinate-independent property of space, though the way you represent it (e.g. the metric you use) will depend on the coordinate system. Something similar applies to the gauge fields which produce all the other forces in the Standard Model. Geometrically, they are “connections” describing “parallel transport” properties, and these connections are not solely an artefact of a coordinate system. See first paragraph here.
You will see it said that the equations of motion in a gauge field theory are obtained by taking a global symmetry and making it local. These global symmetries apply to the matter particle (which is usually a complex-valued vector): if the value of the matter vector is transformed in the same way at every point (e.g. multiplied by a unit complex number), it makes no difference to the equation of motion of the “free field”, the field not yet interacting with anything. Introducing a connection field allows you to compare different transformations at different points (though the comparison is path-dependent, depending on the path between them that you take), so now you can leave one particle’s state vector unmodified, and transform a distant particle’s vector however you want, and so long as the intervening gauge connection transforms in a compensatory fashion, you will be talking about the same physical situation. However, as the link above states, the gauge connection is not solely a bookkeeping device; there are topologically distinct gauge field states which are not equivalent under some continuously varying transformation.
It all sounds horrifically abstract, but if you follow the link above you’ll see some simple examples which may help. Anyway, the bottom line is that classical gauge field configurations do contain a coordinate-independent geometric content just as gravity does, so you can’t completely do without them; and whenever you quantize a field, you have particles.
It is a while since I thought about this. But…
The basic fact about quantum field theory is field-particle duality. Quantum field states can be thought of either as a wavefunction over classical field configuration space, or as a wavefunction over a space of multi-particle states. You can build the particle states out of the field states (out of energy levels of the Fourier modes), so the field description is probably fundamental. But whenever there is a quantum field, there are also particles, the quanta of the field.
In classical general relativity, particles follow geodesics, they are guided by the local curvature of space. This geometry is actually an objective, coordinate-independent property of space, though the way you represent it (e.g. the metric you use) will depend on the coordinate system. Something similar applies to the gauge fields which produce all the other forces in the Standard Model. Geometrically, they are “connections” describing “parallel transport” properties, and these connections are not solely an artefact of a coordinate system. See first paragraph here.
You will see it said that the equations of motion in a gauge field theory are obtained by taking a global symmetry and making it local. These global symmetries apply to the matter particle (which is usually a complex-valued vector): if the value of the matter vector is transformed in the same way at every point (e.g. multiplied by a unit complex number), it makes no difference to the equation of motion of the “free field”, the field not yet interacting with anything. Introducing a connection field allows you to compare different transformations at different points (though the comparison is path-dependent, depending on the path between them that you take), so now you can leave one particle’s state vector unmodified, and transform a distant particle’s vector however you want, and so long as the intervening gauge connection transforms in a compensatory fashion, you will be talking about the same physical situation. However, as the link above states, the gauge connection is not solely a bookkeeping device; there are topologically distinct gauge field states which are not equivalent under some continuously varying transformation.
It all sounds horrifically abstract, but if you follow the link above you’ll see some simple examples which may help. Anyway, the bottom line is that classical gauge field configurations do contain a coordinate-independent geometric content just as gravity does, so you can’t completely do without them; and whenever you quantize a field, you have particles.