What is a quantum field?
A quantum field is a list of questions attached to every region, everything answerable inside it without going out to look. Physics uses the word field for two objects. One is a value at every place. The other, the one the Standard Model is written in, gives each region every question its thermometers, plates and clocks could settle between them. Questions in two regions too far apart for light to cross give the same answers in either order of asking. No arrow sits at any point. Add up many copies of one thermal oscillation and the sum behaves as a free quantum field, its two halves depending on the order of asking exactly as position and momentum do. A field's value at a place is what every detector there agrees on once repairing is done.
Also in Chapter 22: Why Do All the Clocks Agree?.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 28: What Is a Particle, What Is a Wave, and Why Does It Look Like Both?watch a universe make its own particles