so what constitutes a field? is my back yard a field?

I'd say pretty much any area where grass is the dominant terrain feature.

If there happens to be numerous good-sized trees in your back yard, one could argue that it is Forest Domain.

If there are lots of trees with bit stretches of grasslands between them, it'd be both

If humans have "taken over the land" then it's Field (a regular grassland would be Prairie not Field, unless people regularly grew stuff on it, mowed it etc.) So we're talking stuff like farms, gardens/conservatories, cultivated forests and such.

In my games:

A back yard, like a house, is a domicile - it is associated with a family/person and therefore hearth domain. Leave the house/yard and you're into city domain.

A field would be any area governed by mankind for the purpose of agriculture or recreation - even if it's fallow.

Prarie would be the untamed version. Plus trees = forest.

as the Field is a spirit of Man I would say that any area of ground that is worked on or has recently been worked on by people.

I would class an apple orchard as either field or forest domain, prolly erring towards field. The same with a back yard thats either field or Heath.

The main thing that makes a field domain is that Man has had a hand in its creation unlike forest or wilderness areas.

A field is a commutative ring with identity such that every non-zero element is a unit.

Or you could say it is an abelian group with a second binary operation such that the group minus the identity under the first binary operation is also an abelian group under the second binary opperation. But this is a much more clumsy definition.

I have yet to run a shaman, but would the size of the field make any difference? Can it be part of the domain if it is a 20'x20' backyard? Or does it need to be a minimum of an acre, for example?

Size only makes a difference in the sense that a spirit is bound to its domain. So, for instance, if you were in an apple orchard with field and forest domains in the middle, but to either side, the trees get really thick or disappear, then the field spirit would be bound only to those areas considered "field" while a forest spirit would be bound only to those areas considered "forest". The two can overlap, but the right one needs to be present.

So your back yard could well be a "field". But what you're going to need a spirit to do in the confines of a 20'x20' area is a mystery to me. Unless you can invoke it in great form, that is.