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field has 34 distinct synonyms spread across 10 of its 21 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a region where a battle is being (or has been) fought
“they made a tour of Civil War battlefields”
somewhere (away from a studio or office or library or laboratory) where practical work is done or data is collected
“anthropologists do much of their work in the field”
the space around a radiating body within which its electromagnetic oscillations can exert force on another similar body not in contact with it
a particular kind of commercial enterprise
“they are outstanding in their field”
a piece of land prepared for playing a game
“the home crowd cheered when Princeton took the field”
extensive tract of level open land
“they emerged from the woods onto a vast open plain”
(mathematics) a set of elements such that addition and multiplication are commutative and associative and multiplication is distributive over addition and there are two elements 0 and 1
“the set of all rational numbers is a field”
a region in which active military operations are in progress
“the army was in the field awaiting action”
all of the horses in a particular horse race
all the competitors in a particular contest or sporting event
a geographic region (land or sea) under which something valuable is found
“the diamond fields of South Africa”
the area that is visible (as through an optical instrument)
a place where planes take off and land
catch or pick up (balls) in baseball or cricket
answer adequately or successfully
“The lawyer fielded all questions from the press”
Synonyms, antonyms and the broader and narrower relations for field come from Princeton University’s WordNet. Full sources and licences.
select (a team or individual player) for a game
“The Buckeyes fielded a young new quarterback for the Rose Bowl”