I think that the two are acceptable Genitive can be translated as "I see no book/I see no field" while Acc is more "I don't see the (particular) book/the field"

Mary, with negation - both. Actually the situation is a bit paradoxal: style guides (from 70s. well, we have exactly one respectable style guide - Розенталь's book) mark the gemitive form as more 'literary'. At the same time some guy here in 'answers' said that for him genitive sounds more colloquial:) Anyway: 'genitive' was considered The norm (except some specific cases). During 20th century accusative was getting more and more common... meanwhile taking unexpected grammatical functions. The most common of which is explained really well by Yuri. But take literally his 'more like'. It is not that we actually obtained 'the', it's just a shade. In MY perception (it is an ongoing process so other people may feel a different way), usinf Gen. for 'the book' is ok (and the old literary norm), while using Acc. you emphasize this 'the'. I.e. it is matter of your taste/choice and... moon. Now with names of persons the opposite happens: Я не видел Маши - is a bit like 'I saw/have see no Masha'. Я не видел Маши полгода - is a bit like 'not a bit of Masha' (genitive in hthe sense of 'partitive') With an important detail: it doesn't sound that playful, it is an acceptable literary expression (and a valid shade of meaning). Playful variation would be 'я не видел никакой Маши' - not a single Masha. Unfortunately, the aforementioned style guide gives a bit more detail.... And I checked the modern descriptive grammar of Russian... they have noticed more possible shades than I.

Глагол "видеть" используется с винительным падежом. Видеть кого? что? И.п. книга - В.п. - книгу И.п. поле - В.п. - поле А "книги" и "поля" - это уже родительный падеж. Разве не так? На самом деле этот вопрос поставит в тупик большинство носителей русского языка ) Поэтому если вы скажете любой из этих вариантов, вас поймут и не заметят подвоха ))

All your examples are correct. In old Russian we used transitive verbs with nouns in genitive to show the absence of something. The endings of both cases coincided therefore genitive case was easily replaced by the accusative in modern Russian. But some relics survived. If you have doubts, chose accusative.

I sure it depends on the case. For example: Я не вижу книгУ «я не вижу (что? ) ту книгу» or «я не вижу (чего? ) той книгИ» .