I have read in a book sentence: "operation first requires that a permit be obtained"
As I understand this sentence is a passive voice in the infinitive form but why here "be" is used without "to"?
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There are times when infinitives lack a 'to'. These are called bare infinitives.
However, what you see in the phrase "operation first requires that a permit be obtained" is not an infinitive but a subjunctive. (It is true that the sentence would also make sense with an infinitive: "...requires a permit to be obtained". Here you would need to include the "to" and exclude the "that".)
Usually the present subjunctive is identical to the present indicative (in the case of the 1st person singular, 2nd personal singular, and all the persons in the plural) but differs in the 3rd person singular by the lack of terminal "s". E.g. "I asked that she sing".
However, for the verb "to be", the form "be" is the present subjunctive for all persons.