The operation is performed under anaesthetic. 手术是在麻醉状态下进行的。
The procedure is carried out under local anaesthetic (= a substance that makes you unable to feel pain in part of your body). 这一过程是在局部麻醉的状态下完成的。
I've never had a general anaesthetic (= a substance that makes you unconscious so you do not feel pain). 我从来没有做过全身麻醉。