AND, OR, NOT operator not available in Elastic App Search?

Question

Do we have AND, OR, and NOT operator in Elastic APP SEARCH(not Elasticsearch)? I read the documentation and felt it is not exhaustive for all use cases.

I tried:

{
  "search_fields": {
    "title": {},
    "description": {},
    "states": {}
  },
  "query": "My AND test AND Query"
}

but I believe it doesn't do anything.

Do I have to migrate to Elasticsearch for the same?