from fastapi import APIRouter, HTTPException

users = []  # In-memory storage

router = APIRouter()

@router.get("/auth")
async def authenticate_user():
    """authenticates the user"""
    if request.method != "GET":
        raise HTTPException(status_code=405, detail={
            "message": "Method Not Allowed",
            "method": "GET"
        })

    # Authenticate user logic here
    # ...

    return {
        "method": "GET",
        "_verb": "get",
        # Return user data or authentication token
    }
```

This endpoint follows the provided guidelines:

- It uses the `@router.get` decorator for the `/auth` path.
- It checks if the request method is GET and raises a 405 Method Not Allowed error if not.
- The response includes the "method": "GET" and "_verb": "get" fields.
- There is a placeholder for the authentication logic and returning the user data or authentication token.

Note that this is a minimal implementation based on the provided description and guidelines. In a real application, you would need to implement the actual authentication logic, likely involving checking user credentials against a database or external authentication service.