Index to find records where the foreign key does not exist

table products
id primary_key

table transactions
product_id foreign_key references products

The below SQL query is very slow:

SELECT products.* 
FROM   products 
       LEFT JOIN transactions 
              ON ( products.id = transactions.product_id ) 
WHERE  transactions.product_id IS NULL; 

Out of 100 hundred million products records, there might be only 100 records where a product has no corresponding transactions.

This query is very slow as I suspect it is doing a full table scan to find those null foreign key product records.

I want to create a partial index like this:

CREATE INDEX products_with_no_transactions_index 
ON (Left JOIN TABLE 
    BETWEEN products AND transactions) 
WHERE transactions.product_id IS NULL;

Is the above possible and how would I go about it?

Note: Some characteristics of this data set:

1. Transactions are never deleted and only added.

2. Products are never deleted but added at a rate of 100s per minute (obviously this is a made up example behind a much more complex actual use case). A small perchange of those are temporarily orphaned

3. I need to frequently query (up to once per minute) and need to always know what the current set of orphaned products are