The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Use Numeric Column Types For Numeric Values (query line: 23): Referencing a numeric value (e.g. 581280193) as a string in a WHERE clause might result in poor performance. Possible impacts of storing numbers as varchars: more space will be used, you won't be able to perform arithmetic operations, the data won't be self-validated, aggregation functions like SUM won't work, the output may sort incorrectly and more. If the column is numeric, remove the quotes from the constant value, to make sure a numeric comparison is done.

Optimal indexes for this query:

CREATE INDEX transaction_detail_idx_line_descr_av_id_transactio ON transaction_detail (line_object_description,av_transaction_id,transaction_date);

The optimized query:

SELECT
        t1.av_transaction_id,
        round(SUM((t1.gross_line_amount - t1.pos_discount_amount)),
        2) AS total_amount_with_discount,
        round(SUM((t1.gross_line_amount)),
        2) AS total_amount,
        round(SUM((t1.pos_discount_amount)),
        2) AS total_discount,
        round(SUM((t2.gross_line_amount)),
        2) AS total_sales_tax 
    FROM
        transaction_detail AS t1 
    INNER JOIN
        transaction_detail AS t2 
            ON t1.av_transaction_id = t2.av_transaction_id 
            AND t1.transaction_date = t2.transaction_date 
    WHERE
        (
            t1.sku_id IS NOT NULL 
            OR t1.line_action_display_descr = 'sold'
        ) 
        AND t2.line_object_description = 'S6 Sales Tax' 
        AND t1.av_transaction_id = '581280193' 
    GROUP BY
        t1.av_transaction_id