why is a video file with .mts extension so huge?
HD video is very, very large at high quality.  450MB for two minutes isn't actually that bad.  To put it in perspective, assuming you were shooting 1080P and 24fps, if there was no compression applied, that same 2 minutes of video would be 6 gigabytes of information.

The reason that videos you download or watch on bluray disks are so much smaller is that they are not source video, but rather highly compressed final output video.  When you compress video, a lot of quality is lost.  It isn't quality that the human eye can easily distinguish, but it is quality that impacts the quality of future encodings and the quality of edited results.

For best quality, you want to take those high quality, large files you captured, edit them to whatever the final output should be and then do a one time compression down to a final output format.  That final output won't be suitable for editing, but it will be perfectly suitable for viewing at a much smaller size.

If you have no desire to edit it and simply want the basic video to be smaller, using a free tool like Handbrake or FFMPEG will easily allow you to transcode to h.264 and a much, much smaller file size.  I recommend using two-pass VBR to maximize the quality you get for the size.