Is it permissible for me to combine the Dhuhr and Asr prayers because I have a physics class that runs from 3:00 to 7:00, knowing that the teacher does not allow prayer in the middle of the lesson, and there are no other available times for the class?

Prayer must be a priority for a Muslim. The agreed-upon excuses for combining prayers for a resident are rain and illness. Some scholars permit combining prayers for a resident in case of hardship, based on the hadith of Ibn Abbas (may Allah be pleased with him) that the Prophet (peace be upon him) combined the Dhuhr and Asr prayers, and the Maghrib and Isha prayers in Medina, without fear or rain, to alleviate hardship for his Ummah. If you need to attend a lesson and pay money for it, then stipulate to the teacher that you be allowed to leave to perform prayer on time. If that is not possible, then there is no blame upon you for combining Asr prayer with Dhuhr prayer by performing it early, provided that you do not make this a habit.