Regardless of what you use for power a rocket has to eject mass from the rear to propel you forward. Newton's second law. The problem is that as you increase

Regardless of what you use for power a rocket has to eject mass from the rear to propel you forward. Newton's second law. The problem is that as you increase burn times (like years at 1G), you need to increase the amount of mass you are pushing out the back. But to do this you increase the mass of your rocket which means you need to push even more mass out and it becomes a vicious circle of exponentially increasing rocket mass. The idea of accelerating at 1G for the entire trip only works if you have a source of propulsion that doesn't obey Newton's second law. Otherwise there literally isn't enough mass in the galaxy to make it work. The caveat being that if you can somehow exploit relativistic mass to effectively multiply your fuel it might be possible, but my math isn't good enough to work it out. My gut feeling is that it would require an unreasonable amount of power however, even for an extremely powerful nuclear power plant.