The lagrangian of quantum electro dynamics is mc -+ c =ch x show that this lagrangian is gauge invariant. what is the euler-lagrange equation for the fields a,? what is the euler-lagrange equation for the field transform this equation in into an equation

Calculate the heat capacity per object when the total energy is 4 quanta. (think of this in terms of increasing from 3.5 quanta of energy in the system to 4.5 quanta of energy in the system, if that were possible.) c4 = __ j/k/object

Consider an ordinary, helium-filled party balloon with a volume of 2.2 ft3. the lifting force on the balloon due to the outside air is the net resultant of the pressure distribution exerted on the exterior surface of the balloon. using this fact, we can derive archimedes’ principle, namely that the upward force on the balloon is equal to the weight of the air displaced by the balloon. assuming that the balloon is at sea level, where the air density is 0.002377 slug/ft3, calculate the maximum weight that can be lifted by the balloon. note: the molecular weight of air is 28.8 and that of helium is 4.

Avehicle has an oil leak that is causing the entire oil pan to be wet, but inspection reveals no exact source after cleaning off the oil residue. technician a says to install a fluorescent dye in the crankcase and operate the engine, then re-inspect for leaks with a special light (black light). technician b says the oil leak may be coming from a source at the top of the engine, such as a valve cover gasket. who is correct?