A If the solution of a field vanishes on-shell does it mean anything?

AI Thread Summary
The action S=S(a,b,c) describes a functional relationship among fields a, b, and c, where the solution for field c is expressed as f(a,b). When f(a,b)=0, it indicates that c vanishes on-shell, meaning that c's behavior is entirely determined by fields a and b when they satisfy the equations of motion. This on-shell condition signifies that field c lacks independent dynamics, acting as a constraint on the system. Additionally, such conditions may arise from underlying symmetries or conservation laws within the action S. Overall, the vanishing of field c on-shell reveals important insights into the system's dynamics and symmetries.
Baela
Messages
17
Reaction score
2
Let us consider an action ##S=S(a,b,c)## which is a functional of the fields ##a,\, b,\,## and ##c##. The solution of the field ##c## is given by the expression ##f(a,b)##. On taking into account the relations obtained from the solutions for ##a## and ##b##, we find that ##f(a,b)=0##. If the solution for the field ##c## vanishes on-shell, does it mean anything particular?
 
Physics news on Phys.org


Yes, the fact that the solution for the field ##c## vanishes on-shell has a specific meaning in this context. It means that when the fields ##a## and ##b## satisfy the equations of motion, the field ##c## automatically satisfies the equation ##f(a,b)=0##. This is known as the on-shell condition for the field ##c##.

Physically, this on-shell condition indicates that the field ##c## does not have any independent dynamics and its behavior is completely determined by the fields ##a## and ##b##. This can be interpreted as a constraint on the dynamics of the system, where the value of ##c## is completely determined by the values of ##a## and ##b## at every point in spacetime.

In some cases, the on-shell condition for a field may also arise due to symmetries or conservation laws in the system. For example, if the action ##S## is invariant under a certain symmetry transformation, then the on-shell condition for the corresponding field would be a consequence of this symmetry.

In summary, the vanishing of the solution for a field on-shell has a significant meaning and can provide insights into the dynamics and symmetries of the system.
 
Thread 'Question about pressure of a liquid'
I am looking at pressure in liquids and I am testing my idea. The vertical tube is 100m, the contraption is filled with water. The vertical tube is very thin(maybe 1mm^2 cross section). The area of the base is ~100m^2. Will he top half be launched in the air if suddenly it cracked?- assuming its light enough. I want to test my idea that if I had a thin long ruber tube that I lifted up, then the pressure at "red lines" will be high and that the $force = pressure * area$ would be massive...
I feel it should be solvable we just need to find a perfect pattern, and there will be a general pattern since the forces acting are based on a single function, so..... you can't actually say it is unsolvable right? Cause imaging 3 bodies actually existed somwhere in this universe then nature isn't gonna wait till we predict it! And yea I have checked in many places that tiny changes cause large changes so it becomes chaos........ but still I just can't accept that it is impossible to solve...
Back
Top