Is the Lagrangian Invariant or Variant in a Coordinate System Shift?

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In summary, the conversation is discussing whether the Lagrangian is invariant or variant and whether it is a scalar or vector product. One person argues that the Lagrangian has the symmetries of the system it represents, while the other argues that it depends on the specific Lagrangian equation. The definition of invariant is also mentioned, stating that if there is a change, the Lagrangian will still look the same.
  • #1
shounakbhatta
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Hello,

Is Lagrangian invariant?

I am in a conversation, where one is saying that:

"Shifting the coordinate system changes the value of the potential energy with respect to the same reference level, that's why the Lagrangian changes"

While the other:

"Shifting the coordinate system, doesn't shift the zero reference level of potential for the system..
The reference level of potential is fixed for the system once it is decided upon."

So, is Lagrangian variant or invariant?

Please help.

Thanks.
 
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  • #2
The Lagrangian has the symmetries of the system that it represents.
 
  • #3
In the case can we consider that is it variant or invariant?

Also, is it a scalar or a vector product?
 
  • #4
it depends what the Lagrangian is. some Lagrangian equations will be variant and some will be invariant.

edit: the definition of invariant, is that if you make some change, then the Lagrangian will still look the same. So if you shift the coordinate system but the Lagrangian still looks the same, this means the Lagrangian is invariant with respect to a coordinate shift.
 
  • #5
If it is a variant in a equation then it cannot be scalar?

Is it that it becomes scalar as well as a vector?
 

Related to Is the Lagrangian Invariant or Variant in a Coordinate System Shift?

1. What is Lagrangian invariance?

Lagrangian invariance is a fundamental principle in physics that states that the equations of motion for a physical system should remain the same regardless of the coordinate system used to describe it. This means that the laws of physics should be independent of the specific reference frame chosen.

2. Why is Lagrangian invariance important?

Lagrangian invariance is important because it allows us to formulate the laws of physics in a way that is independent of the specific coordinate system used. This makes it easier to analyze and solve complex physical systems, and also ensures that the laws of physics hold true in all reference frames.

3. How is Lagrangian invariance related to symmetries?

Lagrangian invariance is closely related to symmetries in physics. A symmetry is a transformation that leaves the physical system unchanged. The principle of Lagrangian invariance states that the equations of motion should remain the same under these symmetries.

4. What are some examples of Lagrangian invariance in action?

One example of Lagrangian invariance is in the laws of conservation of energy and momentum. These laws hold true regardless of the reference frame used to describe the system, demonstrating the invariance of these physical quantities. Another example is the principle of relativity, which states that the laws of physics should be the same for all observers in uniform motion.

5. How is Lagrangian invariance used in practical applications?

Lagrangian invariance is used in a variety of practical applications in physics, such as in classical mechanics, quantum mechanics, and field theory. It allows physicists to formulate and solve complex physical systems, and has been foundational in the development of theories such as general relativity and the standard model of particle physics.

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