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hideelo
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The title sort of says it all, but I'll clarify a bit. Is there any intuition for what Lagrangians are and what action is. I'm asking in all generality, not just for classical mechanics.
dextercioby said:In a nutshell, they are very handy calculational tools, especially when doing quantum field theory, one of the 2 most successful theories of physics. Intuition is built once you read the proper sources. I'd consider Landau&Lifshits' classical mechanics gem.
Hi, I definitely subscribe this but I would like to add: Lagrangians are nothing else but the formulation and application of a variational principle. It works since nature seems to use the shortest path. It begins from classical mechanics of some particles, is great if you come then to field lagrangians and they are used in classical mechanics and QFT wildely.hideelo said:The title sort of says it all, but I'll clarify a bit. Is there any intuition for what Lagrangians are and what action is. I'm asking in all generality, not just for classical mechanics.
I'll check it outdextercioby said:In a nutshell, they are very handy calculational tools, especially when doing quantum field theory, one of the 2 most successful theories of physics. Intuition is built once you read the proper sources. I'd consider Landau&Lifshits' classical mechanics gem.
A Lagrangian is a mathematical function that describes the dynamics of a physical system in terms of its position and velocity. It is important because it allows us to model and analyze complex physical systems using the principles of classical mechanics.
The action of a physical system is defined as the integral of the Lagrangian over time. In other words, the action is a measure of the total energy of a system over a specific period of time. The Lagrangian is therefore an essential component in calculating the action of a system.
Intuition is crucial in understanding Lagrangians and action because these concepts are highly abstract and mathematical. Intuition allows us to make connections between mathematical equations and physical phenomena, making it easier to interpret and apply the concepts to real-world situations.
One example is the use of Lagrangians and action in classical mechanics to describe the motion of a pendulum. The Lagrangian takes into account the position and velocity of the pendulum, and the action is calculated as the integral of the Lagrangian over time. This allows us to predict the motion of the pendulum and understand its energy and forces at any given point in time.
No, Lagrangians and action can also be applied to other areas of physics, such as quantum mechanics and field theory. In these fields, the concepts are used to describe the behavior of particles and fields, and to calculate the probabilities of different physical outcomes.