# Questions tagged [action]

The action is the integral of the Lagrangian over time, or the integral of the Lagrangian Density over both time and space.

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### Massive spin-1 field and Proca Lagrangian

In his book Quantum Field Theory and the Standard Model, Matthew D. Schwartz derives the Lagrangian for the massive spin 1 field (section 8.2.2). In eq. (8.23) he finds this to be \begin{align} \...
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### Variation of action with vectors

Assume an action $$S= \int{d^2x \;\vec{v}\cdot(\partial_\mu\vec{v}\times\partial_\nu\vec{v}})\;\epsilon^{\mu\nu}$$ where $\vec{v}$ a 3-vector field $\vec{v}=(v_1,v_2,v_3$) and $\epsilon^{\mu\nu}$ ...
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### How do we get Maupertuis Principle from Hamilton's Principle?

Maupertuis principle says that if we know the initial and final coordinates but not time, the total energy and the fact that energy is conserved, we can choose the "right" path from all mathematically ...
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### Palatini action (General Relativity)

I'm reading this lecture notes (Lecture III: Ashtekar variables for general relativity) about Tetrad Formalism in General Relativity. In page 8-9 the Palatini action is defined (basically the Einstein-...
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### Assumptions reg. Kinetic energy and Potential energy in the Lagrangian formulation

I have recently been introduced to Lagrangian mechanics. My previous exposure to Lagrangian math has been in the form of optimizing constrained functions using Lagrange multipliers. I get the math ...
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### Can we construct a system in which two distinct paths give the same actions? If so, how does the system evolve? [duplicate]

Say we construct the Lagrangian for a system and minimise the action, what happens if this is not unique? In other words the action is minimised by two distinct (not infinitesimally separated) paths. ...
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### Principle of least action with non-conservative forces?

See this excerpt from Kinematic and Dynamic Simulation of Multibody Systems page 122-123: Consider a system characterized by a set of $n$ independent coordiunates $q_i$. Let $L=T-V$ be the system ...
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### Tensor density and the coefficient $\sqrt{-g}$

Usually it is claimed that we use the coefficient $$\sqrt{-g}$$ for the action in the curved spacetime, to make the integrand treats as a scalar but not as a scalar density under general coordinate ...
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### Deeper Meaning to the Nature of Lagrangian

Is there a more fundamental reason for the Classical Lagrangian to be $T-V$ and Electromagnetic Lagrangian to be $T-V+ qA.v$ or is it simply because we can derive Newton's Second Law and Lorentz Force ...
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### Is there a deep reason why action comes from a local lagrangian?

In both classical and quantum physics Lagrangians play a very important role. In classical physics, paths that extremize the action $S$ are the solutions of the Euler-Lagrange equations, and the ...
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### What does “up to a total derivative” really mean and how should I know when to use it?

I am a mathematician who is taking a quantum field theory course without much prior pyhsics. We have had the term "up to a total derivative" a few times, yet every time I asked what it meant I didn't ...
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### How does a falling rock minimize action?

Consider a single two dimensional system with a rock that is influenced by gravity. The Action of this system is defined as $\int_0^\infty [T(\dot x(t))-V(x(t))]dt$, where $T$ is the kinetic and $V$ ...
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### Action for extended objects

Take a spacetime $M$, with some $k$-manifold embedding $$X : \Sigma \to M$$ The image of $X$ represents some extended object (a $k$-brane as the string theory people say). If we only care about the ...
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### Sign of gravitational action

I am reading this paper on Black hole phase transition in AdS, but for the life of me I cannot get the signs right for the expression of the Action of a Black Hole in AdS (eq (2.9)). Consider the AdS ...
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### How do the Euler-Lagrange equations generalise to an arbitrary manifold?

So every formalism for the EL equations I have seen relies on choosing a coordinate chart. However, if we had say, a field on a sphere, then we can’t have global coordinates. How, in principle, ...
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### Effective action for ferromagnetism and ferroelectricity

In Three Lectures On Topological Phases Of Matter section 2.1 mentioned, that: $$I^\prime = \int dt d^3x \; \left(\vec{a}\vec{E}+\vec{b}\vec{B}\right)$$ correspond to ferromagnetism and ...