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Can Noether's theorem be understood intuitively?

Noether's theorem is one of those surprisingly clear results of mathematical calculations, for which I am inclined to think that some kind of intuitive understanding should or must be possible. ...
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Gelfand-Yaglom theorem for functional determinants

What is the 'Gelfand-Yaglom' Theorem? I have heard that it is used to calculate Functional determinants by solving an initial value problem of the form $Hy(x)-zy(x)=0$ with $y(0)=0$ and $y'(0)=1$. ...
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8k views

The Planck constant $\hbar$, the angular momentum, and the action

Is there anything interesting to say about the fact that the Planck constant $\hbar$, the angular momentum, and the action have the same units or is it a pure coincidence?
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Intuitive explanation for why time symmetry implies conservation of energy?

According to Noether's Theorem, every physical symmetry leads to a conservation law. For example, time-translation symmetry (the laws of physics don't change over time) implies conservation of energy,...
3k views

Variation of Action with time coordinate variations

I was trying to derive equation (65) in the review by László B. Szabados in Living Reviews in Relativity (2002, Article 4) This slightly unusual then usual classical mechanics because it includes a ...
3k views

Invariance of action $\Rightarrow$ covariance of field equations?

Invariance of action $\Rightarrow$ covariance of field equations? Is this statement true? I have only seen examples of this, like the invariance of Electromagnetic action under Lorentz ...
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9k views

Hamilton's characteristic and principal functions and separability

Just hoping for some clarity regarding Hamilton's characteristic function $W$. When we take a time independent Hamiltonian we can separate the Principal function $S$ up into the characteristic ...
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What variables does the action $S$ depend on?

Action is defined as, $$S ~=~ \int L(q, q', t) dt,$$ but my question is what variables does $S$ depend on? Is $S = S(q, t)$ or $S = S(q, q', t)$ where $q' := \frac{dq}{dt}$? In Wikipedia I've ...
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623 views

Connection between Noether's Theorem and classical definitions of energy / momentum

In classical mechanics, change in momentum $\Delta \mathbf p$ and change in kinetic energy $\Delta T$ of a particle are defined as follows in terms of the net force acting on the particle \$\mathbf F_\...
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