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4
questions
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2
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Confusion about potential energy, field energy, kinetic energy
I have some confusion about potential energy in Newtonian mechanics and field energy in classical Field mechanics. I have many questions but they are all strongly related.
In Newtonian mechanics, we ...
- 2,982
7
votes
2
answers
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Lagrangian potential for Newtonian gravity
In the Wikipedia site for Lagrangian (field theory) the Lagrangian density for Newtonian gravity is given by
$${\cal L}(\mathbf{x},t) = \frac{1}{2}\rho(\mathbf{x},t)\mathbf{v}^2 -\rho(\mathbf{x},t) \...
- 105
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1
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Doesn't the "Mexican hat" potential give a misleading impression that the barrier height between two vacua is finite?
For $\mathbb{Z}_2$ symmetry breaking in a Classical Field Theory described by a potential $$V(\phi)=\lambda(\phi^2-v^2)^2,\tag{1}$$ there is a finite energy barrier of height $\epsilon=\lambda v^4$ ...
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4
votes
3
answers
534
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Energy contributions of Hamiltonian density
In Lancaster and Blundell, Quantum Field Theory for the Gifted Amateur, p.99, the Hamiltonian density is
\begin{equation}
\mathcal{H}=\frac{1}{2}[\partial_0\phi(x)]^2+\frac{1}{2}[\nabla\phi(x)]^2+\...
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