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I) Here we will assume that OP is taking about a relativistic point particle with zero spin in a Minkowski spacetime with metric $\eta_{\mu\nu}$ of sign convention $(−,+,+,+)$. Also we put $c=1$ for simplicity. (OP mentioned that the particle has charge but since it is free that is irrelevant.) Note that the relativistic point particle has world-line ...

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I assume that by "potential $V$ of the scalar field" is meant "everything that stands on the right of $\partial \overline \phi \partial \phi$ in the scalar field's lagrangian", e.g. $V=-m^2 \overline \phi \phi$ for the complex KG field. Assuming that $V$ is invariant under $U(1)$ gauge transformations, you can introduce a covariant derivative in the usual ...

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Well, not really. We COULD write hamiltonian as square root - if we know, what is a square root of an operator. Of course we have simple approximation: $$\sqrt{1+x}=1+\frac x2-\frac{x^2}{8}+O(x^3)$$ Using this we could write your hamiltonian as: $$\mathcal H=mc^2\sqrt{1+\frac{p^2}{m^2c^2}}=mc^2+\frac{p^2}{2m}+O(p^4).$$ The problem is that this form of ...

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Fermionic coherent states with a truly classical behavior are constructed in the survey Zhang, W. M., & Gilmore, R. (1990). Coherent states: theory and some applications. Reviews of Modern Physics, 62(4), 867. http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.62.867 A second kind of fermionic coherent states is obtained by treating the ...

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