# Questions tagged [klein-gordon-equation]

The Klein-Gordon Equation or the Klein-Fock-Gordon Equation is an equation in quantum field theory which initially was discovered by Schrodinger but discarded by him soon after.

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### Canonical quantization of relativistic particle using Fourier transform

Suppose I want to quantize the Hamiltonian of a relativistic particle on space-time $\mathbb{R}^{4}$. Setting $c=1$ for simplicity, the energy of the particle is given by $w(p) = \sqrt{|p|^{2}+m^{2}}$,...
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### Choice of hypersurface in Klein-Gordon inner product

Let $M$ be a globally hyperbolic spacetime, with metric $g_{\mu\nu}$. Consider the covariant Klein-Gordon equation $$(g^{\mu\nu}\nabla_{\mu}\nabla_{\nu}+m^{2})\phi=0$$ Define the following indefinite ...
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### How can the linear combination of infinite normalized Klein-Gordon fields be a normalizable field?

In the context of a Klein-Gordon field with charge $e$, mass $m$, immersed in an external classical electric field $A_\mu = (A_0(z), 0)$, I am asked to calculate the charge density of the field ...
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### Check of the Green function for the Klein-Gordon equation [closed]

In order to derive the Green function for the Klein-Gordon equation, one considers $$\Box G(x-x')+m^2G(x-x')=\delta^4(x-x')$$ where $\delta^4(x)=\delta(x_0)\delta(x_1)\delta(x_2)\delta(x_4)$. The ...
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### In QFT what is the frequency of oscillation in time of a scalar field mode? Does it depend on the number of particles in the mode?

In classical field theory, for a given real scalar field $\phi$, each mode $\vec{k}$ vibrates in time at a frequency $\omega = \sqrt{\vec{k}^2 + \mu^2}$ with $\mu$ being the mass. In quantum field ...
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### Question on Peskin & Schroeder's QFT: Noether's Theorem; finding conserved currents

So, I am trying to learn how to find conserved currents using what I see in P&S's "Intro to QFT"; sec.2.2 pg.17-18. Particularly, I am working through the example in the text for the ...
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I was watching this video tutorial for the derivation of Energy (chapter 3) from the Klein-Gordon equation where they had taken the two equations of $$(P^\mu P_\mu-m^2)\psi=0$$ and (-(K^0)^2+\...