# 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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### Reason for considering the positive root

In eqn. (3.11) of Srednicki's QFT book only the positive root is considered; i.e., $\omega = + \sqrt{(k^2 + m^2 )}$ Why the negative root is not considered? And what is the $\omega$?
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### In Klein-Gordon, why should infinite downwards photon cascades be possible?

Here is a simple point about the standard interpretation of the Klein-Gordon equation that for the life of me I've never been able to understand: Why would the existence of true negative energy ...
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### Why use Fourier expansion in Quantum Field Theory?

I have just begun studying quantum field theory and am following the book by Peskin and Schroeder for that. So while quantising the Klein Gordon field, we Fourier expand the field and then work only ...
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### Lorentz transformation of classical Klein–Gordon field

I'm trying to see that the invariance of the Klein–Gordon field implies that the Fourier coefficients $a(\mathbf{k})$ transform like scalars: $a'(\Lambda\mathbf{k})=a(\mathbf{k}).$ Starting from the ...
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### Is a solution to the Klein-Gordon equation homeomorphic (or even diffeomorphic) to a solution of an equation with a different covariance group?

Consider some solution $\psi(x,t)$ to the linear Klein-Gordon equation: $-\partial^2_t \psi + \nabla^2 \psi = m^2 \psi$. Up to homeomorphism, can $\psi$ serve as a solution to some other equation ...
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### What is the Lagrangian from which the Klein-Gordon equation is derived in QFT?

Is there a well-known Lagrangian that, writing the corresponding eq of motion, gives the Klein-Gordon Equation in QFT? If so, what is it? What is the canonical conjugate momentum? I derive the same ...
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### Why doesn't the Klein-Gordon equation allow for conservation of probability?

I read somewhere that the Klein-Gordon equation doesn't allow for conservation of probability. Can someone prove this mathematically?
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### Counterpart of the Klein Gordon Equation on the “Coordinate Shell”

The relation $$\psi=Ce^{i/\hbar(Et-\mathbf{p}\cdot\mathbf{x})}\tag{1}$$ satisfies the Klein Gordon equation on the mass shell, i.e. for $E^2=p^2+m^2$. Now let's think in the reverse direction. ...
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### Massless limit of the Klein-Gordon propagator

I am working with the propagator associated to the Klein-Gordon equation, as derived in "Quantum Physics a functional integral point of view", James Glimm, Arthur Jaffe or as derived here: http://www....
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### Can the Klein-Gordon Equation represent Particles with non-zero spin?

Every Solution of the Dirac Equation is also a solution of the Klein-Gordon equation. So the K-G equation does not necessarily represent particles with non-zero spin. Would it be incorrect to ...
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### What the theta in schwinger function and what is theta formula?

What the theta in schwinger function and what is theta formula? is theta formula general solution of klein gordon equation? if so, what is its coefficient of $\exp\left(-ipx\right)$?
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### Why is there a minus sign in this wave equation derivation?

My book on quantum mechanics suggests a derivation of the wave equation $$\left(\Delta - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \right) \psi(\bar{r},t) = 0$$ from the photon energy-impulse ...