# 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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### Why Klein-Gordon Equation violate postulate of quantum mechanics?

In QFT for gifted amateur, authors stated the probability current may be negative, a negative probability violates the Copenhagen interpretation. However, in the book QFT by Srednicki mentioned the ...
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### Waves in quantum field theory

There are two sources of 'waviness" in quantum field theory: waves in the underlying classical field, and the Schrodinger equation. I'm learning QFT using the notes by David Tong (I believe they ...
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### Why does the Klein-Gordon harmonic oscillator have non-normalizable states?

The equation given here is the vector Klein-Gordon equation for the Harmonic oscillator potential. I have read about it in some papers. As far as I know, it gives the correct energy eigenvalues but ...
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### Validity of Euler-Lagrange Equation in Quantum Theory [duplicate]

Lagrangian density for a single-spin 0-real-bosonic field ($\phi$) is given by, $$\mathcal{L}=-\frac{1}{2}\partial_\mu \phi \partial^\mu \phi-\frac{m^2}{2}\phi^2$$ Now if we formulate the Euler ...
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### Is there a “square root” of Klein–Gordon equation which is different from Dirac equation?

Legend has it that Dirac arrives at the Dirac equation (all equations are in Planck units $c= \hbar = 1$ in this post): $$i\gamma^\mu\partial_\mu\psi - m\psi =0$$ by taking the square root of the ...
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### Why does the 3-point function of a real scalar field vanish?

$$\langle0\lvert T\hat\phi(x_1)\hat\phi(x_2)\hat\phi(x_3)\rvert0\rangle$$ I'm looking for an intuition to it, if not an actual interpretation. Otherwise, I know how to get the result 0 using Wick's ...
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### Lorentz-invariant measure in Klein-Gordon field

What is the exact reason why the solution of the classical Klein-Gordon equation is written as a mode expansion with a Lorentz invariant measure and after that the coefficients are promoted to ...
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### Derivation of operator version of the classical wave equation

I have the following summarised derivation for the operator version of the classical wave equation for massless and material particle. My question is about the statement: However, a problem is that ...
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### Is the Klein-Gordon Equation an equation for a Classical field or a Quantum Field?

When Canonically Quantising the Klein-Gordon Field you usually start with the Klein-Gordon Equation, from which you can guess a corresponding Lagrangian Density. Then utilising this information along ...
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### Why is it okay to replace the momentum operator with $p_x + im \omega x$?

In this paper the momentum operator was replaced with something that looked very similar to the ladder operator for the non relativistic harmonic oscillator. They started with the Klein Gordon ...
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### Retarded vs Feynman Klein-Gordon Propagators

Although I follow all the manipulations -- Green's functions, choice of contour/i$\epsilon$ prescription, etc -- I seem to be struggling with too many trees. The forest remains blurry. In ...
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### Fourier expansions of Klein Gordon field not Lorentz invariant?

I’m working in Peskin and Schroeders book on QFT and noticed that they expanded a solution to the Klein Gordon equation in a manner that seems to me not to be be Lorentz invariant even though the ...
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### Fourier transform of field variables rearrangement

I’m working in Peskin and Schroeders book on QFT These are the Fourier transforms of the field solutions to the Klein-Gordon equation: I don’t understand how to get from (2.25) to (2.27) The logical ...
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### Tensor Question (Klein–Gordon equation) [closed]

I have a question following the derivation of the Klein-Gordon equation from a lagrangian. From Eq. (13d), where does $\delta^\mu_\nu$ come from? I guess it's a conversion factor of some sort.
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### Transparent Boundary Conditions 1D Klein Gordon

The wave equation is an example of an equation for which there are simple transparent boundary conditions. We can factorize the wave operator \partial_t^2 -\partial_x^2 = (\partial_t - \partial_x)(\...
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### Can I write a complex field, in some cases, as a real field?

I am learning quantum field theory. Now I am considering this case: Suppose a spin-0 particle which obeys the Klein-Gordon field equation and its anti-particle obeying the same equation do not have ...
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### Scalar fields and spinors in 0+1D

As part of learning about SUSY quantum mechanics, I am trying to get a grasp on the following Lagrnagians in 1 (temporal dimension): But since these early times the treatment and methods of field ...
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### What's wrong with this “proof” that QFT violates causality?

In An Introduction to Quantum Field Theory, by Peskin and Schroeder, when discussing the quantized real Klein-Gordon field ($\phi=\phi^\dagger$), they show the commutator $[\phi(x),\phi(y)]$ vanishes ...