# 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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### Solution of Klein-Gordon field in Schwarzschild metric

I was trying to understand the behavior of scalar field in the vicinity of black hole and I set up the Klein-Gordon equation in the background of Schwarzschild metric. But I am having difficulty in ...
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### Interacting Fields in QFT

I am trying to work through Peskin and Schröder and am a little stuck in Chapter 4 [section 4.2 p. 83 below eq. (4.13)], when he first treats interacting fields. The subject is the quartic interaction ...
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### Can local rotations lead to a gauge theory?

I was reading about the relation between electromagnetism and the complex Klein-Gordon field. The KG field had a global $U(1)$ symmetry and upon demanding that even a local phase transformation must ...
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### When can we quantise with ladder operators?

So I am now nearing the end of my first QFT course and in it we quantised the KleinGordon and Dirac fields using ladder operators, however this method seems very specific to these fields. We ...
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### Coupled Oscillator's Stiffness and speed of light

In Schwabl book (Advanced Quantum Mechanics) page 258, in his triumph to show the relation between the coupled oscillators and Klein-Gordon equation he finds the following relation which is the ...
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### What's a physical interpretation of the two terms that appear in the mode expansion of solutions of the Klein-Gordon equation?

For simplicity, let's say we consider a real scalar field in a purely classical context. A general solution of the Klein-Gordon equation can be written as: \begin{align} \phi(x)&= \int \frac{{\...
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### Conserved charge commutation relation under $SU(2)$ symmetry in two complex Klein-Gordon fields

I'm trying to show that conserved charges of two complex equal-mass Klein-Gordon fields under $SU(2)$ transformation fulfill the following commutation relation: $$[Q^j, Q^k]=i\epsilon^{jkl}Q^l .$$ I ...
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### Mode Expansion in Klein-Gordon QFT

I have a confusion regarding the mode expansion of the Klein-Gordon field theory. I am following Peskin and Schroeder. My questions are about how we formally get to the expansion of the KG QFT in ...
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### How can $⟨0|ϕ(x)|p⟩=e^{ip⋅x}$ be mathematically shown?

I was reading Peskin and Schroeder's quantum field theory and going through the book mathematically. Then I got stuck at one equation. Consider a single, non-interacting real scalar field. The book ...
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### $\phi^{4}$ theory

Consider a scalar field theory with a $\phi^{4}$ interaction term $$\mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)^{2}-\frac{1}{2}m^{2}\phi^{2}-\frac{\lambda}{4!}\phi^{4},$$ where $\lambda\ll 1$. I am ...
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### How does spin influence the dynamics of quantum mechanical systems?

I have just been introduced to the Klein-Gordon Equation and the Dirac Equation for the first time. The way they were explained to me, these equations govern the (relativistic) evolution of spin-0 and ...
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### Derivation of the Klein-Gordon solution via Fourier Transforms

I recently graduate with a bachelor's in physics, and I've been trying to take the next steps toward learning QFT. To this end, I have been working through Peskin and Schroeder's textbook step-by-step....
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### Quantization of field with other complete orthogonal system

I've learned the quantization of Klein-Gordon field using Fourier expansion. I understand that this process is kind of exchanging complex fourier coefficients to operator and makes it satisfying the ...
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### Klein-Gordon equation with position-dependent mass [closed]

Does there exist a general solution for a differential equation like: $$\ddot{\phi}(x,t) - \partial^2_x\phi(x,t) + \phi(x,t)m^2(x) = 0,$$ where $m(x)$ is a known function.
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