# 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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### Dimensional analysis of quantized Klein-Gordon Field

For the free Klein-Gordon Lagrangian density: $$\mathcal{L}=\frac{1}{2}\partial^{\mu}\phi\partial_{\mu} \phi-m^2\phi^2 .$$ Since we need the dimension of Lagrangian density equal to 4 (in this case ...
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### Klein-Gordon equation coupled to scalar curvature

Consider the Klein-Gordon equation of the form $$\square_g \psi - m^2 \psi - \xi R \psi \enspace = \enspace 0 \quad .$$ This equation describes the relativistic propagation of a scalar field with mass ...
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### Relation between low-energy modes of phonon and infinite oscillator limit

The Klein-Gordan equation is often described as coupled oscillators, taking the limit $l\rightarrow \infty$ to reduce to wave equation with linear dispersion relation. I'm considering here the ...
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### How can I find an operator originally expressed in terms of raising and lowering operators in terms of the field operators?

I'm following this book on QFT called "Quantum Field Theory of Point Particles and Strings" by Brian Hatfield. After the end of the scalar field theory section on Exercise 3.6, it asks us to ...
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### Peskin and Schroeder confusion on promoting Classical Klein-Gordon equation to quantum field equation

I am reading "An introduction to quantum field theory" by Peskin and Schroeder and I am confused. I appreciate your help. Here's the context to my question: In chapter 2, the book introduces ...
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### Path integral in a boundary QFT

I'm trying to compute the following path integral \begin{equation} Z = \int\mathcal{D}\phi\exp\left(-\int_{\mathbb{R}^d_+}\frac{d^dx}{2}\phi(-\partial_\mu^2 + m^2)\phi \right) \propto \frac{1}{\sqrt{\...
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### Klein-Gordon equation with imaginary mass

I was wondering if someone could provide me the name of the following equation $$\square \varphi - \tilde{m}^2 \varphi = 0,$$ where $\square := \partial_t^2 - \nabla^2$. I am specifically seeking ...
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### Could the Dirac Eq./Klein-Gordon Eq. handle solutions with finite extinction times?

I was reading in Wikipedia about how the Dirac Equation and the Klein-Gordon Equation where built to introduce in the Schrödinger equation the relativistic description of the Energy–momentum relation: ...
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### Why didn't the Klein-Gordon equation suggest antimatter like the Dirac equation did?

I have heard the story that the Dirac equation suggested the existence of antimatter due to the existence of negative energy solutions. The Klein-Gordon equation also has negative energy solutions. ...
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### What is the interpretation of the quantum field operator solving the Klein-Gordon equation?

Does the quantum field operator $\hat \psi^\dagger(x)$ solving the KGE mean that we should think that every quantum field configuration evolves under a KGE field equation. Or do we just understand it ...
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### Can we solve the Klein-Gordon equation in the Schrodinger picture?

In QFT, the Klein-Gordon equation is solved with the field operator $\hat \psi(x)$/$\hat \psi^\dagger(x)$ in the Heisenberg picture, and (as I understand it) gives the evolution of a single on-mass-...
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### The two ways to get Schrodinger equation from Klein-Gordon equation

We can take the Klein-Gordon equation describing the evolution of a complex scalar field. Taking the non-relativistic limit yields a classical wave equation that is identical in form to the ...
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### Does Heisenberg picture only work for time-dependent Schrödinger equation not Klein-Gordon equation?

For a Klein-Gordon field, our QFT lecture notes say we use the following relationship to define the Heisenberg picture. $$i \frac{dQ}{dt} = [Q,H]$$ which leads to $$Q(t) = e^{iHT}Q(0)e^{-iHt}$$ ...
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### Klein-Gordon Hamiltonian in terms of Fourier transformed variables

The Klein-Gordon Hamiltonian density is a function of four complex variables $\psi , \psi ^* , \pi , \pi ^*$. Suppose we make the change to Fourier transformed variables. Then the Fourier expansions ...
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