# Tagged Questions

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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### Schroedinger and Klein-Gordon equation and their complex conjugate

Let's consider the Schroedinger equation $$i\hbar\frac{\partial}{\partial t}\psi=-\frac{\hbar}{2m}\nabla^2\psi$$ If I have a wavefunction $\psi$ as a solution, then its ...
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### Components of Dirac equation solve the Klein Gordan equation derivation

On page 90 of this set of lecture notes on quantum field theory, http://www.damtp.cam.ac.uk/user/tong/qft/four.pdf a simple derivation is given to show that each component Dirac equation solves the ...
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### Comparison of vacua and annihilation operators of Klein-Gordon theory and phi-fourth theory

The ground state or vacuum of an interacting theory is, in general, different from the ground state or vacuum of a free theory. In what cases are the two vacuums the same as each other? Can an ...
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### Limits used to find non-rel limit of the Klein-Gordon equation

I just have a question regarding assessing the non-relativistic limit of the Klein-Gordon equation. In the book I'm following (Quantum Mechanics by Bransden & Joachain) they use the limits (Chpt. ...
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### Classical Klein-Gordon theory is a free relativistic theory

The classical Klein-Gordon theory for a real scalar field is called a relativistic free theory. It is called a free theory because the dynamics of the degrees of freedom in the momentum space of the ...
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### SHO in QM and Klein Gordon field in 1+0D QFT

The SHO in QM with mass $m=1$ has action $$S[x] = \int dt \frac{1}{2} \dot x^2 + \frac{1}{2}\omega^2 x^2$$ by integration by parts we see this is the same as 1 dim Klein Gordon QFT action with ...
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### Which information is lost, if we model photons via the Klein-Gordon equation?

The Klein-Gordon equation describes relativistic spin-0 particles. Each component of the Dirac equation fulfils the K-G equation, c.f. here. If one decides (for whatever reasons) to model photons via ...
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### Deriving Schrodinger equation from QFT with the definition $\psi(\textbf{x},t)\equiv \langle 0|\phi_0(\textbf{x},t)|\psi\rangle$

In the book "Quantum Field theory and the Standard Model" by Matthew Schwartz, he uses the equation $$\partial_t^2\phi_0=(\nabla^2-m^2)\phi_0$$ (i.e., the Klein-Gordon equation for the free ...
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### Question about source terms in scalar quantum field theory

I'm having a bit of a mental block when trying to interpret the inhomogeneous Klein-Gordon equation $$(\Box +m^{2})\phi(x,t)=j(x,t)$$ In particular, how does one interpret the term on the right-hand ...
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### Where does the factor of half appear from in the Klein-Gordon Lagrangian?

The lagangian density of a scalar field or a Klein-Gordon field has the form of \begin{align} \mathcal{L} = \frac{1}{2} \partial_\mu \phi \partial^\mu \phi - \frac{1}{2} m^2 \phi^2. \end{align} ...
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### Why Use the Non-Relativistic Momentum Operator in Relativistic Quantum Mechanics?

In deriving the Klein Gordon equation one starts out with the relativistic energy relation E^2 = p^2 + m^2 and substitutes the quantum momentum operator that corresponds to non-relativistic QM, p = -i ...
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### Momentum of 1-D real scalar Klein-Gordon quantum field on segment

I'm trying to get into QFT and as such I try to quantize a real scalar field with Klein-Gordon field equation (Lagrangian density) on a segment of lenght L and with fixed ends. I get orthonormal basis ...