# 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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### The idea of analytical continuation method to solve the Klein-Gordon equation, how and why?

For simplicity, let's consider a two dimensional version of Klein-Gorden equation: $$(\partial_t^2-\partial_x^2-\partial_y^2+m^2) G(\vec{x},t) = -\delta(\vec{x})\delta(t)$$ From the previous posts: ...
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### What is the name of this Lagrangian and how can I find its equations of motion?

I would appreciate if someone tell me how I should go about finding eom. for the following Lagrangian:$$L=-\frac{1}{2}\phi(\Box + m^2)\phi$$
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### How to obtain the explicit form of Green's function of the Klein-Gordon equation?

The definition of the green's function for the Klein-Gordon equation reads: $$(\partial_t^2-\nabla^2+m^2)G(\vec{x},t)=-\delta(t)\delta(\vec{x})$$ According to these resources: Green's function ...
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### Klein-Gordon equation only for spinless particles?

We can derive the Klein-Gordon equation using the relativistic energy-momentum relation, and here, I have no problem, it is an easy thing to do. However, I found by research that it applies only to ...
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### Noether's Theorem and scale invariance

Noether's theorem usually considers coordinate/field transformations which leave the Lagrangian invariant up to a divergence term, i.e. $$\mathcal{L} \rightarrow \mathcal{L} + \partial_{\mu}f^{\mu}$$ ...
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### Why is $V=(1/2) m^2 \phi^2$ for a free relativistic scalar field of mass $m$?

Bit of a basic question here but how come for a free relativistic scalar field of mass $m$ such as Klein Gordon theory, we take the potential to be $$V=\frac{1}{2} m^2 \phi^2$$ Is the mass term ...
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### Is there supersymmetry between Dirac and Klein Gordon solutions?

Usually supersymmetry is explained at the level of the action of a quantum field theory, and there are two ways to go down from QFT to relativistic quantum mechanics: either a non-covariant way where ...
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### Quantum field operators in HEP and CMT

For a real scalar field (which is a bosonic field) we have these commutation relations : $$\left[\phi(x,t),\phi(y,t)\right]=0 \qquad \qquad \left[\phi(x,t),\pi(y,t)\right]=\delta(x-y).\tag{1}$$ But ...
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### How to derive the theory of quantum mechanics from quantum field theory?

I have read the book on quantum field theory for some time, but I still do not get the physics underline those tedious calculations. The thing confused me most is how quantum mechanics relates to ...
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### Klein paradox for bosons and fermions

I am reading this paper about the Klein paradox, i.e. transmission of relativistic particles incident on a potential step of height $V_0 > E + mc^2 > 2mc^2$ with $E$ the energy of the incident ...
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### Green's function for the Klein-Gordon equation diverging?

I'm trying to work out the propagator for the free scalar field theory (i.e., the Green's function for the Klein-Gordon equation). On pages 23 and 24 of Zee's Quantum Field Theory in a Nutshell (you ...
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### Doubts taking the second functional derivative of the Klein Gordon action

I have very little background with functional derivatives and I would like to clarify some issues. I am trying to compute the second functional derivative of the Klein Gordon action expressed in real ...
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### Expanding free scalar field in terms of ladder operators

I'm having some difficulty with the finer points of expanding a field in terms of ladder operators. Note that this is not identical to the other related question I asked. From Peskin / Schroeder; ...
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### Field expansion in Peskin & Schroeder

Peskin and Schroeder state something which I'm not fully understanding. More specificially I think it's just phrased in a way I'm not understanding. In the Schrodinger picture we can expand the real ...