# 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 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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### What are the symmetries of the Schrödinger functional?

Given the definition here. What are the symmetries of: $$\mathcal{S}[\phi_2,t_2;\phi_1,t_1]=\langle\,\phi_2\,|e^{-iH(t_2-t_1)/\hbar}|\,\phi_1\,\rangle.$$ which is the amplitude to go from the field ...
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### Time dependence of ladder operators in QFT

I'm currently going through Matthew D. Schwartz book Quantum Field Theory and the Standard Model, p. 23. For free (non interacting) field theories we are able to quantise the field by expanding our ...
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### $SU(2)$ doublets from the transformation law of a matrix of scalar fields

If we have a $2 \times 2$ $SU(2)_L$ and $SU(2)_R$ matrix $\Phi=\begin{bmatrix} a & c \\ b & d \end{bmatrix}$, where a, b, c and d are four complex Klein-Gordon fields, that under a gauge ...
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### Is causality violated in QFT?

I'm studying QFT, and Peskin is his book takes a couple of paragraphs to talk about causality in QFT, using the Klein-Gordon field as an example. The book says on p. 28: To really discuss causality, ...
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### Gauge invariance of Klein-Gordon equation in electromagnetic field

I would like to show, that the following two equations: are invariant under a local $U(1)$ transformation: Before coming to my question, I will show you what I did: I defined the local U(1) ...
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### Time evolution operator and Klein-Gordon-Equation

The basis of classical QM is the postulate of a time evolution operator $$|\alpha,t_0;t\rangle=U(t,t')|\alpha,t_0;t'\rangle$$ Is it correct to interpret this postulate as All future states are ...
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### Why is the annihilation operator associated with the positive frequency solutions?

I am looking for a qualitative explanation, if possible, of the following passage from Peskin & Schroeder, bottom of page 26, concerning the quantised real Klein-Gordon field: A positive ...
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### Relationship between the Klein-Gordon equation and Poincaré invariance

Derivations of the Klein-Gordon equation such as the one given by Phoenix in here, are based on studying the wave equation of the wave function of a relativistic particle. In this case, the Klein-...