# 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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Greetings I urgently need help with questions 2 and 3 from the attached exercise. If answer can be posted same way as my question (written of paper) that would be much appreciated. I am sorry for any ...
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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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### Is $\gamma_\mu \gamma^\mu$ a unit operator?

Is the term: $$γ^μ γ_μ$$ An identity matrix? Since,if we start with both the Dirac equation, $$(iγ^μ ∂_μ-m)Ѱ=0$$ We find that, $$iγ^μ ∂_μ=m$$ If we square both sides, we get, $$-γ^μ γ_μ∂^μ ∂_μ=m^{2}$$...
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### How to write Lagrangian of field with vector and scalar potential

I am beginner of quantum field theory. I have a basic question. Lagrangian of a electron in the potential has the form of $${1\over2}m{\bf v}^2-e\Phi+e \bf v \cdot A$$ Lagrangian in quantum field ...
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As someone who has recently started doing QFT I have some (algebraic) confusion about the following derivation. Starting with the Lagrangian of a complex scalar field $$\mathcal{L} =\partial_\mu \psi^... 1answer 54 views ### Coupled Oscillator's Stiffness and speed of light In Schwabl book (Advanced Quantum Mechanics) page 258, in his triumph to show the relation between the coupled oscillators and Klein-Gordon equation he finds the following relation which is the ... 0answers 49 views ### Conserved charge commutation relation under SU(2) symmetry in two complex Klein-Gordon fields I'm trying to show that conserved charges of two complex equal-mass Klein-Gordon fields under SU(2) transformation fulfill the following commutation relation:$$ [Q^j, Q^k]=i\epsilon^{jkl}Q^l .I ... 0answers 19 views ### 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{{\... 1answer 118 views ### 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 ... 0answers 25 views ### Klein Gordon Hamiltonian commutator with annihilation (creation) operator Probably I'm missing something trivial here. When calculating a commutator of Klein Gordon Hamiltonian with annihilation/creation operator it seems that the operators are inserted under the integral, ... 1answer 41 views ### 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 ... 1answer 42 views ### 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.... 0answers 48 views ### 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 ... 1answer 47 views ### 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,$$where m(x) is a known function. 0answers 32 views ### Is the phase velocity of plane wave solutions of the Klein-Gordon equation larger than c? The phase velocity is given by$$ v= \frac{\omega}{k} \, .$$Using the usual dispersion relation$$ E^2 = p^2c^2+ m^2c^4 \leftrightarrow \omega^2 \hbar^2= k^2\hbar^2 c^2 + m^2c^4$$yields$$ v= \frac{\...
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I refer to this set of lecture notes by Hugh Osborn, equation 4.184 on p.70. We expand an action $S[\phi]$ around a background field $\varphi(x) = \phi(x) -f(x)$ If we expand the action $S[\phi]$ ...
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### Is the scalar propagator an even function?

The scalar propagator for the Klein-Gordon Lagrangian is given by: $$D(x-y)=\int \frac{d^{4} k}{(2 \pi)^{4}} \frac{e^{i k(x-y)}}{k^{2}-m^{2}+i \varepsilon}$$ I need to know if it is an even ...
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### WKB solution in QFT: classical action and particle vs antiparticle case

Consider the theory of a complex scalar field $$S[\psi, \psi^\dagger] = -\int d^4x \left(\hbar \partial_\mu \psi^\dagger \partial^\mu\psi + \hbar^{-1} m^2 |\psi|^2\right)$$ giving the Klein-Gordon ...
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### Classical action is zero in Klein-Gordon theory for a particle wavepacket

I'm interested in rewriting actions in the form $$S = -\int H dt + \int p_i dx^i,$$ (where $H$ is the Hamiltonian and the $p_i$ are conjugate momenta) and then evaluating them along a classical ...
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