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.

364 questions
Filter by
Sorted by
Tagged with
230 views

59 views

How to interpret the concept that a (scalar) field is a linear superposition of harmonic oscillators?

I've reading an introduction lecture on QFT, but I didn't started very well. I have troubles to understand some concepts of the very first example (But I think that they apply with the other fields): ...
64 views

Where do the particle and antiparticle wavefunctions originate from in the Klein Gordon equation?

In my textbook (Sakurai) it is given that $$\left(D_\mu D^\mu+m^2\right)\Psi(\mathbf{x},t)=0$$ where $D_\mu=\partial_\mu+ieA_\mu$ is the covariant derivative. It states that since it is a second ...
141 views

Quantization of Klein-Gordon field between two boundaries

Consider a real scalar $\phi(x,t)$ with mass $m$ in $1+1$ dimensional spacetime, described by the 2d free Klein-Gordon action. $\phi(x,t)$ lives on an interval $0 \leq x \leq L$, and is subject to ...
118 views

Obtaining mode decomposition of quantum field in a box with Dirichlet condition

I am considering the Klein Gordon Equation in a box with Dirichlet conditions (i.e., $\hat{\phi}(x,t)|_{boundary} = 0$). 1-D functions that obey the Dirichlet condition on interval $[0,L]$ are of the ...
412 views

Commutator of canonical fields in Quantum Field Theory

Let $\phi(\vec{x},t)$ denote the canonical fields and $\pi(\vec{x},t)$ denote the canonical impulses where they're given by: \phi(x)=\int\frac{d^3\vec{p}}{(2\pi)^3\sqrt{2\omega_{\...
206 views

Lagragian density of a massless scalar field

I have seen in some books that the simplest Lagrangian density of a massless scalar field is $$\mathscr{L}=\dfrac{1}{2}\partial^\mu\phi\partial_\mu\phi=\dfrac{1}{2}\left(\partial_\mu\phi\right)^2.$$ ...
984 views

124 views

Klein Gordon equation in tensorial form

The problem is to show that $$\psi=\psi_0e^{iP_\mu x^\mu}$$ is a solution to Klein Gordon equation $$(\partial _\mu \partial ^ \mu +m^2)\psi=0$$ if and only if the 4-momentum $p _\mu$ satisfies the ...
86 views

Klein-Gordon and localizability

If we consider the theory of a single relativistic point particle, quantized using whatever appropriate method, the wavefunction simply obeys the Klein-Gordon equation, which allows for a fairly wide ...
156 views

Contradictory solutions to the Klein-Gordon equation as an initial value problem (canonical formulation)

I'm going to begin with a prelude about constructing the solution using the action/Lagrangian formalism in order to provide context and a point of comparison for the canonical one. The main question ...
94 views

335 views

367 views

Fourier transforming the Klein-Gordon equation

I'm aware of the fact that there are similar questions on this forum but I could not find an answer that fits my problem. Many textbooks state that a general solution to the Klein-Gordon equation \...
236 views

Explicitly proving that the Hamiltonian is Lorentz covariant

I want to show explicitly that the Hamiltonian $$H = -\Omega V + \int d\tilde{\textbf{k}} \omega (a^\dagger(\textbf{k}) a(\textbf{k}) + b(\textbf{k}) b^\dagger(\textbf{k}) )$$ is Lorentz covariant....
448 views

Solution of Klein-Gordon field in Schwarzschild metric

I was trying to understand the behavior of scalar field in the vicinity of black hole and I set up the Klein-Gordon equation in the background of Schwarzschild metric. But I am having difficulty in ...
172 views

182 views

Vacuum energy of a real Klein-Gordon field

Hamiltonian for a Klein-Gordon field can be written as - $$H= \int \frac{d^3p}{(2\pi)^3 \omega_{\vec{p}}}[a^{\dagger}_\vec{p}a_\vec{p}+\frac{1}{2}(2\pi)^3\delta^{(3)}(0).\tag{1}]$$ In one of my ...
87 views

Time evolution operator of Klein-Gordon field

If $U(t)=e^{itH}$ is the time evolution operator. And $|\phi \rangle$ is a state of a field at particular time $t_1$ and $|\phi' \rangle$ is the state of a (free) Klein Gordon field at a time $t_2$. ...
225 views

I have a question about the usage of the Schwinger-Dyson-Equation for the Klein-Gordon-Field. $$i <0|T (\delta S / \delta \phi(x) ) \phi(x_1)\ldots |0>+<0|T\delta(x-x_1)\ldots|0>=0 .\tag{... 1answer 979 views Derivation of the Klein Gordon Propagator I'm learning some quantum field theory. I'm currently using the book An Introduction to Quantum Field Theory by Peskin and Schroeder. I have a problem that I can't figure out at the moment. It is ... 0answers 90 views Do we need to know first time derivatives of Klein-Gordon fields to make future predictions? In the quantisation of the Klein Gordon field, because it has a second derivative, we need to know the values of the field and also the first derivative in order to predict future values of the field. ... 1answer 509 views “Deriving” Lorenz Gauge Condition from the Lagrangian I am studying QFT with Mandl & Shaw, Quantum Field Theory and ran into Problem 2.3 (page 37 in the Second Edition) that says: Problem 2.3: Show that the Lagrangian density$$\mathscr{L} = -...
The usual Klein-Gordon Lagrangian reads $$\mathscr{L}= \frac{1}{2}( \partial _{\mu} \Phi \partial ^{\mu} \Phi -m^2 \Phi^2) \, . \tag1$$ Without additional symmetry ...