Archives for May, 2026
plane wave schrodinger wave solution – Transformation under a Lorentz Transform
Key Result - The phase can be Lorentz-transformed, but the Schrödinger dispersion relation is not Lorentz invariant. Start with the free-particle Schrödinger plane wave:ψ(x,t)=Aei(kx−ωt)\psi(x,t)=A e^{i(kx-\omega t)}ψ(x,t)=Aei(kx−ωt) Using de Broglie relations,p=ℏk,E=ℏωp=\hbar…
Lorentz Invariance of Scalar Fields
This is one of the foundational derivations in relativistic quantum field theory: showing that the Klein–Gordon scalar field transforms consistently under Lorentz transformations and that the theory is Lorentz invariant.…
Treating a bipartite Hamiltonian relativistically
For a relativistic bipartite system, you usually do not start with a simple Hamiltonian likeH=HA⊗IB+IA⊗HB+HintH = H_A \otimes I_B + I_A \otimes H_B + H_{\text{int}}H=HA⊗IB+IA⊗HB+Hint unless you are in a…
Why there are no macroscopic Spinor Fields?
1. What Is a Spinor Field? A spinor field is a field describing spin-12\frac1221 particles: electrons quarks neutrinos The Dirac field is the standard example:ψ(x)\psi(x)ψ(x) Unlike scalar or vector fields,…
What is the difference between δ and ∂ in this derivation
For the derivation of the Least Action Principle in classical field theory , what is the difference between δ and ∂? This is one of the most important conceptual distinctions…
The principle of stationary action derivation
Start with the actionS=∫d4x L(ϕ,∂μϕ)S=\int d^4x \, \mathcal{L}(\phi,\partial_\mu \phi)S=∫d4xL(ϕ,∂μϕ) The physical field configuration is the one for which a small variation of the field,ϕ(x)→ϕ(x)+δϕ(x)\phi(x)\rightarrow \phi(x)+\delta\phi(x)ϕ(x)→ϕ(x)+δϕ(x) does not change the action to…