Archives for Quantum Field Theory
Is QFT Linear?
Yes — but with an important distinction:The field equations are often linear for free fields, but interacting QFT is not linear.\boxed{\text{The field equations are often linear for free fields, but interacting QFT is not linear.}}The field equations are often linear for free fields, but interacting QFT is not linear. Let’s do a few concrete Weyl-vector examples. 1. Expand…
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…
Slow Moving vs Fast Moving Electrons – Photon Interaction
Electron–Photon Interaction: Slow vs Fast Electrons Is There a Difference Between a Slow-Moving and a Fast-Moving Electron Interacting with a Photon? Yes — the interaction depends strongly on the electron’s…
Historical Context of the Coupling Constant
Origin of the QED Coupling Constant The Coupling Constant in QED The QED coupling constant is one of the most famous “mystery numbers” in physics, better known as the fine-structure…
The Coupling Constant in QED
The Coupling Constant in QED The QED coupling constant is one of the most famous “mystery numbers” in physics, better known as the fine-structure constant, usually denoted: $$\alpha = \frac{e^2}{4…
Relativistic Particle in Complex Spacetime – A New Take on 4D Reality
From the August 2009 paper (Progress of Theoretical Physics) by Takayuki Hori Relativistic Particle in Complex Spacetime – A New Take on 4D Reality The 2009 paper “Relativistic Particle in…