Archives for Quantum Field Theory - Page 2
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…
Free Scalar Field Equation – Solved using matrix mechanics
Free Scalar Field: Field Equation and Matrix Mechanics Solution Field Equation for a Free Scalar Field The action for a free scalar field φ(x) in four-dimensional spacetime is given by:…
Dipole Approximation in Electron-Photon Interaction
Dipole Approximation for Electron-Photon Interaction The dipole approximation assumes that the wavelength of the electromagnetic field is much larger than the spatial extent of the electron wavefunction. In this case,…
Electron interacts with a photon – Schrodinger equation and it’s solution
Schrödinger Equation for Electron-Photon Interaction The system includes: An electron with wavefunction ψe(r, t), A photon field described by the vector potential A(r, t). The total Hamiltonian includes: The electron's…