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Vor 4 Tagen · In 1928, building on 2×2 spin matrices which he purported to have discovered independently of Wolfgang Pauli's work on non-relativistic spin systems (Dirac told Abraham Pais, "I believe I got these [matrices] independently of Pauli and possibly Pauli got these independently of me."), he proposed the Dirac equation as a relativistic equation of motion for the wave function of the electron.
- British
- Theoretical physics
Vor 3 Tagen · The Dirac equation. To tackle the problems with the Klein-Gordon equation, Dirac formulated the now-famous. Dirac equation ( DE) ˆEψ = (α ⋅ ˆp + βm)ψ. Expressed with operators ˆE = i ∂ ∂t and ˆp = − i∇, the equation takes form. i∂ψ ∂t = − iαx∂ψ ∂x − iαy∂ψ ∂y − iαz∂ψ ∂z + βmψ. From the equation ...
Vor 5 Tagen · In differential geometry, the four-gradient (or 4-gradient) is the four-vector analogue of the gradient from vector calculus . In special relativity and in quantum mechanics, the four-gradient is used to define the properties and relations between the various physical four-vectors and tensors .
Vor 4 Tagen · γ μ are the Dirac matrices, G a μ is the 8-component (=,, …,) SU(3) gauge field, λ a are the 3 × 3 Gell-Mann matrices, generators of the SU(3) color group, G a μν represents the gluon field strength tensor, and; g s is the strong coupling constant.
Vor einem Tag · We consider the Dirac equations in static spherically-symmetric space-times, and we present a type of spinor field whose structure allows the separation of elevation angle and radial coordinate in very general situations. We demonstrate that after such a separation of variables the Dirac equations reduce to two equations that can always be integrated, at least in principle. To prove that ours ...
Vor 4 Tagen · To address this, we introduce double-ring perfect vectorial vortex beams that leverage the axicon phase to theoretically generate double-ring structures through a Fourier transform. By applying a transformation matrix and introducing a cross phase, we can manipulate the beam distribution. This approach is expected to enhance for development of ...
Vor 5 Tagen · Affine transformations cannot be applied to vectors the same way as they are to points for (at least) two reasons: Vectors have no position, hence adding t would be meaningless and invalid. The way such a transformation should be applied to a vector depends on the relationship captured in the vector ! Offset between two points: X ( v) = v ′ = Mv.
