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In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form , or including electromagnetic interactions, it describes all spin-1/2 massive particles , called "Dirac particles", such as electrons and quarks for which parity is a symmetry .
In k-space, this shows up as a hypercone, which have doubly degenerate bands which also meet at Dirac points. [11] Dirac semimetals contain both time reversal and spatial inversion symmetry; when one of these is broken, the Dirac points are split into two constituent Weyl points, and the material becomes a Weyl semimetal.
Two of the six Dirac points are independent, while the rest are equivalent by symmetry. In the vicinity of the K-points the energy depends linearly on the wave vector, similar to a relativistic particle. [4] [6] Since an elementary cell of the lattice has a basis of two atoms, the wave function has an effective 2-spinor structure.
Soon after in 1928, Dirac found an equation from the first successful unification of special relativity and quantum mechanics applied to the electron, now called the Dirac equation. In this, the wave function is a spinor represented by four complex-valued components: [20] two for the electron and two for the electron's antiparticle, the ...
Square wave may refer to: Square wave (waveform) Cross seas, also known as square waves This page was last edited on 7 ...
The Dirac velocity gives the gradient of the dispersion at large momenta , is the mass of particle or object. In the case of massless Dirac matter, such as the fermionic quasiparticles in graphene or Weyl semimetals, the energy-momentum relation is linear,
Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case.
In Dirac's theory the fields are quantized for the first time and it is also the first time that the Planck constant enters the expressions. In his original work, Dirac took the phases of the different electromagnetic modes ( Fourier components of the field) and the mode energies as dynamic variables to quantize (i.e., he reinterpreted them as ...