其实我们也用不到那么多的表示, Lorentz 群在量子场论中常见的非平庸表示就仨, 分别为量子幺正表示 U:{\text{O}}\left( {1,3} \right) \to {\text{GL}}\left( {{L^2}} \right) , 旋量表示 D:{\text{O}}\left( {1,3} \right) \to {\text{GL}}\left( {{\text{Dirac spinor}}\;...
#Irreducible representation of SO(3,1) and Lorentz spinors#SL(2,C) group and the Lorentz transformation#Chiral transformation and spinor algebra#Lorentz spinors and the Dirac equation#Electromagnetic interaction and gyromagnetic ratio of the electron#Gamma matrix algebra and PCT in Dirac spinor ...
13.3 The Lorentz Transformation Historically, the so-called Lorentz transformation equations were introduced prior to the development of Einsteinian relativity theory, but in an ad hoc manner without rigorous justification.* The equations can be obtained, however, solely on the basis of the two fundam...
These diagonal realizations are characterized by six functions phi/sub i/ which must satisfy a system of transformation equations. Inequivalent categories of solutions for the phi/sub i/ give rise to different electromagnetic fields. The Dirac monopole and Coulomb potentials follow directly from two ...
ViewTableofContents:http://pop.aip/resource/1/PHPAEN/v18/i3 PublishedbytheAmericanInstituteofPhysics. RelatedArticles Trendstoequilibriumforaclassofrelativisticdiffusions J.Math.Phys.52,113703(2011) OnerealfunctioninsteadoftheDiracspinorfunction J.Math.Phys.52,082303(2011) MathematicalmodelII.Basicparticle...
ψ is the Dirac or Pauli curent depending on the level of energy involved. As it is well-known the torsion tensor can be expressed in spinor form by the Fock-Ivanenko expression [8] S νρµ = − 1 2 ǫ νρµσ ¯ ...
In the textbook proofs of the Lorentz covariance of the Dirac equation, one treats the wave function as a spinor and gamma matrices as scalars, leading to a quite complicated formalism with several pedagogic drawbacks. As an alternative, I propose to teach the Dirac equation and its Lorentz ...
Not only does this description give the well-known formula for any Lorentz transformation matrix L in terms of the matrix S , which enters the transformation law of a Dirac spinor ψ( x ) under L , it also gives an explicit and apparently new inverse formula expressing S in terms of L...
We have studied the relativistic effects on the mean spin entanglement of two massive Dirac particles using the simultaneous eigen-spinors of the Foldy-Woutheysen mean spin operator and the Dirac Hamiltonian. We have obtained the transformation matrix from the spinor with specific momentum to the ...
Quantum fields of any spin are expanded in terms of the (spinor) coefficients relating these two bases; their transformation properties under Lorentz transformations,T,C andP are given. The correct spin-statistics relation is found from (anti) commutators of the field components. The relation ...