Derivation of Dirac's equation from the Evans wave equation

被引:14
作者
Evans, MW
机构
关键词
Evans wave equation; general relativity; Dirac equation in general and special relativity; metric four-vector;
D O I
10.1023/B:FOPL.0000019653.48266.23
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The Evans wave equation [1] of general relativity is expressed in spinor form, thus producing the Dirac equation in general relativity. The Dirac equation in special relativity is recovered in the limit of Euclidean or flat spacetime. By deriving the Dirac equation from the Evans equation it is demonstrated that, the former originates in a novel metric compatibility condition, a geometrical constraint on the metric vector q(mu) used to define the Einstein metric tensor. Contrary to some claims by Ryder, it is shown that the Dirac equation cannot be deduced unequivocally from a Lorentz boost in special relativity. It is shown that the usually accepted method in Clifford algebra and special relativity of equating the outer product of two Pauli spinors to a three-vector in the Pauli basis leads to the paradoxical result X = Y = Z = 0. The method devised in this paper for deriving the Dirac equation from the Evans equation does not use this paradoxical result.
引用
收藏
页码:149 / 166
页数:18
相关论文
共 7 条
  • [1] Atkins P.W., 1983, MOL QUANTUM MECH
  • [2] Carroll Sean M., 1997, LECT NOTES GEN RELAT
  • [3] EVANS MW, 2004, IN PRESS FDN PHYS LE
  • [4] EVANS MW, 2003, IN PRESS FDN PHYS LE, V16, P367
  • [5] MILEWSKI EM, 1987, VECTOR ANAL PROBLEM
  • [6] Ryder L H, 1987, Quantum Field Theory
  • [7] SACHS M, 2003, MACHS PRINCIPLE ORIG