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Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

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The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors.A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations.With the introduction of intrinsic W-parity,a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin.A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry.Based on the framework of gravitational quantum field theory proposed in Ref.[1] with the postulate of gauge invariance and coordinate independence,we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime.Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincaré symmetry P(1,5)=SO(1,5)×P1,5 as well as the charge spin gauge symmetry SU(2).The theory leads to the prediction of doubly electrically charged bosons.A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries.A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime.The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects.The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor,and its symmetric part provides a generalized Einstein equation of gravity.An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.

gravitational gauge field theorymaximal symmetry of massless Dirac fermionextra dimensionsmass generation

Yue-Liang Wu

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CAS Key Laboratory of Theoretical Physics Institute of Theoretical Physics, Chinese Academy of Sciences,Beijing 100190, China

International Centre for Theoretical Physics Asia-Pacific(ICTP-AP)University of Chinese Academy of Sciences(UCAS),Beijing 100049, China

Supported by National Science Foundation of China (NSFC)Supported by National Science Foundation of China (NSFC)Supported by National Science Foundation of China (NSFC)Strategic Priority Research Program of the Chinese Academy of SciencesCAS Center for Excellence in Particle Physics (CCEPP)

116900221147523711121064XDB23030100

2017

10.1088/1674-1137/41/10/103106

中国物理C(英文版)
中国物理学会　中国科学院高能物理研究所　中国科学院近代物理研究所

中国物理C(英文版)

CSTPCDCSCDSCI
影响因子：0.347
ISSN：1674-1137
年,卷(期)：2017.41(10)
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