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The Theory of Local Mass Dimension One Fermions of Spin One Half

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Abstract

About a decade ago the present author in collaboration with Daniel Grumiller presented an ‘unexpected theoretical discovery’ of spin one-half fermions with mass dimension one (Ahluwalia-Khalilova and Grumiller in Phys Rev D 72:067701 arXiv:hep-th/0410192, 2005, JCAP 0507:012, arXiv:hep-th/0412080, 2005). In the decade that followed a significant number of groups explored intriguing mathematical and physical properties of the new construct. However, the formalism suffered from two troubling features, that of non-locality and a subtle violation of Lorentz symmetry. Here, we trace the origin of both of these issues to a hidden freedom in the definition of duals of spinors and the associated field adjoints. In the process, for the first time, we provide a quantum theory of spin one-half fermions that is free from all the mentioned issues. The interactions of the new fermions are restricted to dimension-four quartic self interaction, and also to a dimension-four coupling with the Higgs. A generalised Yukawa coupling of the new fermions with neutrinos provides an hitherto unsuspected source of lepton-number violation. The new fermions thus present a first-principle dark matter partner to Dirac fermions of the standard model of high energy physics with contrasting mass dimensions—that of three halves for the latter versus one of the former without mutating the statistics from fermionic to bosonic.

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Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology Guwahati, Guwahati, 781 039, India

    Dharam Vir Ahluwalia

  2. Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune, 411 007, India

    Dharam Vir Ahluwalia

  3. Theoretical Physics Division, Physical Research Laboratory, Ahmedabad, 380 009, India

    Dharam Vir Ahluwalia

  4. Centre for the Studies of the Glass Bead Game, Chaugon, Bir, Himachal Pradesh, 176 077, India

    Dharam Vir Ahluwalia

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Communicated by Jayme Vaz

In memory of papaji, Shri Bikram Singh Ahluwalia.

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Ahluwalia, D.V. The Theory of Local Mass Dimension One Fermions of Spin One Half. Adv. Appl. Clifford Algebras 27, 2247–2285 (2017). https://doi.org/10.1007/s00006-017-0775-1

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