Spin-half mass dimension one fermions and their higher-spin generalizations
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part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-900277-x
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Review
Spin-half mass dimension one fermions and their higher-spin generalizations Cheng-Yang Leea Center for Theoretical Physics, College of Physical Science and Technology, Sichuan University, Chengdu 610064, P.R. China Received 8 December 2019 / Accepted 22 July 2020 Published online 21 September 2020 Abstract. A self-contained review on spin-half mass dimension one fermions and their higher-spin generalizations is presented. Starting from the two-component left-handed Weyl spinors, the Dirac spinors and Elko (eigenspinors of the charge conjugation operator) are constructed. After elaborating on their similarities and differences, we generalize the spin-half Elko to higher-spin. The field operators constructed from Elko and their higher-spin generalizations are shown to be of mass dimension one with positive-definite free Hamiltonians. The physical significance of higher-spin mass dimension one particles and further extensions in the context of Lounesto classification are discussed.
1 Introduction In 1928, Dirac wrote down an equation that revolutionized our understanding of the universe [1]. Ninety years later, it remains to be one of the most beautiful equations in science. Enamoured by its rich mathematical structure and empirical successes, an unspoken consensus has quietly but surely permeated through the scientific community – a massive spin-half fermion must be described by the Dirac equation. In 2005, Ahluwalia and Grumiller made a fundamental theoretical discovery – a massive spin-half fermion of mass dimension one [2,3]. This was an unexpected result contrary to the longstanding consensus with important implications for quantum field theory (QFT) and physics beyond the Standard Model (SM). These fermions have two surprising properties – They satisfy the Klein–Gordon but not the Dirac equation and are of mass dimension one instead of three-half. Therefore, they have renormalizable quartic self-interactions, making them potential dark matter candidates. What underlies this construct was a structure already known to mathematicians studying spinors and Clifford algebra [4]. A systematic classification shows that the Dirac and Weyl spinors are not the only possible spin-half representations of the Lorentz group. In fact, there exists two other classes of spinors known as the flag-pole and flag-dipole spinors. Elko, the eigenspinor of the charge-conjugation operator associated with mass dimension one fermions, was shown to be a flag-pole spinor [5]. a
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2004
The European Physical Journal Special Topics
The works of Ahluwalia and Grumiller have received increasing attentions in various areas ranging from cosmology [6–19], quantum field theory [20–25], particle phenomenologies [26–30] and mathematics [5,31–41]. The works accomplished so far strongly suggest that the relationships between spinors and QFT have an even deeper and richer structure than previously exp
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