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"An Exceptionally Simple Theory of Everything" is a physics preprint proposing a basis for a unified field theory, very often referred to as "E8 Theory",〔 which attempts to describe all known fundamental interactions in physics and to stand as a possible theory of everything. The paper was posted to the physics arXiv by Antony Garrett Lisi on November 6, 2007, and was not submitted to a peer-reviewed scientific journal. The title is a pun on the algebra used, the Lie algebra of the largest "simple", "exceptional" Lie group, E8. The paper's goal is to describe how the combined structure and dynamics of all gravitational and Standard Model particle fields, including fermions, are part of the E8 Lie algebra.〔 In the paper, Lisi states that all three generations of fermions do not directly embed in E8 with correct quantum numbers and spins, but that they might be described via a triality transformation, noting that the theory is incomplete and that a correct description of the relationship between triality and generations, if it exists, awaits a better understanding. The theory received accolades from a few physicists amid a flurry of media coverage, but also met with widespread skepticism. ''Scientific American'' reported in March 2008 that the theory was being "largely but not entirely ignored" by the mainstream physics community, with a few physicists picking up the work to develop it further. In a follow-up paper, Lee Smolin proposed a spontaneous symmetry breaking mechanism for obtaining the classical action in Lisi's model, and speculated on the path to its quantization.〔 In July 2009, Jacques Distler and Skip Garibaldi published a critical paper in ''Communications in Mathematical Physics'' called "There is no 'Theory of Everything' inside E8",〔 arguing that Lisi's theory, and a large class of related models, cannot work. They offer a direct proof that it is impossible to embed all three generations of fermions in E8, or to obtain even the one-generation Standard Model without the presence of an antigeneration. In response to Distler and Garibaldi's paper, Lisi argued, in a new paper "An Explicit Embedding of Gravity and the Standard Model in E8",〔 peer reviewed and published in a conference proceedings, that some assumptions about fermion embeddings are unnecessary and that the antigeneration is not by itself a problem sufficient to rule out the one-generation Standard Model. In December 2010 and May 2011, Lisi wrote in the popular magazine Scientific American a feature article on the E8 Theory of Everything and an entry in the blog section of the magazine addressing some of the criticism of his theory and how it has progressed, noting that the theory is still incomplete and makes only tenuous predictions, with the three generation issue remaining as a significant problem.〔 ==Overview== Lisi's model is a variant and extension of a Grand Unification Theory (a "GUT", describing electromagnetism, the weak interaction and the strong interaction) to include gravitation, a Higgs boson and fermions in an attempt to describe all fields of the Standard Model and gravity as different parts of one field over four-dimensional spacetime. More specifically, Lisi combines the left-right symmetric Pati–Salam GUT with a MacDowell–Mansouri description of gravity, using the spin connection and gravitational frame combined with a Higgs boson, necessitating a cosmological constant. The model is formulated as a gauge theory, using a modified BF action, with E8 as the Lie group. Mathematically, this is an E8 principal bundle, with connection, over a four-dimensional base manifold. Lisi's embedding of the Standard Model gauge group in E8 leads him to predict the existence of 22 new bosonic particles at an undetermined mass scale. Lisi states that the fermions enter via an unconventional use of the BRST technique, as Grassmann number fields valued in part of the E8 Lie algebra. The bosons are combined with these fermions as one-form and Grassmann number parts of a kind of superconnection, each valued in separate parts of the E8 Lie algebra. The curvature of this superconnection is calculated, producing the Riemann curvature, gauge field curvature, gravitational torsion, covariant derivative of the Higgs, and the covariant Dirac derivative of the fermions. This curvature is used to build the modified BF action by hand, in an attempt to match the dynamics of the Standard Model and gravity. In the paper, Lisi describes several deficiencies in this model. The most important deficiency is noted as an incorrect, or "poorly understood", inclusion of the second and third generations of fermions in E8, relying on triality. This deficiency, and the incomplete nature of the model, precludes the prediction of masses for new or existing particles. Also, Lisi notes the use of explicit symmetry breaking in building his action, rather than offering a more desirable spontaneous symmetry breaking mechanism. And, no attempt is made to provide a quantum description of the theory—this being left for future work. About it, Lee Smolin proposed a spontaneous symmetry breaking mechanism for obtaining the action in Lisi's model, and speculates on the path to its quantization as a spin foam.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「An Exceptionally Simple Theory of Everything」の詳細全文を読む スポンサード リンク
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