We show that three generations of leptons and quarks with unbroken Standard Model gauge symmetry SU (3) c × U (1) em can be described using the algebra of complexified sedenions C ⊗ S. A primitive idempotent is constructed by selecting a special direction, and the action of this projector on the basis of C ⊗ S can be used to uniquely split the algebra into three complex octonion subalgebras C ⊗ O. These subalgebras all share a common quaternionic subalgebra. The left adjoint actions of the 8 C-dimensional C ⊗ O subalgebras on themselves generates three copies of the Clifford algebra C (6). It was previously shown that the minimal left ideals of C (6) describe a single generation of fermions with unbroken SU (3) c × U (1) em gauge symmetry. Extending this construction from C ⊗ O to C ⊗ S naturally leads to a description of exactly three generations.

The Elko field of Ahluwalia and Grumiller is a quantum field for massive spin-1/2 particles. It has been suggested as a candidate for dark matter. We discuss our attempts to interpret the Elko field as a quantum field in the sense of Weinberg. Our work suggests that one should investigate quantum fields based on representations of the full Poincaré group which belong to one of the nonstandard Wigner classes.

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A B S T R A C TNumerous studies have shown that listeners can use phonological cues such as word stress and consonant clusters to find word boundaries in fluent speech. This paper investigates whether they can also use language-specific restrictions on vowel positioning for native speech segmentation. We show that English adults can exploit the fact that typical English words do not end in a lax vowel (e.g. [*diːtʊ]) in order to segment unknown words in a nonsense phrase-picture matching task, in contrast to the null results in prior studies using lexical tasks. However, they only used this cue in quiet listening conditions, and not in the presence of background noise. Thus, like consonant clusters, the lax vowel constraint is vulnerable in adverse listening conditions.

The Elko quantum field was introduced by Ahluwalia and Grumiller, who proposed it as a candidate for dark matter. We study the Elko field in Weinberg's formalism for quantum field theory. We prove that if one takes the symmetry group to be the full Poincaré group then the Elko field is not a quantum field in the sense of Weinberg. This confirms results of Ahluwalia, Lee and Schritt, who showed using a different approach that the Elko field does not transform covariantly under rotations and hence has a preferred axis.