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Is there more to Dirac's gamma matrices than meets the eye? It turns out that gamma zero can be factorized into a product of three operators. This revelation facilitates the expansion of Dirac's space-time algebra to Clifford algebra Cl (0 , 6). The resultant rich geometric structure can be leveraged to establish a combined framework of the standard model and gravity, wherein a gravi-weak interaction between the vierbein field and the extended weak gauge field is allowed. Inspired by the composite Higgs model, we examine the vierbein field as an effective description of the fermion–antifermion condensation. The compositeness of space-time manifests itself at an energy scale which is different from the Planck scale. We propose that all the regular classical Lagrangian terms are of quantum condensation origin, thus possibly addressing the cosmological constant problem provided that we exercise extreme caution in the renormalization procedure that entails multiplications of divergent integrals. The Clifford algebra approach also permits a weaker form of charge conjugation without particle–antiparticle interchange, which leads to a Majorana-type mass that conserves lepton number. Additionally, in the context of spontaneous breaking of two global U (1) symmetries, we explore a three-Higgs-doublet model which could explain the fermion mass hierarchies. [ABSTRACT FROM AUTHOR]

Since the introduction of quaternion by Hamilton in 1843, quaternions have been used in a lot of applications. One of the most interesting qualities is that we can use quaternions to carry out rotations and operate on other quaternions; this characteristic of the quaternions inspired us to investigate how the quantum states and quantum operator work in the field of quaternions and how we can use it to construct a quantum neural network. This new type of quantum neural network (QNN) is developed in the quaternion algebra framework that is isomorphic to the rotor algebra G 3 + of the geometric algebra and is based on the so-called qubit neuron model. The quaternion quantum neural network (QQNN) is tested and shows robust performance. [ABSTRACT FROM AUTHOR]

Inspired by Laughlin's theory of the fractional quantum Hall effect, we explore the topological nature of the quark–gluon plasma (QGP) and the nucleons in the context of the Clifford algebra. In our model, each quark is transformed into a composite particle via the simultaneous attachment of a spin monopole and an isospin monopole. This is induced by a novel kind of meson endowed with both spin and isospin degrees of freedom. The interactions in the strongly coupled quark–gluon system are governed by the topological winding number of the monopoles, which is an odd integer to ensure that the overall wave function is antisymmetric. The states of the QGP and the nucleons are thus uniquely determined by the combination of the monopole winding number m and the total quark number N. The radius squared of the QGP droplet is expected to be proportional to m N. We anticipate the observation of such proportionality in the heavy ion collision experiments. [ABSTRACT FROM AUTHOR]