Related papers: Application of Generalized Quaternion in Physics
This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation…
We discus the role of QCD (Quantum Chromodynamics) to low energy phenomena involving the color-spin symmetry of the quark model. We then combine it with orbital and isospin symmetry to obtain wave functions with the proper permutation…
Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…
A considerable amount of the standard model's three-generation structure can be realised from just the $8\hspace{.3mm}\mathbb{C}$-dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can…
Four global gauge transformation of the free fermion Lagrangian is considered. One of these transformations has S(1) symmetry, other transformation has SU(2) symmetry, and two others have SU(3) symmetry. It is supposed, that these…
We describe our recent lattice study of SU(4) gauge theory with fermions in the fundamental and sextet representations. In this theory, a new type of baryon consists of quarks in both representations. The spectrum of these "chimera baryons"…
We review recent developments in our understanding of the dynamics of strongly-coupled chiral $SU(N)$ gauge theories in four dimensions, problems which are potentially important in our quest to go beyond the standard $SU(3)_{QCD} \times…
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for…
Quantum chromodynamics in two spacetime dimensions admits a finite non-invertible symmetry described mathematically by a fusion category. This symmetry is spontaneously broken at long distances, leading to distinct vacua. When the theory…
Chiral tetrahedral molecules can be dealt under the standard of quaternionic algebra. Specifically, non-commutativity of quaternions is a feature directly related to the chirality of molecules. It is shown that a quaternionic representation…
These lectures provide an overview of Quantum Chromodynamics (QCD), the SU(3) gauge theory of the strong interactions. The running of the strong coupling and the associated property of Asymptotic Freedom are analyzed. Some selected…
We investigate quantum chromodynamics with two colors at nonvanishing density using Dyson-Schwinger equations. Lattice methods do not have a complex action problem in this theory. Thus, we can benchmark our results and the effect of…
This paper presents some preliminary discussion on the possible relevance of the Okubonions, i.e. the real Okubo algebra $\mathcal{O}$, in quantum chromodynamics (QCD). The Okubo algebra lacks a unit element and sits in the adjoint…
We discuss the possible applications supersymmetric theories might find in the field of elementary particle physics. The supersymmetric generalization of the $SU(3)\times SU(2)\times U(1)$ standard model is discussed in detail. Special…
The dressing of bare massless quarks is described with a spatial theory based on the self-consistent solution of the QCD field equations. After quantization these equations are expressed in terms of quark and gluon creation and annihilation…
We study thermodynamics of strongly coupled lattice QCD with two colors of massless staggered fermions as a function of the baryon chemical potential $\mu$ in 3+1 dimensions using a new cluster algorithm. We find evidence that the model…
Motivated by the growing attention devoted to the Quantum Chromodynamics sector of the Standard Model, and the recent observations of non-standard hadronic states, a possible substructure of quarks $q_{f}\equiv C_{ij}|k_{i}k_{j}\rangle $ in…
We analyse the $\theta$-angle physics associated to extensions of the standard model of particle interactions featuring new strongly coupled sectors. We start by providing a pedagogical review of the $\theta$-angle physics for Quantum…
The strong interaction - governed by Quantum Chromodynamics (QCD) - shapes the structure of the visible universe. At about 10 $\mu$s after the big bang, the primordial matter made up of quarks and gluons plus leptons, photons and neutrinos,…
We review the phenomenon of color coherence in quantum chromodynamics (QCD), its implications for hard and soft processes with nuclei, and its experimental manifestations. The relation of factorization theorems in QCD with color coherence…