相关论文: Covering groups of the gauge group for the standar…

These are introductory notes on symmetries in quantum field theory and how they apply to particle physics. The notes cover the fundamentals of group theory, their representations, Lie groups, and Lie algebras, along with an elaborate…

Higgs fields are attributes of classical gauge theory on a principal bundle $P\to X$ whose structure Lie group $G$ if is reducible to a closed subgroup $H$. They are represented by sections of the quotient bundle $P/H\to X$. A problem lies…

We consider a quark-lepton symmetry model of unification of the strong and electromagnetic interactions. The model has the gauge group $SU(4)\times U(1)_{Y}$ and the minimal Higgs structure consisting of one complex quartet of scalar…

We determine the number and distribution of the fermion states in the standard model based on the possible fermion representations of the gauge bosons. By extracting the even parity scalars from the fermion states we suggest the existence…

In this review, the fundamental concepts of group theory and representation theory are introduced. Special emphasis is placed on the unitary irreducible representations of the $SU(N)$ Lie group, the Poincare group, Little Group, discrete…

The aim of this work is to find a simple mathematical framework for our established description of particle physics. We demonstrate that the particular gauge structure, group representations and charge assignments of the Standard Model…

We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $P\to X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/H\to X$ are treated as classical…

Many models of beyond Standard Model physics connect flavor symmetry with a discrete group. Having this symmetry arise spontaneously from a gauge theory maintains compatibility with quantum gravity and can be used to systematically prevent…

Finite symmetries abound in particle physics, from the weak doublets and generation triplets to the baryon octet and many others. These are usually studied by starting from a Lie group, and breaking the symmetry by choosing a particular…

We consider classical gauge theory on a principal bundle P->X in a case of spontaneous symmetry breaking characterized by the reduction of a structure group G of P->X to its closed subgroup H. This reduction is ensured by the existence of…

We present a classification of all scalar Lie point symmetries of the Standard Model with one or two real gauge-singlet scalars (SM+S and SM+2S). By analyzing the associated field equations, we identify all realizable and inequivalent Lie…

The gauge group of strong and electroweak interactions in Nature could be any of the four that share the same Lie algebra, $SU(3)_c\times SU(2)_L\times U(1)_Y/Z_p\equiv G_p$ with $Z_p=\left\{Z_6,Z_3,Z_2,Z_1\right\}$. Each of these cases…

In this set of four lectures I will discuss some aspects of the Standard Model (SM) as a quantum field theory and related phenomenological observations which have played a crucial role in establishing the $SU(2)_{L} \times U(1)_{Y}$ gauge…

We discuss a question whether the observed Weinberg angle and Higgs mass are calculable in the formalism based on a construction in which the electroweak gauge group $SU(2)\times U(1)_{Y}$ is embedded in the graded Lie group $SU(2/1)$. Here…

We give a brief overview how to couple general relativity to the Standard Model of elementary particles, within the higher gauge theory framework, suitable for the spinfoam quantization procedure. We begin by providing a short review of all…

We reconstruct the Lagrangian of a left-right symmetric model with the gauge group $SU(2)_L\times SU(2)_R\times U(1)_Y \times \pi_4(SU(2)_L\times SU(2)_R\times U(1)_Y) $. The Higgs fields appear as gauge fields on discrete gauge group…

We study several aspects of the quantum structure of the minimal potentially realistic renormalizable $\mathrm{SO}(10)$ Higgs model in which the $\mathbf{45}\oplus \mathbf{126}$ scalars spontaneously break the symmetry down to the Standard…

We consider the pair of degenerate compatible antibrackets satisfying a generalization of the axioms imposed in the triplectic quantization of gauge theories. We show that this actually encodes a Lie group structure, with the antibrackets…

We examine a dual theory of a Supersymmetric Standard Model(SSM) in terms of an $SU(3)_C$ gauge group. In this scenario, it is naturally understood that at least one quark (the top quark) should be heavy, i.e., almost the same order as the…

The gauge field term in the Standard Model Lagrangian is slightly rewritten, suggesting that the three gauge couplings have absorbed factors which depend on the dimensions of the corresponding gauge groups. The ratios of the physical…