Related papers: Theory of Classical Higgs Fields. I. Matter Fields
Some mathematical aspects of using the translation group as an internal symmetry group in a gauge field theory are presented and discussed. The traditional manner in which gravitation can be accounted for by the introduction of a global…
We define a discrete gauge-invariant Yang-Mills-Higgs action on spacetime simplicial meshes. The formulation is a generalization of classical lattice gauge theory, and we prove consistency of the action in the sense of approximation theory.…
A field theory with local transformations belonging to the quantum group SU_q(n) is defined on a classical spacetime, with gauge potentials belonging to a quantum Lie algebra. Gauge transformations are defined for the potentials which lead…
We present a short review of theories based on warped extra dimensions (motivated by the hierarchy problem of the Standard Model) which can accomodate a Higgs boson in the range suggested by the recent LHC results at 7 TeV. Using the…
In a previous paper (hep-th/9801040), the superconnection formalism was used to fit the Higgs field into a U(n) gauge theory with particular emphasis on the n=2 case, aiming at the reconstruction of certain parts of the Standard Model. The…
In this paper we study $G$-Higgs bundles over an elliptic curve when the structure group $G$ is a classical complex reductive Lie group. Modifying the notion of family, we define a new moduli problem for the classification of semistable…
Based upon a first principle, the generalized gauge principle, we construct a general model with $G_L\times G'_R \times Z_2$ gauge symmetry, where $Z_2=\pi_4(G_L)$ is the fourth homotopy group of the gauge group $G_L$, by means of the…
We consider the unification of gauge, Higgs as well as the matter fields in a 6D N=2 supersymmetric SU(8) gauge theory. The gauge symmetry SU(8) is broken down to SU(4) x SU(2)_L x SU(2)_R x U(1)^2 in 4D through T^2/Z_6 orbifold…
The Connes and Lott reformulation of the strong and electroweak model represents a promising application of noncommutative geometry. In this scheme the Higgs field naturally appears in the theory as a particular `gauge boson', connected to…
The Higgs model is generalized so that in addition to the radial Higgs field there are fields which correspond to the themasy and entropy. The model is further generalized to include state and sign parameters. A reduction to the standard…
A principal Higgs bundle $(P,\phi)$ over a singular curve $X$ is a pair consisting of a principal bundle $P$ and a morphism $\phi:X\to\text{Ad}P \otimes \Omega^1_X$. We construct the moduli space of principal Higgs G-bundles over an…
A quantum field theory formalism is reviewed that leads to a self-consistent, finite quantum gravity, Yang-Mills and Higgs theory, which is unitary and gauge invariant to all orders of perturbation theory. The gauge hierarchy problem is…
A quadratic Leibniz algebra $(\mathbb{V},[ \cdot, \cdot ],\kappa)$ gives rise to a canonical Yang-Mills type functional $S$ over every space-time manifold. The gauge fields consist of 1-forms $A$ taking values in $\mathbb{V}$ and 2-forms…
We argue that, ideally, the ways to measure magnitudes in non-quantum theories of physics (spacetime, field theory), limit drastically their possible mathematical models. In particular, gauge invariance in the Yang-Mills framework, is a…
Unitary representations of the fundamental group of a Kahler manifold correspond to polystable vector bundles (with vanishing Chern classes). Semisimple linear representations correspond to polystable Higgs bundles. In this paper we find…
Physics associated with the Higgs field potential is rich and interesting and deserves a concise summary for a broader audience to appreciate the beauty and the challenges of this subject. We discuss the role of the Higgs potential in…
Based on local gauge invariance, four different kinds of fundamental interactions in Nature are unified in a theory which has $SU(3)_c \otimes SU(2)_L \otimes U(1) \otimes_s Gravitational Gauge Group$ gauge symmetry. In this approach,…
We prove a closed formula counting semistable twisted Higgs bundles of fixed rank and degree over a smooth projective curve defined over a finite field. We also prove a formula for the Donaldson-Thomas invariants of the moduli spaces of…
We explore a novel way of deriving the effective Higgs Lagrangian from strongly interacting vector-like gauge theories. We consider the N=1 supersymmetric extension of gauge theories and interpret the auxiliary field associated with the low…
We argue that a general system of scalar fields and gauge fields manifesting vacuum degeneracy induces a principal groupoid bundle over spacetime and that the pattern of spontaneous symmetry breaking and the Higgs mechanism are encoded by…