Fundamental Gauge Symmetries Research Articles

Gravitational wave imprint of new symmetry breaking * *JS is Supported by the National Natural Science Foundation of China (11647601, 11690022, 11675243) and also Supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB23030100). Wei Chao is Supported by the National Natural Science Foundation of China (11775025)

It is believed that there are more fundamental gauge symmetries beyond those described by the Standard Model of particle physics. The scales of these new gauge symmetries are usually too high to be reachable by particle colliders. Considering that the phase transition (PT) relating to the spontaneous breaking of new gauge symmetries to the electroweak symmetry might be strongly first order, we propose considering the stochastic gravitational waves (GW) arising from this phase transition as an indirect way of detecting these new fundamental gauge symmetries. As an illustration, we explore the possibility of detecting the stochastic GW generated from the PT of in the space-based interferometer detectors. Our study demonstrates that the GW energy spectrum is reachable by the LISA, Tianqin, Taiji, BBO, and DECIGO experiments only for the case where the spontaneous breaking of is triggered by at least two electroweak singlet scalars.

Modified Anyonic Particle and Its Fundamental Gauge Symmetries

In this article, we study the possibility of changing a physical degree of freedom of a particle to its quantum spin after quantization is applied. Our approach to do such a survey is increasing the fundamental symmetries of the anyonic particle model with the help of the symplectic formalism of constrained systems. After extracting the corresponding Poisson structure of all constraints, we compare the effect of gauging on the phase spaces, the number of physical degrees of freedom, canonical structures of both primary and gauged models, and the spin of the anyon, in terms of its energy.

Reformulation of the symmetries of first-order general relativity

We report a new internal gauge symmetry of the n-dimensional Palatini action with cosmological term () that is the generalization of three-dimensional local translations. This symmetry is obtained through the direct application of the converse of Noether’s second theorem on the theory under consideration. We show that diffeomorphisms can be expressed as linear combinations of it and local Lorentz transformations with field-dependent parameters up to terms involving the variational derivatives of the action. As a result, the new internal symmetry together with local Lorentz transformations can be adopted as the fundamental gauge symmetries of general relativity. Although their gauge algebra is open in general, it allows us to recover, without resorting to the equations of motion, the very well-known Lie algebra satisfied by translations and Lorentz transformations in three dimensions. We also report the analog of the new gauge symmetry for the Holst action with cosmological term, finding that it explicitly depends on the Immirzi parameter. The same result concerning its relation to diffeomorphisms and the open character of the gauge algebra also hold in this case. Finally, we consider the non-minimal coupling of a scalar field to gravity in n dimensions and establish that the new gauge symmetry is affected by this matter field. Our results indicate that general relativity in dimension greater than three can be thought of as a gauge theory.

Toward black hole entropy in shape dynamics

Shape dynamics is a classical theory of gravity which agrees with general relativity in many important cases, but possesses different gauge symmetries and constraints. Rather than spacetime diffeomorphism invariance, shape dynamics takes spatial diffeomorphism invariance and spatial Weyl invariance as the fundamental gauge symmetries associated with the gravitational field. Since the area of the event horizon of a black hole transforms under a generic spatial Weyl transformation, there has been some doubt that one can speak sensibly about the thermodynamics of black holes in shape dynamics. The purpose of this paper is to show that by treating the event horizon of a black hole as an interior boundary, one can recover familiar notions of black hole thermodynamics in shape dynamics and define a gauge invariant entropy that agrees with general relativity.

Hamiltonian dynamics and gauge symmetry for three-dimensional Palatini theory with cosmological constant

A pure Dirac's framework for 3D Palatini's theory with cosmological constant is performed. By considering the complete phase space, we find out the full structure of the constraints, and their corresponding algebra is computed explicitly. We report that in order to obtain a well defined algebra among the constraints, the gauge group must be $SO(2,1)$. In addition, we obtain the extended action, the extended Hamiltonian, the fundamental gauge symmetry, and the Dirac brackets of the theory. Finally, we compare our results with those reported in the literature.

Taylor–Lagrange renormalization and gauge theories in four dimensions

The treatment of gauge theories within the recently proposed Taylor–Lagrange renormalization scheme (TLRS) is examined in detail. The conservation of gauge symmetry is demonstrated directly at the physical dimension D = 4 for specific examples of fermion and boson self energies and vertices of QED and QCD. Comparisons with dimensional regularization and Bogoliubov–Parasiuk–Hepp–Zimmermann (BPHZ) substractions, improved by algebraic regularization based on the quantum action principle, exhibit clearly the important mathematical properties of the TLRS leading to conservation of this fundamental gauge symmetry.

Fermion masses in emergent electroweak symmetry breaking

We consider the generation of fermion masses in an emergent model of electroweak symmetry breaking with composite W,Z gauge bosons. A universal bulk fermion profile in a warped extra dimension is used for all fermion flavors. Electroweak symmetry is broken at the UV (or Planck) scale where boundary mass terms are added to generate the fermion flavor structure. This leads to flavor-dependent nonuniversality in the gauge couplings. The effects are suppressed for the light fermion generations but are enhanced for the top quark where the \( Zt\bar{t} \) and \( Wt\bar{b} \) couplings can deviate at the 10–20% level in the minimal setup. By the AdS/CFT correspondence our model implies that electroweak symmetry is not a fundamental gauge symmetry. Instead the Standard Model with massive fermions and W,Z gauge bosons is an effective chiral Lagrangian for some underlying confining strong dynamics at the TeV scale, where mass is generated without a Higgs mechanism.

U⋆(1,1)noncommutative gauge theory as the foundation of two-time physics in field theory

A very simple field theory in noncommutative phase space X^{M},P^{M} in d+2 dimensions, with a gauge symmetry based on noncommutative u*(1,1), furnishes the foundation for the field theoretic formulation of Two-Time Physics. This leads to a remarkable unification of several gauge principles in d dimensions, including Maxwell, Einstein and high spin gauge principles, packaged together into one of the simplest fundamental gauge symmetries in noncommutative quantum phase space in d+2 dimensions. A gauge invariant action is constructed and its nonlinear equations of motion are analyzed. Besides elegantly reproducing the first quantized worldline theory with all background fields, the field theory prescribes unique interactions among the gauge fields. A matrix version of the theory, with a large N limit, is also outlined

Possible Effects of a Composite Iso-Scalar Weak Boson in a Left-Right Symmetric Preon Model

We assume that a fundamental gauge symmetry is never brokenj, and any short range interactions should be secondary, appearing as residual effects of some fundamental gauge interactions. On this assumption the weak interaction is considered to be a secondary effective one among composite quarks, leptons and weak bosons with respective appropriate preon and/or anti-Preon configurations bounded by a new fundamental gauge interaction. In this work, applying a fermion-boson type preon scheme and supposing confinement and a preon line rule (like the OZI-rule) for the confining force, we concentrate to investigate lower mass limit of the additional iso-scalar particle, whose existence in naturally expected in our scheme, permitted by a low energy experiment

Excited weak vector bosons facing the high energy and high precision frontier

If the recently discovered weak bosons W ± and Z were manifestations of a composite structure of the weak interactions rather than the commonly assumed gauge bosons of a fundamental gauge symmetry one is naturally led to expect a corresponding spectrum of excited weak vector bosons. Experiments at LEP I/SLC and LEP II may be uniquely suited to shed light on this question with their power to perform high precision tests of the standard model.

Field theories without fundamental gauge symmetries

By using the lack of dependence of the form of the kinetic energy for a nonrelativistic free particle as an example, it is argued that a physical law with a less extended range of application (non-relativistic energy momentum relation) often follows from a more extended one (in this case the relativistic relation) without too much dependence on the details of the latter. We extend the lesson from such examples to the ideal of random dynamics: no fundamental laws are needed to be known. Almost any random fundamental model will give the correct main features for the range of physical conditions accessible to us today (energies less than 1000 GeV) even if it is wrong in detail. This suggests the programme of attempting to ‘derive’ the various symmetries and other features of physics known today from random models at least without the feature to be derived. As an example, D. Forster, M. Ninomiya and myself ‘ derive ’ gauge invariance in this way (Forster et al ., Phys. Lett . B 94, 135 (1980)), and show that it has at least a nonzero probability for being effectively a symmetry. In fact we show that a certain nongauge-symmetric lattice model has zero mass photons for a whole range of its parameters, so that it is not necessary to fine tune it to get massless photons. It comes about by means of a formal gauge symmetry achieved by introducing a superfluous number of field variables. The achievements in our programme of random dynamics up till now are briefly reviewed. In particular, Lorentz invariance may be understood as a low energy phenomenon (S. Chadha, M. Ninomiya and myself). An analogy between the development of physics as one goes to lower and lower energies and that of living species through the history of the Earth is put forward.