Non-abelian whole gauge symmetry

2015 ◽  
Vol 10 (3) ◽  
pp. 2834-2870
Author(s):  
Renato Doria
Keyword(s):  
Gauge Symmetry ◽  
Conservation Laws ◽  
Symmetry Group ◽  
Gauge Group ◽  
Brst Symmetry ◽  
Noether Theorem ◽  
Physical Processes ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Physical Laws

The wholeness principle is analysed for non-abelian gauge symmetry. This principle states that nature acts through grouping. It says that physical laws should be derived from elds associations. At this work, we consider on the possibility of introducting a non-abelian elds set fAaIg under a common gauge parameter.A Yang-Mills extension is studied. Taking the SU(N) symmetry group with different potential elds rotating under a same group, new elds strengths are developed. They express covariant entities which are granular, collective, correlated, and not necessarily Lie algebra valued. They yield new scalars and a Lagrangian beyond Yang-Mills is obtained. Classical equations are derived and (2N + 7) equations are developed. A further step is on how such non-abelian whole symmetry is implemented at SU(N) gauge group. For this, it is studied on the algebra closure and Jacobi identities, Bianchi identities, Noether theorem, gauge xing, BRST symmetry, conservation laws, covariance, charges algebra. As result, one notices that it is installed at SU(N) symmetry independentlyon the number of involved elds. Given this consistency, Yang-Mills should not more be considered as the unique Lagrangian performed from SU(N).Introducting the BRST symmetry an invariant Leff is stablished. The BRST charge associated to the N-potential elds system is calculated and its nilpotency property obtained.Others conservations laws involving ghost scale, global charges are evalued showing that this whole symmetry extension preserve the original Yang-Mills algebra. Also the ghost number is conserved. These results imply that Yang-Mills should be understood as a pattern and not as a specic Lagrangian.Concluding, an extended Lagrangian can be constructed. It is possible to implement a non-abelian whole gauge symmetry based on a elds set fAaIg. Its physical feature is a systemic interpretation for the physical processes. Understand complexity from whole gauge symmetry.

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

scholarly journals Superfield approach to nilpotent symmetries in 3D Jackiw–Pi model of massive non-Abelian theory

2014 ◽  
Vol 92 (9) ◽  
pp. 1033-1042 ◽  
Author(s):  
S. Gupta ◽  
R. Kumar ◽  
R.P. Malik
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Point Of View ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

In the available literature, only the Becchi–Rouet–Stora–Tyutin (BRST) symmetries are known for the Jackiw–Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent [Formula: see text] and absolutely anticommuting (sbsab + sabsb = 0) (anti-)BRST transformations s(a)b corresponding to the usual Yang–Mills gauge transformations of this model by exploiting the “augmented” superfield formalism where the horizontality condition and gauge invariant restrictions blend together in a meaningful manner. There is a non-Yang–Mills (NYM) symmetry in this theory, too. However, we do not touch the NYM symmetry in our present endeavor. This superfield formalism leads to the derivation of an (anti-)BRST invariant Curci–Ferrari restriction, which plays a key role in the proof of absolute anticommutativity of s(a)b. The derivation of the proper anti-BRST symmetry transformations is important from the point of view of geometrical objects called gerbes. A novel feature of our present investigation is the derivation of the (anti-)BRST transformations for the auxiliary field ρ from our superfield formalism, which is neither generated by the (anti-)BRST charges nor obtained from the requirements of nilpotency and (or) absolute anticommutativity of the (anti-)BRST symmetries for our present 3D non-Abelian 1-form gauge theory.

MAGNETOFLUID UNIFICATION IN YANG–MILLS LAGRANGIAN

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3630-3637 ◽  
Author(s):  
A. SULAIMAN ◽  
A. FAJARUDIN ◽  
T. P. DJUN ◽  
L. T. HANDOKO
Keyword(s):  
Gauge Symmetry ◽  
Gauge Field ◽  
Lagrangian Approach ◽  
General Description ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Relativistic Fluid ◽  
Physical Consequences

The magnetofluid unification is constructed using lagrangian approach by imposing a non-Abelian gauge symmetry to the matter inside the fluid. The model provides a general description for relativistic fluid interacting with either Abelian or non-Abelian gauge field. The differences with the hybrid magnetofluid model are discussed, and some physical consequences of this formalism are briefly worked out.

scholarly journals Non-Abelian Gauge Symmetry in the Causal Epstein–Glaser Approach

1997 ◽  
Vol 12 (24) ◽  
pp. 4461-4476 ◽  
Author(s):  
Tobias Hurth
Keyword(s):  
Perturbation Theory ◽  
Gauge Symmetry ◽  
Gauge Invariance ◽  
Fock Space ◽  
Dimensional Space ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Tree Graphs ◽  
Adiabatic Switching ◽  
Dimensional Space Time

Non-Abelian gauge symmetry in (3 + 1)-dimensional space–time is analyzed in the causal Epstein–Glaser framework. In this formalism, the technical details concerning the well-known UV and IR problem in quantum field theory are separated and reduced to well-defined problems, namely the causal splitting and the adiabatic switching of operator-valued distributions. Non-Abelian gauge invariance in perturbation theory is completely discussed in the well-defined Fock space of free asymptotic fields. The LSZ formalism is not used in this construction. The linear operator condition of asymptotic gauge invariance is sufficient for the unitarity of the S matrix in the physical subspace and the usual Slavnov–Taylor identities. We explicitly derive the most general specific coupling compatible with this condition. By analyzing only tree graphs in the second order of perturbation theory we show that the well-known Yang–Mills couplings with anticommuting ghosts are the only ones which are compatible with asymptotic gauge invariance. The required generalizations for linear gauges are given.

PREPOTENTIALS AND UNCONSTRAINED BRST FOR YANG-MILLS AND p-FORMS

1992 ◽  
Vol 07 (22) ◽  
pp. 2039-2049
Author(s):  
MARIO ABUD ◽  
JEAN-PIERRE ADER ◽  
LUIGI CAPPIELLO
Keyword(s):  
Gauge Group ◽  
Brst Symmetry ◽  
Universal Enveloping Algebra ◽  
Yang Mills ◽  
Enveloping Algebra ◽  
Geometrical Description

We study the unconstrained formulation of the BRST symmetry of the Yang-Mills theory. The system of fields entering in the corresponding BRST2 algebra is given a geometrical description in terms of non-homogeneous forms belonging to the universal enveloping algebra of the gauge group. The extension of the BRST2 symmetry to non-Abelian p-forms is also discussed.

A non-abelian model SU(N) × SU(N)

2015 ◽  
Vol 8 (1) ◽  
pp. 1988-2004
Author(s):  
Renato Doria ◽  
M. J. Neves
Keyword(s):  
Gauge Symmetry ◽  
Momentum Space ◽  
Brst Symmetry ◽  
Power Counting ◽  
Physical Application ◽  
Tree Level ◽  
Color Symmetry ◽  
Yang Mills ◽  
Loop Approximation ◽  
Feynman Rules

A composite non-abelian model SU(N) × SU(N) is proposed as possible extension of the Yang-Mills symmetry. We obtain the corresponding gauge symmetry of the model and the most general lagrangian invariant by SU(N) × SU(N). The corresponding Feynman rules of the model are studied. Propagators and vertices are derived in the momentum space. As physical application, instead of considering the color symmetry SUc(3) for QCD, we substitute it by the combination SUc(3) × SUc(3). It yields a possibility to go beyond QCD symmetry in the sense that quarks are preserved with three colors. This extension provides composite quarks in triplets and sextets multiplets accomplished with the usual massless gluons plus massive gluons. We present a power counting analysis that satisfies the renormalization conditions as well as one studies the structure of radiative corrections to one loop approximation. Unitary condition is verified at tree level. Tachyons are avoided. For end, one extracts a BRST symmetry from lagrangian and Slavnov-Tayloridentities.

scholarly journals Exploring the landscape of CHL strings on Td

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Anamaría Font ◽  
Bernardo Fraiman ◽  
Mariana Graña ◽  
Carmen A. Núñez ◽  
Héctor Parra De Freitas
Keyword(s):  
Gauge Group ◽  
Moduli Space ◽  
Dynkin Diagram ◽  
Fundamental Groups ◽  
Computer Algorithms ◽  
Abelian Gauge ◽  
Reduced Rank ◽  
Systematic Exploration ◽  
String Models ◽  
Simply Connected

Abstract Compactifications of the heterotic string on special Td/ℤ2 orbifolds realize a landscape of string models with 16 supercharges and a gauge group on the left-moving sector of reduced rank d + 8. The momenta of untwisted and twisted states span a lattice known as the Mikhailov lattice II(d), which is not self-dual for d > 1. By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d ≤ 2, and give a list of maximally enhanced points where the U(1)d+8 enhances to a rank d + 8 non-Abelian gauge group. For d = 1, these groups are simply-laced and simply-connected, and in fact can be obtained from the Dynkin diagram of E10. For d = 2 there are also symplectic and doubly-connected groups. For the latter we find the precise form of their fundamental groups from embeddings of lattices into the dual of II(2). Our results easily generalize to d > 2.

scholarly journals Construction and Characterization of Representations of SU(7) for GUT Model Builders

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1044
Author(s):  
Daniel Jones ◽  
Jeffery A. Secrest
Keyword(s):  
Gauge Symmetry ◽  
Symmetry Group ◽  
Lie Group ◽  
Cartan Subalgebra ◽  
Natural Extension ◽  
Grand Unification ◽  
Raising And Lowering Operators ◽  
Higher Dimensional ◽  
Lowering Operators

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

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