Gravity as an internal Yang-Mills gauge field theory of the Poincar� group

1981 ◽  
Vol 13 (10) ◽  
pp. 947-962 ◽  
Author(s):  
J�rg Hennig ◽  
J�rgen Nitsch
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Field Theory ◽  
Yang Mills

SYMMETRY BREAKING IN GAUGE FIELD THEORY DUE TO NONCOMMUTATIVE SPACETIME

2005 ◽  
Vol 14 (02) ◽  
pp. 215-218 ◽  
Author(s):  
B. G. SIDHARTH
Keyword(s):  
Field Theory ◽  
Symmetry Breaking ◽  
Gauge Field ◽  
Gauge Field Theory ◽  
Yang Mills ◽  
Interaction Field ◽  
Breaking Mechanism ◽  
Noncommutative Spacetime ◽  
Usual Theory

It is well known that a typical Yang–Mills Gauge Field is mediated by massless Bosons. It is only through a symmetry breaking mechanism, as in the Salam–Weinberg model that the quanta of such an interaction field acquire a mass in the usual theory. Here, we demonstrate that without taking recourse to the usual symmetry breaking mechanism, it is still possible to achieve this, given a noncommutative geometrical underpinning for spacetime.

A UNIFIED GAUGE FIELD LAGRANGIAN FOR ELECTROWEAK STRONG AND GRAVITATIONAL INTERACTION

1994 ◽  
Vol 03 (01) ◽  
pp. 313-316
Author(s):  
THEO VERWIMP
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Particle Physics ◽  
Principal Bundle ◽  
Gravitational Interaction ◽  
Electroweak Interaction ◽  
The Other ◽  
Gauge Field Theory ◽  
Yang Mills ◽  
Fundamental Interactions

Gravity can be descibed as a gauge field theory where connection and curvature are so(2,3)-valued. In the standard gauge field theory for strong and electroweak interaction corresponding quantities take their value in the su(3)⊕su(2)⊕u(1) algebra. Therefore, unification of gravity with the other fundamental interactions is obtained by using the non-compact simple real Lie algebra so*(14)⊃so(2,3)⊕su(3)⊕su(2)⊕u(1) as a unifying algebra. The so*(14) gauge field defined by a connection one-form on the SO*(14) principal fiber bundle unifies the fundamental interactions in particle physics, gravity included. The unified gauge field Lagrangian is defined by the Yang-Mills Weil form on the SO*(14) principal bundle.

Discovery of the first Yang–Mills gauge particle — The gluon

2015 ◽  
Vol 30 (34) ◽  
pp. 1530066
Author(s):  
Sau Lan Wu
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Field Theory ◽  
Higgs Particle ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Experimental Discovery ◽  
Chen Ning Yang

This article “Discovery of the First Yang–Mills Gauge Particle — The Gluon” is dedicated to Professor Chen Ning Yang. The Gluon is the first Yang–Mills non-Abelian gauge particle discovered experimentally. The Yang–Mills non-Abelian gauge field theory was proposed by Yang and Mills in 1954, sixty years ago. The experimental discovery of the first Yang–Mills non-Abelian gauge particle — the gluon — in the spring of 1979 is summarized, together with some of the subsequent developments, including the role of the gluon in the recent discovery of the Higgs particle.

scholarly journals Octonionic ternary gauge field theories revisited

2014 ◽  
Vol 11 (03) ◽  
pp. 1450013 ◽  
Author(s):  
Carlos Castro
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Gauge Field Theory ◽  
Gauge Fields ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Closure Relations ◽  
Nonassociative Geometry

An octonionic ternary gauge field theory is explicitly constructed based on a ternary-bracket defined earlier by Yamazaki. The ternary infinitesimal gauge transformations do obey the key closure relations [δ1, δ2] = δ3. An invariant action for the octonionic-valued gauge fields is displayed after solving the previous problems in formulating a nonassociative octonionic ternary gauge field theory. These octonionic ternary gauge field theories constructed here deserve further investigation. In particular, to study their relation to Yang–Mills theories based on the G2 group which is the automorphism group of the octonions and their relevance to noncommutative and nonassociative geometry.

Riemann–Weyl in Deleuze's Bergsonism and the Constitution of the Contemporary Physico-Mathematical Space

2015 ◽  
Vol 9 (1) ◽  
pp. 59-87 ◽  
Author(s):  
Martin Calamari
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Fibre Bundle ◽  
History Of Mathematics ◽  
Gauge Field Theory ◽  
Contemporary Science ◽  
Explicit Mention ◽  
History Of ◽  
Key Features ◽  
Bernhard Riemann

In recent years, the ideas of the mathematician Bernhard Riemann (1826–66) have come to the fore as one of Deleuze's principal sources of inspiration in regard to his engagements with mathematics, and the history of mathematics. Nevertheless, some relevant aspects and implications of Deleuze's philosophical reception and appropriation of Riemann's thought remain unexplored. In the first part of the paper I will begin by reconsidering the first explicit mention of Riemann in Deleuze's work, namely, in the second chapter of Bergsonism (1966). In this context, as I intend to show first, Deleuze's synthesis of some key features of the Riemannian theory of multiplicities (manifolds) is entirely dependent, both textually and conceptually, on his reading of another prominent figure in the history of mathematics: Hermann Weyl (1885–1955). This aspect has been largely underestimated, if not entirely neglected. However, as I attempt to bring out in the second part of the paper, reframing the understanding of Deleuze's philosophical engagement with Riemann's mathematics through the Riemann–Weyl conjunction can allow us to disclose some unexplored aspects of Deleuze's further elaboration of his theory of multiplicities (rhizomatic multiplicities, smooth spaces) and profound confrontation with contemporary science (fibre bundle topology and gauge field theory). This finally permits delineation of a correlation between Deleuze's plane of immanence and the contemporary physico-mathematical space of fundamental interactions.

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