The Dawning of Gauge Theory

O’Raifeartaigh, L.; Mills, Robert

doi:10.1119/1.18781

Cited by 83 publications

(97 citation statements)

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“…Gauge theories are very successful in high energy physics to understand and to explain fundamental interactions (see, e.g., [1,2]). Important solutions in gauge theories are topological strings like the so-called Abrikosov-Nielson-Olesen string [3,4].…”

Section: Reviewing Remarksmentioning

confidence: 99%

The gauge theory of dislocations: Static solutions of screw and edge dislocations

Lazar¹,

Anastassiadis²

2009

Philosophical Magazine

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We investigate the T (3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations bilinear in the elastic distortion tensor and dislocation density tensor for the force and pseudomoment stresses of an isotropic solid. The constitutive relations contain six material parameters. In this theory both the force and pseudomoment stresses are asymmetric. The theory possesses four characteristic lengths ℓ 1 , ℓ 2 , ℓ 3 and ℓ 4 which are given explicitely. We first derive the three-dimensional Green tensor of the master equation for the force stresses in the translational gauge theory of dislocations. We then investigate the situation of generalized plane strain (anti-plane strain and plane strain). Using the stress function method, we find modified stress functions for screw and edge dislocations. The solution of the screw dislocation is given in terms of one independent length ℓ 1 = ℓ 4 . For the problem of an edge dislocation, only two characteristic lengths ℓ 2 and ℓ 3 arise with one of them being the same ℓ 2 = ℓ 1 as for the screw dislocation. Thus, this theory possesses only two independent lengths for generalized plane strain. If the two lengths ℓ 2 and ℓ 3 of an edge dislocation are equal, we obtain an edge dislocation which is the gauge theoretical version of a modified Volterra edge dislocation. In the case of symmetric stresses we recover well known results obtained earlier.

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Section: Reviewing Remarksmentioning

confidence: 99%

The gauge theory of dislocations: Static solutions of screw and edge dislocations

Lazar¹,

Anastassiadis²

2009

Philosophical Magazine

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“…Further, London showed that Schrödinger's wave function was proportional to Weyl's scale factor. Weyl seized upon this result and raised London's result to the level of a principle [10], referred to as Weyl's quantum principle [11]. This, together with Weyl's display that the gauge potentials formed the scale factor in his geometry, led to the electromagnetic gauge fields.…”

Section: Discussionmentioning

confidence: 99%

“…This, together with Weyl's display that the gauge potentials formed the scale factor in his geometry, led to the electromagnetic gauge fields. Providing the basis for all the subsequent gauge fieldwork that Einstein referred to in 1940 and the work that has followed in the search for a description of the weak and the strong nuclear forces [11].…”

Section: Discussionmentioning

confidence: 99%

Energy and Entropy as the Fundaments of Theoretical Physics

Williams

2002

Entropy

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“…Note that the use of such reference tetrads has a long history, dating back to Weyl's 1929 paper [6]. To show that the Dirac bispinor Lagrangian depends only on a tetrad and a scalar field, requires an appropriate choice of reference tetrad.…”

Section: Introductionmentioning

confidence: 99%