scholarly journals Z 3-Graded exterior differential calculus and gauge theories of higher order

1996 ◽  
Vol 36 (4) ◽  
pp. 441-454 ◽  
Author(s):  
Richard Kerner
Keyword(s):  
Differential Calculus ◽  
Gauge Theories ◽  
Higher Order ◽  
Exterior Differential

Higher-order induced axial-vector isoscalar neutral current in gauge theories

1979 ◽  
Vol 19 (7) ◽  
pp. 2165-2178 ◽  
Author(s):  
R. N. Mohapatra ◽  
G. Senjanović
Keyword(s):  
Gauge Theories ◽  
Neutral Current ◽  
Axial Vector ◽  
Higher Order

scholarly journals Uq(N) GAUGE THEORIES

1994 ◽  
Vol 09 (30) ◽  
pp. 2835-2847 ◽  
Author(s):  
LEONARDO CASTELLANI
Keyword(s):  
Quantum Groups ◽  
Differential Calculus ◽  
Gauge Theories ◽  
Space Time ◽  
Yang Mills ◽  
Commutation Relations ◽  
Transformation Rules ◽  
Field Strengths

Improving on an earlier proposal, we construct the gauge theories of the quantum groups U q(N). We find that these theories are also consistent with an ordinary (commuting) space-time. The bicovariance conditions of the quantum differential calculus are essential in our construction. The gauge potentials and the field strengths are q-commuting "fields," and satisfy q-commutation relations with the gauge parameters. The transformation rules of the potentials generalize the ordinary infinitesimal gauge variations. For particular deformations of U (N) ("minimal deformations"), the algebra of quantum gauge variations is shown to close, provided the gauge parameters satisfy appropriate q-commutations. The q-Lagrangian invariant under the U q(N) variations has the Yang–Mills form [Formula: see text], the "quantum metric" gij being a generalization of the Killing metric.

The differential calculus of screws: Theory, geometrical interpretation, and applications

2009 ◽  
Vol 223 (6) ◽  
pp. 1449-1468 ◽  
Author(s):  
J J Cervantes-Sánchez ◽  
J M Rico-Martínez ◽  
G González-Montiel ◽  
E J González-Galván
Keyword(s):  
Differential Calculus ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Higher Order ◽  
Abstract Concepts ◽  
Serial Manipulators ◽  
Kinematic Chains ◽  
Finite Displacements ◽  
Typical Shape ◽  
Derivatives Of

This article presents a novel and original formula for the higher-order time derivatives, and also for the partial derivatives of screws, which are successively computed in terms of Lie products, thus leading to the automation of the differentiation process. Through the process and, due to the pure geometric nature of the derivation approach, an enlightening physical interpretation of several screw derivatives is accomplished. Important applications for the proposed formula include higher-order kinematic analysis of open and closed kinematic chains and also the kinematic synthesis of serial and parallel manipulators. More specifically, the existence of a natural relationship is shown between the differential calculus of screws and the Lie subalgebras associated with the expected finite displacements of the end effector of an open kinematic chain. In this regard, a simple and comprehensible methodology is obtained, which considerably reduces the abstraction level frequently required when one resorts to more abstract concepts, such as Lie groups or Lie subalgebras; thus keeping the required mathematical background to the extent that is strictly necessary for kinematic purposes. Furthermore, by following the approach proposed in this article, the elements of Lie subalgebra arise in a natural way — due to the corresponding changes in screws through time — and they also have the typical shape of the so-called ordered Lie products that characterize those screws that are compatible with the feasible joint displacements of an arbitrary serial manipulator. Finally, several application examples — involving typical, serial manipulators — are presented in order to prove the feasibility and validity of the proposed method.

scholarly journals Higher-order Sudakov resummation in coupled gauge theories

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Georgios Billis ◽  
Frank J. Tackmann ◽  
Jim Talbert
Keyword(s):  
Gauge Theories ◽  
Higher Order

scholarly journals AN INTRODUCTION TO NONCOMMUTATIVE DIFFERENTIAL GEOMETRY ON QUANTUM GROUPS

1993 ◽  
Vol 08 (10) ◽  
pp. 1667-1706 ◽  
Author(s):  
PAOLO ASCHIERI ◽  
LEONARDO CASTELLANI
Keyword(s):  
Differential Geometry ◽  
Quantum Group ◽  
Explicit Form ◽  
Quantum Groups ◽  
Differential Calculus ◽  
Gauge Theories ◽  
Classical Case ◽  
Contraction Operator ◽  
Lie Derivative ◽  
Tensor Fields

We give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case (q→1 limit). The Lie derivative and the contraction operator on forms and tensor fields are found. A new, explicit form of the Cartan-Maurer equations is presented. The example of a bicovariant differential calculus on the quantum group GL q(2) is given in detail. The softening of a quantum group is considered, and we introduce q curvatures satisfying q Bianchi identities, a basic ingredient for the construction of q gravity and q gauge theories.

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