Gauge Theories and Differential Geometry

Lance Bailey (Editor)

Series: Physics Research and Technology, Mathematics Research Developments
BISAC: SCI055000

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This book revisits the mathematical foundations of thermodynamics and gauge theory by using new differential geometric methods coming from the formal theory of systems of partial differential equations and Lie pseudogroups. The gauge theory of gravity is also established, in which spinorial and ventorial matter fields serve as gravitating sources. The potential applications of the present gauge theory of gravity, including quantum-vacuum-energy gravity, cosmological constant problem and gravity-gauge unification is also addressed. The third chapter focuses on a gravitational gauge theory with spin connection and vierbein as fundamental variables of gravity.

Next, the place and physical significance of Poincaré gauge theory of gravity (PGTG) in the framework of gauge approach to gravitation is discussed. A cutoff regularization method in gauge theory is discussed in Chapter Five. The remaining chapters in the book focus on differential geometry, in particular, the authors show how fractional differential derived from fractional difference provides a basis to expand a theory of fractional differential geometry which would apply to non-differentiable manifolds; a review of the infinitesimal Baker-Campbell-Hausdorff formula is provided and the book concludes with a short communication where the authors focus on local stability, and describe how this leads naturally into the question of finite-time singularities and generalized soliton solutions.
(Imprint: Nova)

Preface

Chapter 1
From Thermodynamics to Gauge Theory: The Virial Theorem Revisited
(J.-F. Pommaret, CERMICS, Ecole des Ponts ParisTech, France)
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Chapter 2
Gravitational Gauge Theory of Spinorial and Vectorial Gravitating Matter Fields
(Jian Qi Shen, Centre for Optical and Electromagnetic Research, Zijingang Campus, Zhejiang University, Hangzhou, China, and others)

Chapter 3
Gravitational Gauge Theory as a Route to Gravity-Gauge Unification
(Jian Qi Shen, Centre for Optical and Electromagnetic Research, Zijingang Campus, Zhejiang University, Hangzhou, China, and others)

Chapter 4
Poincaré Gauge Theory of Gravity, Gravitational Interaction and Regular Accelerating Universe
(A. V. Minkevich, Department of Theoretical Physics and Astrophysics, Belarussian State University, Minsk, Belarus, and others)

Chapter 5
Cutoff Regularization Method in Gauge Theories
(G. Cynolter and E. Lendvai, MTA-ELTE Theoretical Physics Research Group, Etvs University, Budapest, Hungary)

Chapter 6
An Approach to Fractional Differential Geometry and Fractal Space-Time via Fractional Calculus for Non-Differentiable Functions
(Guy Jumarie, University of Quebec at Montreal, Department of Mathematics, Down Town St Montreal, Qc, Canada)

Chapter 7
A Note on the Infinitesimal Baker-Campbell-Hausdorff Formula
(Hirokazu Nishimura and Hirowaki Takamiya, Institute of Mathematics, University of Tsukuba, Tsukuba, Ibarakim, Japan, and others)

Chapter 8
On the Curve Diffusion Flow: Invariant Functionals and Gauge Transformations
(Glen Wheeler, University of Wollongong, Australia)

Index

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