The mathematical foundations of gauge theory revisited

@article{Pommaret2013TheMF,
  title={The mathematical foundations of gauge theory revisited},
  author={J. F. Pommaret},
  journal={arXiv: Analysis of PDEs},
  year={2013}
}
  • J. Pommaret
  • Published 17 October 2013
  • Physics
  • arXiv: Analysis of PDEs
We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies or hydrodynamics, though using the same group theoretical methods and despite the well known couplings existing between elasticity and electromagnetism (piezzoelectricity, photoelasticity, streaming birefringence). The purpose of this paper is to avoid such contradictions by using new… 
In : Gauge Theories and Differential Geometry
In 1870, R. Clausius found the virial theorem which amounts to introduce the trace of the stress tensor when studying the foundations of thermodynamics, as a way to relate the absolute temperature of
Why Gravitational Waves Cannot Exist
The purpose of this short but difficult paper is to revisit the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT) in the light of a modern approach to nonlinear systems
From Elasticity to Electromagnetism: Beyond the Mirror.
The first purpose of this short but striking paper is to revisit Elasticity (EL) and Electromagnetism (EM) by comparing the structure of these two theories and examining with details their well known
Nonlinear Conformal Electromagnetism and Gravitation
In 1909 the brothers E. and F. Cosserat discovered a new nonlinear group theoretical approach to elasticity (EL), with the only experimental need to measure the EL constants. In a modern language,
CLAUSIUS/COSSERAT/MAXWELL/WEYL EQUATIONS: THE VIRIAL THEOREM REVISITED
In 1870, R. Clausius found the virial theorem which amounts to introduce the trace of the stress tensor when studying the foundations of thermodynamics, as a way to relate the absolute temperature of
Nonlinear Conformal Electromagnetism
In 1909 the brothers E. and F. Cosserat discovered a new nonlinear group theoretical approach to elasticity (EL), with the only experimental need to measure the EL constants. In a modern language,
Algebraic analysis and general relativity
The purpose of this paper, which is largely self-contained though it is a difficult task, is to revisit the mathematical foundations of General Relativity (GR) after one century, in the light of the
Differential algebra and mathematical physics
Many equations of mathematical physics are described by differential polynomials, that is by polynomials in the derivatives of a certain number of functions. However, up to the knowledge of the
Differential Homological Algebra and General Relativity
In 1916, F.S. Macaulay developed specific localization techniques for dealing with "unmixed polynomial ideals" in commutative algebra, transforming them into what he called "inverse systems" of
Computer Algebra and Lanczos Potential.
We found in 2016 a few results on the mathematical structure of the conformal Killing differential sequence in arbitrary dimension $n$, in particular the rank and order changes of the successive
...
...

References

SHOWING 1-10 OF 62 REFERENCES
The mathematical foundations of general relativity revisited
The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and
MAGNETIC MONOPOLES, FIBER BUNDLES, AND GAUGE FIELDS
The reports in this monograph have shown great enthusiasm and exuberance for the unification of various interactions through the concept of gauge fields. I would like to emphasize a point that has
SOME RESEARCHES ON GAUGE THEORIES OF GRAVITATION
It is suggested that the geometrical properties of space-time with some gauge symmetries can be determined by the physical properties of matter with the same gauge symmetries. With this principle
"Sur une forme nouvelle des ´ equations de la M´ ecanique"
We present in modern language the contents of the famous note published by Henri Poincare in 1901 "Sur une forme nouvelle des ´ equations de la Mecanique", in which he proves that, when a Lie algebra
Spencer Operator and Applications: From Continuum Mechanics to Mathematical Physics"
The Spencer operator, introduced by D.C. Spencer fifty years ago, is rarely used in mathematics today and, up to our knowledge, has never been used in engineering applications or mathematical
Parametrization of Cosserat equations
The solution space of many systems of ordinary differential (OD) or partial differential (PD) equations in engineering or mathematical physics “can/cannot” be parameterized by a certain number of
Théorie des Corps déformables
THE authors, who are well known by their writings on general elastic theory, here reprint in separate form an appendix contributed by them to M. Chwolson's “Traité de Physique.” The kinematical and
Algebraic analysis of control systems defined by partial differential equations
The present chapter contains the material taught within the module P2 of FAP 2004. The purpose of this intensive course is first to provide an introduction to algebraic analysis. This fashionable
Group interpretation of coupling phenomena
SummaryIt is well known that group theory interferes with constitutive (Hooke, Fourier, Minkowski) laws and coupling phenomena (piezoelectricity, thermoelasticity, photoelasticity, thermoelectricity)
An Introduction to Homological Algebra
An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext
...
...