Applied Mathematics & Optimization
, Volume 69, Issue 3, pp 359392
First online:
Unified Field Theory and Principle of Representation Invariance
 Tian MaAffiliated withDepartment of Mathematics, Sichuan University
 , Shouhong WangAffiliated withDepartment of Mathematics, Indiana University Email author
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The main objectives of this article are to postulate a new principle of representation invariance (PRI), and to refine the unified field model of four interactions, derived using the principle of interaction dynamics (PID). Intuitively, PID takes the variation of the action functional under energymomentum conservation constraint, and PRI requires that physical laws be independent of representations of the gauge groups. One important outcome of this unified field model is a natural duality between the interacting fields (g,A,W ^{ a },S ^{ k }), corresponding to graviton, photon, intermediate vector bosons W ^{±} and Z and gluons, and the adjoint bosonic fields \((\varPhi_{\mu}, \phi^{0}, \phi^{a}_{w}, \phi^{k}_{s})\). This duality predicts two Higgs particles of similar mass with one due to weak interaction and the other due to strong interaction. The unified field model can be naturally decoupled to study individual interactions, leading to (1) modified Einstein equations, giving rise to a unified theory for dark matter and dark energy (Ma and Wang in Discrete Contin. Dyn. Syst., Ser A. 34(2):335–366, 2014), (2) three levels of strong interaction potentials for quark, nucleon/hadron, and atom respectively (Ma and Wang in Duality theory of strong interaction, 2012), and (3) two weak interaction potentials (Ma and Wang in Duality theory of weak interaction, 2012). These potential/force formulas offer a clear mechanism for both quark confinement and asymptotic freedom—a longstanding problem in particle physics (Ma and Wang in Duality theory of strong interaction, 2012).
Keywords
Principle of Interaction Dynamics (PID) Principle of Representation Invariance (PRI) Unified field equations Duality theory of interactions Quark confinement Asymptotic freedom Higgs mechanism Higgs bosons Quark potential Nucleon potential Atom potential Weak interaction potential Strong interaction force formulas Weak interaction force formula Electroweak theory Title
 Unified Field Theory and Principle of Representation Invariance
 Journal

Applied Mathematics & Optimization
Volume 69, Issue 3 , pp 359392
 Cover Date
 201406
 DOI
 10.1007/s0024501392260
 Print ISSN
 00954616
 Online ISSN
 14320606
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Principle of Interaction Dynamics (PID)
 Principle of Representation Invariance (PRI)
 Unified field equations
 Duality theory of interactions
 Quark confinement
 Asymptotic freedom
 Higgs mechanism
 Higgs bosons
 Quark potential
 Nucleon potential
 Atom potential
 Weak interaction potential
 Strong interaction force formulas
 Weak interaction force formula
 Electroweak theory
 Authors

 Tian Ma ^{(1)}
 Shouhong Wang ^{(2)}
 Author Affiliations

 1. Department of Mathematics, Sichuan University, Chengdu, P.R. China
 2. Department of Mathematics, Indiana University, Bloomington, IN, 47405, USA