Abstract
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge–gravity and gravity–geometry correspondences bring about the gravitational gauge–geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.
Highlights
Since Einstein established the general theory of relativity (GR) [1] in 1915, it has become a great challenge for many physicists and mathematicians to unify the -known basic forces
As the general action of hyperunified field theory given in Eq (95) is constructed based on the postulates of gauge invariance and coordinate independence in the locally flat hyper-gravifield spacetime Gh, we shall explicitly show how the gravitational interaction can be described by the gauge interaction in a hidden coordinate formalism and demonstrate the general gauge–gravity correspondence relying on the gravitational origin of gauge symmetry
Either the hyper-spin gauge symmetry group SP(1, Dh − 1) that governs the dynamics of the hyper-spinor field and gauge fields or the emergent general linear symmetry group GL(Dh, R) that describes the dynamics of the Riemannian geometry of hyper-spacetime, it provides a symmetry principle to construct the general action of hyperunified field theory in hyper-spacetime
Summary
Since Einstein established the general theory of relativity (GR) [1] in 1915, it has become a great challenge for many physicists and mathematicians to unify the -known basic forces. Some interesting progress includes the work proposed by Kaluza who extended GR to five-dimensional spacetime [4], and by Klein who proposed the fifth dimension to be curled up into an unobservable small circle [5] In such a Kaluza–Klein theory, the gravitational curvature tensor corresponding to an extra spatial direction behaves as an additional force analogous to electromagnetism. QFT has provided a successful unified description for the electroweak interactions, and for the strong interaction characterized by the quantum chromodynamics (QCD) [23,24] with the gauge symmetry group SU(3). A quantum field theory of gravity [68] was built based on the spin and scaling gauge invariances by treating the gravitational interaction on the same footing as the electroweak and strong interactions, which enables us to provide a unified description for the four basic forces within the framework of QFT. Instead of the metric field in GR, a bicovariant vector field defined in biframe spacetime
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