Abstract
Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energymomentum naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner Minkowski space which can describe gravitation at the classical level. This theory is quantized in the path integral formalism starting with a non-covariant Hamiltonian formulation with unconstrained canonical field variables and a manifestly positive Hamiltonian. The relevant path integral measure and weight are then brought into a Lorentz- and gauge-covariant form allowing to express correlation functions—applying the De Witt-Faddeev-Popov approach—in any meaningful gauge. Next the Feynman rules are developed and the quantum effective action at one loop in a background field approach is renormalized which results in an asymptotically free theory without presence of other fields and in a theory without asymptotic freedom including the Standard Model (SM) fields. Finally the BRST apparatus is developed as preparation for the renormalizability proof to all orders and a sketch of this proof is given.
Highlights
In [1] we have started to explore the consequences of viewing the gravitational energy-momentum pG as different by its very nature from the inertial energy-momentum pI, accepting their observed numerical equality as accidential.As both are conserved this view has led us to look for two different symmetries which through Noether’s theorem generate two different conserved four vectors—one symmetry obviously being space-time translation invariance yielding the conserved inertial energy-momentum pI vector
Note that as for other gauge field theories it is the second term in Equation (106) which determines the sign of the gauge field contribution above—which will in turn determine the sign of the β-function of the quantum gauge field theory of volume-preserving diffeomorphisms of M4
We have quantized the classical gauge theory of volume-preserving diffeomorphisms of M4 in the path integral formalism starting with a Hamiltonian formulation of the theory with unconstrained, though neither Lorentz- nor gauge-covariantly looking canonical field variables and a manifestly positive Hamiltonian
Summary
In [1] we have started to explore the consequences of viewing the gravitational energy-momentum pG as different by its very nature from the inertial energy-momentum pI , accepting their observed numerical equality as accidential. To generate an additional conserved four-vector the field concept has proven to be crucial as only fields can carry the necessary inner degrees of freedom to allow for representations of additional inner symmetry groups—in our case an inner translation group yielding the conserved gravitational energy-momentum vector pG Gauging this inner translation group has naturally led to the gauge field theory of volume-preserving diffeomorphisms of M4 , at the classical level, thereby generalizing the Yang-Mills approach for compact Lie groups acting on a finite number of inner field degrees of freedom ( see [2,3] for the mathematical framework).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
