Asymptotic States and the Definition of the S-matrix in Quantum Gravity

Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energy-momentum naturally leads to the gauge theory of volume-preserving diffeormorphisms of an inner Minkowski space. The generalized asymptotic free scalar, Dirac and gauge fields in that theory are canonically quantized, the Fock spaces of stationary states are constructed and the gravitational limit - mapping the gravitational energy-momentum onto the inertial energy-momentum to account for their observed equality - is introduced. Next the S-matrix in quantum gravity is defined as the gravitational limit of the transition amplitudes of asymptotic in- to out-states in the gauge theory of volume-preserving diffeormorphisms. The so defined S-matrix relates in- and out-states of observable particles carrying gravitational equal to inertial energy-momentum. Finally generalized LSZ reduction formulae for scalar, Dirac and gauge fields are established which allow to express S-matrix elements as the gravitational limit of truncated Fourier-transformed vacuum expectation values of time-ordered products of field operators of the interacting theory. Together with the generating functional of the latter established in an earlier paper [8] any transition amplitude can in principle be computed to any order in perturbative quantum gravity.Comment: 35 page

Quantum Isometrodynamics

Classical Isometrodynamics is quantized in the Euclidean plus axial gauge. The quantization is then generalized to a broad class of gauges and the generating functional for the Green functions of Quantum Isometrodynamics (QID) is derived. Feynman rules in covariant Euclidean gauges are determined and QID is shown to be renormalizable by power counting. Asymptotic states are discussed and new quantum numbers related to the "inner" degrees of freedom introduced. The one-loop effective action in a Euclidean background gauge is formally calculated and shown to be finite and gauge-invariant after renormalization and a consistent definition of the arising "inner" space momentum integrals. Pure QID is shown to be asymptotically free for all dimensions of "inner" space $D$ whereas QID coupled to the Standard Model fields is not asymptotically free for D <= 7. Finally nilpotent BRST transformations for Isometrodynamics are derived along with the BRST symmetry of the theory and a scetch of the general proof of renormalizability for QID is given.Comment: 38 page

Resummation of the Two Distinct Large Logarithms in the Broken O(N)-symmetric ϕ⁴-model

The loop-expansion of the effective potential in the O(N)-symmetric ϕ⁴-model contains generically two types of large logarithms. To resum those systematically a new minimal two-scale subtraction scheme 2MS is introduced in an O(N)-invariant generalization of MS. As the 2MS beta functions depend on the renormalization scale-ratio a large logarithms resummation is performed on them. Two partial 2MS renormalization group equations are derived to turn the beta functions into 2MS running parameters. With the use of standard perturbative boundary conditions, which become applicable in 2MS, the leading logarithmic 2MS effective potential is computed. The calculation indicates that there is no stable vacuum in the broken phase of the theory for 1 < N ≤ 4

A Poincaré gauge theory of gravitation in Minkowski spacetime

The conventional role of spacetime geometry in the description of gravity is pointed out. Global Poincar\acute{\mbox{e}} symmetry as an inner symmetry of field theories defined on a fixed Minkowski spacetime is discussed. Its extension to local {\bf P\/} gauge symmetry and the corresponding {\bf P\/} gauge fields are introduced. Their minimal coupling to matter is obtained. The scaling behaviour of the partition function of a spinor in {\bf P\/} gauge field backgrounds is computed. The corresponding renormalization constraint is used to determine a minimal gauge field dynamics