Asymptotic states and the definition of the S-matrix in quantum gravity
Abstract
Viewing gravitational energy-momentum p_G^\mu as equal by observation, but different in essence from inertial energy-momentum p_I^\mu naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner Minkowski space M4. 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 diffeomorphisms. The so-defined S-matrix relates in- and out-states of observable particles carrying gravitational equal to inertial energy-momentum. Finally, generalized Lehmann-Symanzik-Zimmermann reduction formulae for scalar, Dirac and gauge fields are established which allow us 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 Wiesendanger (2011 arXiv:1103.1012) any transition amplitude can in principle be computed consistently to any order in perturbative quantum gravity.
- Publication:
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Classical and Quantum Gravity
- Pub Date:
- April 2013
- DOI:
- 10.1088/0264-9381/30/7/075024
- arXiv:
- arXiv:1203.0715
- Bibcode:
- 2013CQGra..30g5024W
- Keywords:
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- Mathematical Physics;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory
- E-Print:
- 35 pages