RuprechtKarlsUniversität Heidelberg
Institut für

Anschrift:
Institut für Angewandte Mathematik Im Neuenheimer Feld 205 D69120 Heidelberg 
Tel. + 49 (0) 62 21  54 14100 (Sekretariat) email: gerhardt@math.uniheidelberg.de 
Area of Research:  Partial Differential Equations, Differential Geometry and General Relativity 
A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electromagnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory.
The Einstein equations are the EulerLagrange equations of the EinsteinHilbert functional and quantization of a Lagrangian theory requires to switch from a Lagrangian view to a Hamiltonian view. In a ground breaking paper, Arnowitt, Deser and Misner expressed the EinsteinHilbert Lagrangian in a form which allowed to derive a corresponding Hamilton function by applying the Legendre transformation. However, since the EinsteinHilbert Lagrangian is singular, the Hamiltonian description of gravity is only correct if two additional constraints are satisfied, namely, the Hamilton constraint and the diffeomorphism constraint. Dirac proved how to quantize a constrained Hamiltonian systemat least in principleand his method has been applied to the Hamiltonian setting of gravity. In the general case, when arbitrary globally hyperbolic spacetime metrics are allowed, the problem turned out to be extremely difficult and solutions could only be found by assuming a high degree of symmetry.
However, in a series of papers we achieved the quantization of gravity for general hyperbolic spacetimes and developed a mathematical model which describes the quantized interaction of gravity with a YangMills and Higgs field. An overview of the results can be found here
The quantization of gravity interacting with a YangMills and Higgs field (pdf).
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