Quantum field theory and unification of fundamental interactions

The problems which occur in attempts to quantize general relativity can be avoided if we assume that gravitation is a quantum mechanically induced phenomenon within the framework of a more basic theory. In the research project we treat a theory of induced gravity based on the assumption that spacetime is a relativistic membrane. We start from an action which is a generalization of a minimal surface action and study the classical and quantum equations of motion of an unconstrained membrane. Here the elegant Fock-Schwinger proper time method initiated by Fock, Stueckelberg, Feynman and later thoroughly developed by Horwitz and others, is generalized from point-particles to membranes of arbitrary dimensions. The classical and quantum equations of the membrane can be elagantly written in the forms which are generalizations of the corresponding point-particle equations in curved space. In the future we intend to develop the second quantization of the theory of unconstrained membranes and include fermions into the model.