Abstract
The theory of unconstrained membranes of arbitrary dimension is presented. Their relativistic dynamics is described by an action which is a generalization of the Stueckelberg point-particle action. In the quantum version of the theory, the evolution of a membrane's state is governed by the relativistic Schrödinger equation. Particular stationary solutions correspond to the conventional, constrained membranes. Contrary to the usual practice, our spacetime is identified, not with the embedding space (which brings the problem of compactification), but with a membrane of dimension 4 or higher. A 4-membrane is thus assumed to represent spacetime. The Einstein-Hilbert action emerges as an effective action after functionally integrating out the membrane's embedding functions.
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Pavšič, M. Quantum Gravity Induced from Unconstrained Membranes. Foundations of Physics 28, 1465–1477 (1998). https://doi.org/10.1023/A:1018861312590
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DOI: https://doi.org/10.1023/A:1018861312590