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Topological quantization of free massive bosonic fields. (English) Zbl 1262.81174

Summary: We present a topological quantization of free massive bosonic fields as the first example of a classical field theory with a quantum counterpart to be studied under this formalism. First, we identify certain harmonic map as a geometric representation of this physical system. We take as a concrete example the case of free massive bosonic fields in two dimensions represented by the minimal embedding of a two dimensional surface into a pp-wave spacetime. We use this geometric representation to construct the fiber bundle corresponding to some specific field configurations and then find their topological spectra, defined in terms of the Euler invariant. We discuss the results for some particular configurations and their consequences for the energy of the system.

MSC:

81T75 Noncommutative geometry methods in quantum field theory
81S10 Geometry and quantization, symplectic methods
53D50 Geometric quantization
81T13 Yang-Mills and other gauge theories in quantum field theory
53C43 Differential geometric aspects of harmonic maps
55R10 Fiber bundles in algebraic topology
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