The spectral action principle is a concept in mathematical physics that relates the geometry of a space to the physical properties of a quantum field theory defined on that space through its spectrum of operators. This principle suggests that the dynamics of a physical system can be derived from the eigenvalues of an operator, with the action functional being expressed as a trace over these eigenvalues. It serves as a bridge between spectral geometry and quantum field theory, revealing how geometric features influence the behavior of particles and fields.
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