Abstract
We introduce a spectral approach to non-perturbative field theory within the periodic field formalism. As an example we calculate the real and imaginary parts of the propagator in 1+1 dimensional phi^4 theory, identifying both one-particle and multi-particle contributions. We discuss the computational limits of existing diagonalization algorithms and suggest new quasi-sparse eigenvector methods to handle very large Fock spaces and higher dimensional field theories.
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