Phys. Rev. D 43, 476–484 (1991)Differentiability and continuity of quantum fields on a latticeReceived 3 August 1990; published in the issue dated 15 January 1991 The differentiability and continuity properties of quantized bosonic fields on a lattice are examined. It is shown for free fields that, in the continuum limit, the dominant configurations in the functional integral become discontinuous when the spacetime dimension is greater than 1. It is argued that the same is true for interacting fields. This is unlike the one-dimensional case of quantum mechanics, in which the dominant configurations are continuous but not differentiable. As a consequence of this discontinuity, classically equivalent actions may produce inequivalent quantum field theories upon functional-integral quantization. © 1991 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.43.476
DOI:
10.1103/PhysRevD.43.476
PACS:
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