Differentiability and continuity of quantum fields on a lattice

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 th...

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Bibliographic Details
Published in:Physical review. D, Particles and fields Particles and fields, 1991-01, Vol.43 (2), p.476-484
Main Authors: DELYRA, J. L, FOONG, S. K, GALLIVAN, T. E
Format: Article
Language:English
Subjects:
645400 - High Energy Physics- Field Theory
Classical and quantum physics: mechanics and fields
CONTINUITY EQUATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
Exact sciences and technology
FEYNMAN PATH INTEGRAL
FIELD THEORIES
INTEGRALS
LATTICE FIELD THEORY
PARTIAL DIFFERENTIAL EQUATIONS
Physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM FIELD THEORY
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Summary: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.
ISSN:0556-2821
1089-4918
DOI:10.1103/PhysRevD.43.476