Diagrammatic expansions for the Yang-Mills ground state

Chan, Hue Sun

doi:10.1016/0550-3213(86)90059-3

Nuclear Physics B

1986

DOI: 10.1016/0550-3213(86)90059-3

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Diagrammatic expansions for the Yang-Mills ground state

Hue Sun Chan

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Cited by 5 publications

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“…We regulate the integral by restricting the space-like component of momentum, p 2 < 1/ǫ, just as we did for the Laplacian in the Hamiltonian. The divergence is then cancelled by the counter-term represented by fig.5(b), which is due to the order-h terms in M 2 (ǫ), (5). Taken together these diagrams give Γh 2 as in (41).…”

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confidence: 87%

Short Distance Properties From Large Distance Behavior

Mansfield

Sampaio

Pachos

1998

Int. J. Mod. Phys. A

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For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficents can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counter-terms. We also describe an approximate simplification that occurs for the Sine-Gordon and Sinh-Gordon vacuum functionals.

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confidence: 87%

Short Distance Properties From Large Distance Behavior

Mansfield

Sampaio

Pachos

1998

Int. J. Mod. Phys. A

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Stochastic processes and the non-perturbative structure of the QCD vacuum

Mendes

1992

Z. Phys. C - Particles and Fields

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Yang-Mills beta-function from a large-distance expansion of the Schrödinger functional

Mansfield

Sampaio

1999

Nuclear Physics B

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For slowly varying fields the Yang-Mills Schrödinger functional can be expanded in terms of local functionals. We show how analyticity in a complex scale parameter enables the Schrödinger functional for arbitrarily varying fields to be reconstructed from this expansion. We also construct the form of the Schrödinger equation that determines the coefficients. Solving this in powers of the coupling reproduces the results of the 'standard' perturbative solution of the functional Schrödinger equation which we also describe. In particular the usual result for the beta-function is obtained illustrating how analyticity enables the effects of rapidly varying fields to be computed from the behaviour of slowly varying ones.

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Diagrammatic expansions for the Yang-Mills ground state

Cited by 5 publications

References 12 publications

Short Distance Properties From Large Distance Behavior

Short Distance Properties From Large Distance Behavior

Stochastic processes and the non-perturbative structure of the QCD vacuum

Yang-Mills beta-function from a large-distance expansion of the Schrödinger functional

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