The Exact renormalization group and approximate solutions

@article{Morris1994TheER,
  title={The Exact renormalization group and approximate solutions},
  author={Tim R Morris},
  journal={International Journal of Modern Physics A},
  year={1994},
  volume={9},
  pages={2411-2450}
}
  • T. Morris
  • Published 1994
  • Physics
  • International Journal of Modern Physics A
We investigate the structure of Polchinski’s formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff Green’s functions are given. A promising nonperturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in “irrelevancy” of operators. We illustrate with two simple models of four-dimensional λφ4 theory: the cactus approximation, and a model incorporating the first irrelevant correction to… Expand
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In recent papers it has been noted that the local potential approximation of the Legendre and Wilson-Polchinski flow equations give, within numerical error, identical results for a range of exponentsExpand
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We consider the Polchinski RG equation for a theory of matrix scalar fields interacting with single trace operators and show that it can be written in a Hamiltonian form for a specific choice of theExpand
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We consider a functional relation between a given Wilsonian RG flow, which has to be related to a specific coarse-graining procedure, and an infinite family of (UV cutoff) scale dependent fieldExpand
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References

SHOWING 1-10 OF 27 REFERENCES
Critical Exponents from the Effective Average Action
Abstract We compute the critical behaviour of three-dimensional scalar theories using a new exact non-perturbative evolution equation. Our values for the critical exponents and other universalExpand
Renormalization of Tamm-Dancoff integral equations.
TLDR
A general, nonperturbative approach to renormalization that is well suited for the ultraviolet and, presumably, the infrared divergences found in these systems is introduced. Expand
Nonperturbative study of the fermion propagator in quenched QED in covariant gauges using a renormalizable truncation of the Schwinger-Dyson equation.
The Schwinger-Dyson equation for the fermion propagator in quenched four-dimensional QED is solved using a nonperturbative ansatz for the fermion-photon vertex that satisfies the Ward-TakahashiExpand
Nonperturbative study of the fermion propagator in quenched QED in covariant gauges using a renormalizable truncation of the Schwinger-Dyson equation.
The Schwinger-Dyson equation for the fermion propagator in quenched four-dimensional QED is solved using a nonperturbative ansatz for the fermion-photon vertex that satisfies the Ward-TakahashiExpand
Large-N analysis of the Higgs mass triviality bound
Abstract We calculate the triviality bound on the Higgs mass in scalar field theory models whose global symmetry group SU(2)L × SU(2)custodial ≈ O(4) has been replaced by O(N) and N has been taken toExpand
Critical Phenomena for Field Theorists
Many of us who are not habitually concerned with problems in statistical physics have gradually been becoming aware of dramatic progress in that field. The mystery surrounding the phenomenon ofExpand
Nucl
  • Phys. B231
  • 1984
Phys
  • Lett. B301
  • 1993
Nucl
  • Phys. B290
  • 1987
Phys
  • Rep. 12C
  • 1974
...
1
2
3
...