Reply to Hughes and Savory from T. R. Morris

Morris, Trevor

doi:10.1080/00071669608417917

Cited by 28 publications

(66 citation statements)

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“…An important technical simplification can also be achieved by a sharp momentum cutoff [3]. This guarantees complete integration of the short distance modes, but poses certain problems with analyticity [8,83,84,85,86]. In contrast, a smooth cutoff like (2.18) does not introduce any non-analytical behavior.…”

Section: The Functionalγmentioning

confidence: 99%

Non-perturbative renormalization flow in quantum field theory and statistical physics

2002

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We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative solutions follow from approximations to the general form of the coarse-grained free energy or effective average action. They interpolate between the microphysical laws and the complex macroscopic phenomena. Our approach yields a simple unified description for O(N )-symmetric scalar models in two, three or four dimensions, covering in particular the critical phenomena for the second-order phase transitions, including the Kosterlitz-Thouless transition and the critical behavior of polymer chains. We compute the aspects of the critical equation of state which are universal for a large variety of physical systems and establish a direct connection between microphysical and critical quantities for a liquid-gas transition. Universal features of first-order phase transitions are studied in the context of scalar matrix models. We show that the quantitative treatment of coarse graining is essential for a detailed estimate of the nucleation rate. We discuss quantum statistics in thermal equilibrium or thermal quantum field theory with fermions and bosons and we describe the high temperature symmetry restoration in quantum field theories with spontaneous symmetry breaking. In particular we explore chiral symmetry breaking and the high temperature or high density chiral phase transition in quantum chromodynamics using models with effective four-fermion interactions.This work is dedicated to the 60th birthday of Franz Wegner. *

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Section: The Functionalγmentioning

confidence: 99%

Non-perturbative renormalization flow in quantum field theory and statistical physics

2002

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“…The LPA, which has a long history [5], approximates the renormalization group by allowing interactions only in the form of a general effective potential V ͑f, t͒. [Here t ln͑L 0 ͞L͒, where L 0 ͑L͒ is the overall (effective) cutoff.]…”

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confidence: 99%

Comment on “Fixed-Point Structure of Scalar Fields”

Morris

1996

Phys. Rev. Lett.

105

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“…(4) is a functional equation, it can not be solved directly. We, therefore, limit functional space and expand Γ[φ c ] in powers of derivatives [33,34], (see Eq. (5))…”

Section: Appendixmentioning

confidence: 99%

The Auxiliary Mass Method beyond the Local Potential Approximation

Ogure

Sato

2001

Progress of Theoretical Physics

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We show that the evolution equation of the effective potential in the auxiliary mass method corresponds to a leading approximation of a certain series. This series is derived from an evolution equation of an effective action using a derivative expansion. We derived an expression of the next-to-leading approximation of the evolution equation, which is a simultaneous partial differential equation.Comment: 23 pages, 3 EPS figure

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Reply to Hughes and Savory from T. R. Morris

Cited by 28 publications

References 0 publications

Non-perturbative renormalization flow in quantum field theory and statistical physics

Non-perturbative renormalization flow in quantum field theory and statistical physics

Comment on “Fixed-Point Structure of Scalar Fields”

The Auxiliary Mass Method beyond the Local Potential Approximation

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