New Developments in the Continuous Renormalization Group

Morris, Tim R.

doi:10.1007/0-306-47075-6_10

Cited by 5 publications

(15 citation statements)

References 50 publications

(121 reference statements)

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“…(2.4), prime denotes differentiation with respect to the function's argument (here p 2 /Λ 2 ) and the following shorthand has been introduced: for two functions f (x) and g(y) and a momentum space kernel W (p 2 /Λ 2 ), with Λ being the effective cutoff, 5) where…”

Section: From the Polchinski Equation To General Exact Rgsmentioning

confidence: 99%

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Exact scheme independence at one loop

Arnone¹,

Gatti²,

Morris³

2002

J. High Energy Phys.

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Abstract:The requirement that the quantum partition function be invariant under a renormalization group transformation results in a wide class of exact renormalization group equations, differing in the form of the kernel. Physical quantities should not be sensitive to the particular choice of the kernel. We demonstrate this scheme independence in four dimensional scalar field theory by showing that, even with a general kernel, the one-loop beta function may be expressed only in terms of the effective action vertices, and thus, under very general conditions, the universal result is recovered.

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Section: From the Polchinski Equation To General Exact Rgsmentioning

confidence: 99%

“…Green functions) can be extracted from this Wilsonian effective action S, and that renormalizability is trivially preserved in almost any approximation [2,3], turns these ideas into a powerful framework for considering non-perturbative analytic approximations (see for example refs. [1]- [5], [8], [10]- [14], [18]). …”

Section: Introductionmentioning

confidence: 99%

Exact scheme independence at one loop

Arnone¹,

Gatti²,

Morris³

2002

J. High Energy Phys.

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“…Green functions) can be extracted from S, and that renormalizability is trivially preserved in almost any approximation [2,3], turns these ideas into a powerful framework for considering both perturbative and non-perturbative approximations (see for example refs. [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]). …”

Section: Introduction and Conclusionmentioning

confidence: 99%

“…In the past a number of different versions and ways of deriving the ERG have been proposed [1,2,3,4,5,6,7,9,10,21], which however have been shown to be equivalent under changes of variables [2,3,11,12,13]. Recently, far more general versions of the ERG have been considered * Electronic address: stefano.arnone@roma1.infn.it † Electronic address: A.Gatti@damtp.cam.ac.uk ‡ Electronic address: T.R.Morris@soton.ac.uk; Currently at CERN, Theory Division, CH-1211 Genève 23, Switzerland § Electronic address: O.J.Rosten@soton.ac.uk [13].…”

Section: Introduction and Conclusionmentioning

confidence: 99%

Exact scheme independence at two loops

Gatti²,

et al. 2004

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We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point vertices, is left unspecified. Calculations proceed iteratively, by integrating by parts with respect to the effective cutoff, thus introducing effective propagators, and differentials of vertices that can be expanded using the flow equations; many cancellations occur on using the fact that the effective propagator is the inverse of the classical Wilsonian two-point vertex. We demonstrate the power of these methods by computing the beta function up to two loops in massless four dimensional scalar field theory, obtaining the expected universal coefficients, independent of the details of the regularisation scheme.

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“…Over the years the exact renormalization group (ERG) 1,2,3,4 has grown to become a reliable and accurate framework in the study of non-perturbative phenomena in quantum field theory (see reviews for example in 5,6,7,8 ). In this context the Polchinski ERG approach and the derivative expansion 4,9,10,11 are specially attractive for their power and simplicity.…”

Section: Introductionmentioning

confidence: 99%