Exact scheme independence

Latorre, José I.; Morris, Tim R.

doi:10.1088/1126-6708/2000/11/004

Cited by 98 publications

(164 citation statements)

References 19 publications

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“…The t-derivative on the lhs of (3.39) is taken at fixed Φ: the first term on the rhs of (3.39) is the flow (3.28) at fixed J, and the second term stems from the k-dependence of J(Φ). For example, in the presence of a regulator the effective Lagrangian 40) and hence has the flow (3.39) with (3.24). This flow further simplifies for quadratic regulators R abφ aφb .…”

Section: Flow Of Amputated Correlation Functionsmentioning

confidence: 99%

“…The flows (3.41), (3.42) can be extended to Φ-dependent P k by using the general DS equations (2.12) in the presence of a regulator, see e.g. [40,135]. Then it also nicely encodes reparameterisation invariance.…”

Section: Flow Of Amputated Correlation Functionsmentioning

confidence: 99%

“…and 40) leading to δΓ 2PI δφ ab = J ab and φ ab = G. Note that Γ[φ a , Q, R ab ] already includes the standard subtraction −J ab φ a φ b . We arrive at…”

Section: Flows and Alternative Representationsmentioning

confidence: 99%

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Aspects of the functional renormalisation group

2007

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We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being N PI quantities. We discuss optimisation and derive a functional optimisation criterion.Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson-Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation.

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Section: Flow Of Amputated Correlation Functionsmentioning

confidence: 99%

Section: Flow Of Amputated Correlation Functionsmentioning

confidence: 99%

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Aspects of the functional renormalisation group

2007

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“…Examples can be given from all domains where quantum field theory is applicable: from phase transitions in early universe cosmology, quantum gravity, QCD, through to high temperature superconductivity, to mention just a few. The exact Renormalization Group (RG) [2,25], the continuum version of a Wilsonian RG, provides a powerful framework for considering non-perturbative analytic approximations to quantum field theories [3,4,5,8,26]. This follows from the fact that solutions of the corresponding flow equations, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Fortunately it is possible to formulate more general exact RGs [8], which are gauge invariant [9,10,11,12]. A wonderful extra benefit in this generalised framework is that calculations can proceed with manifest gauge invariance preserved at every stage [9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory

2003

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Abstract:We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularisation scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities. The initial stages can even be computed diagrammatically. The method is formulated within the framework of an exact renormalization group for SU (N ) Yang-Mills gauge theory, incorporating an effective cutoff through a manifest spontaneously broken SU (N |N ) gauge invariance. We demonstrate the technique with a compact calculation of the one-loop beta function, achieving a manifestly universal result, and without gauge fixing, for the first time at finite N .

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Photothermographic and Thermographic Imaging Materials

Whitcomb¹

2002

Kirk-Othmer Encyclopedia of Chemical Technology

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Photothermographic and thermographic imaging technology based on silver carboxylates have evolved into high quality black and white imaging materials suitable for extremely demanding applications such as medical X‐ray and graphic arts films. the unique ability of generating a high quality image that requires only dry processing, without any of the hazards and environmental problems of conventional, wet‐processed films for these applications, has provided significant new commercial opportunities for this technology. Major advances in the state of the art have occurred in this field since photothermography of this type was first introduced as Dry Silver in 1964. This article describes the components and their function in these types of imaging systems, their development over the last 40 years, the advances in basic understanding of the current status of the science behind the technology, and prospects for the future.

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Exact scheme independence

Cited by 98 publications

References 19 publications

Aspects of the functional renormalisation group

Aspects of the functional renormalisation group

A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory

Photothermographic and Thermographic Imaging Materials

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