The Experts below are selected from a list of 229800 Experts worldwide ranked by ideXlab platform
Youngjai Park - One of the best experts on this subject based on the ideXlab platform.
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scale invariant power spectra from a weyl invariant scalar tensor theory
European Physical Journal C, 2016Co-Authors: Yun Soo Myung, Youngjai ParkAbstract:We obtain scale-invariant scalar and tensor power spectra from a Weyl-invariant scalar–tensor theory in de Sitter spacetime. This implies that the Weyl Invariance guarantees the implementation of the scale Invariance of the power spectrum in de Sitter spacetime. We establish a deep connection between the Weyl Invariance of the action and the scale Invariance of the power spectrum in de Sitter spacetime.
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scale invariant power spectra from a weyl invariant scalar tensor theory
arXiv: General Relativity and Quantum Cosmology, 2015Co-Authors: Yun Soo Myung, Youngjai ParkAbstract:We obtain scale-invariant scalar and tensor power spectra from a Weyl-invariant scalar-tensor theory in de Sitter spacetime. This implies that the Weyl-Invariance guarantees to implement the scale-Invariance of power spectrum in de Sitter spacetime. We establish a deep connection between the Weyl-Invariance of the action and scale-Invariance of power spectrum in de Sitter spacetime.
Yun Soo Myung - One of the best experts on this subject based on the ideXlab platform.
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scale invariant power spectra from a weyl invariant scalar tensor theory
European Physical Journal C, 2016Co-Authors: Yun Soo Myung, Youngjai ParkAbstract:We obtain scale-invariant scalar and tensor power spectra from a Weyl-invariant scalar–tensor theory in de Sitter spacetime. This implies that the Weyl Invariance guarantees the implementation of the scale Invariance of the power spectrum in de Sitter spacetime. We establish a deep connection between the Weyl Invariance of the action and the scale Invariance of the power spectrum in de Sitter spacetime.
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scale invariant power spectra from a weyl invariant scalar tensor theory
arXiv: General Relativity and Quantum Cosmology, 2015Co-Authors: Yun Soo Myung, Youngjai ParkAbstract:We obtain scale-invariant scalar and tensor power spectra from a Weyl-invariant scalar-tensor theory in de Sitter spacetime. This implies that the Weyl-Invariance guarantees to implement the scale-Invariance of power spectrum in de Sitter spacetime. We establish a deep connection between the Weyl-Invariance of the action and scale-Invariance of power spectrum in de Sitter spacetime.
Bernard Victorri - One of the best experts on this subject based on the ideXlab platform.
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transformation Invariance in pattern recognition tangent distance and propagation
International Journal of Imaging Systems and Technology, 2000Co-Authors: Patrice Y Simard, J S Denker, Yann Le A Cun, Bernard VictorriAbstract:In pattern recognition, statistical modeling, or regression, the amount of data is a critical factor affecting the performance. If the amount of data and computational resources are unlimited, even trivial algorithms will converge to the optimal solution. However, in the practical case, given limited data and other resources, satisfactory performance requires sophisticated methods to regularize the problem by introducing a priori knowledge. Invariance of the output with respect to certain transformations of the input is a typical example of such a priori knowledge. We introduce the concept of tangent vectors, which compactly represent the essence of these transformation Invariances, and two classes of algorithms, tangent distance and tangent propagation, which make use of these Invariances to improve performance. © 2001 John Wiley & Sons, Inc. Int J Imaging Syst Technol 11, 181–197, 2000
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transformation Invariance in pattern recognition tangent distance and tangent propagation
Neural Information Processing Systems, 1998Co-Authors: Patrice Y Simard, Yann Lecun, J S Denker, Bernard VictorriAbstract:In pattern recognition, statistical modeling, or regression, the amount of data is a critical factor affecting the performance. If the amount of data and computational resources are unlimited, even trivial algorithms will converge to the optimal solution. However, in the practical case, given limited data and other resources, satisfactory performance requires sophisticated methods to regularize the problem by introducing a priori knowledge. Invariance of the output with respect to certain transformations of the input is a typical example of such a priori knowledge. In this chapter, we introduce the concept of tangent vectors, which compactly represent the essence of these transformation Invariances, and two classes of algorithms, “tangent distance” and “tangent propagation”, which make use of these Invariances to improve performance.
Arash Yunesi - One of the best experts on this subject based on the ideXlab platform.
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topics in soft collinear effective theory for gravity the diffeomorphism invariant wilson lines and reparametrization Invariance
Physical Review D, 2020Co-Authors: Sabyasachi Chakraborty, Takemichi Okui, Arash YunesiAbstract:Two topics in soft collinear effective theory (SCET) for gravitational interactions are explored. First, the collinear Wilson lines---necessary building blocks for maintaining multiple copies of diffeomorphism Invariance in gravity SCET---are extended to all orders in the SCET expansion parameter $\ensuremath{\lambda}$, where it has only been known to $O(\ensuremath{\lambda})$ in the literature. Second, implications of reparametrization Invariance (RPI) for the structure of gravity SCET Lagrangians are studied. The utility of RPI is illustrated by an explicit example in which $O({\ensuremath{\lambda}}^{2})$ hard interactions of a collinear graviton are completely predicted by RPI from its $O(\ensuremath{\lambda})$ hard interactions. It is also pointed out that the multiple diffeomorphism Invariances and RPI together require certain relations among $O(\ensuremath{\lambda})$ terms, thereby reducing the number of $O(\ensuremath{\lambda})$ terms that need to be fixed by matching onto the full theory in the first place.
Yu Nakayama - One of the best experts on this subject based on the ideXlab platform.
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Scale Invariance vs conformal Invariance
Physics Reports, 2015Co-Authors: Yu NakayamaAbstract:In this review article, we discuss the distinction and possible equivalence between scale Invariance and conformal Invariance in relativistic quantum field theories. Under some technical assumptions, we can prove that scale invariant quantum field theories in d=2 space–time dimensions necessarily possess the enhanced conformal symmetry. The use of the conformal symmetry is well appreciated in the literature, but the fact that all the scale invariant phenomena in d=2 space–time dimensions enjoy the conformal property relies on the deep structure of the renormalization group. The outstanding question is whether this feature is specific to d=2 space–time dimensions or it holds in higher dimensions, too. As of January 2014, our consensus is that there is no known example of scale invariant but non-conformal field theories in d=4 space–time dimensions under the assumptions of (1) unitarity, (2) Poincare Invariance (causality), (3) discrete spectrum in scaling dimensions, (4) existence of scale current and (5) unbroken scale Invariance in the vacuum. We have a perturbative proof of the enhancement of conformal Invariance from scale Invariance based on the higher dimensional analogue of Zamolodchikov’s cc-theorem, but the non-perturbative proof is yet to come. As a reference we have tried to collect as many interesting examples of scale Invariance in relativistic quantum field theories as possible in this article. We give a complementary holographic argument based on the energy-condition of the gravitational system and the space–time diffeomorphism in order to support the claim of the symmetry enhancement. We believe that the possible enhancement of conformal Invariance from scale Invariance reveals the sublime nature of the renormalization group and space–time with holography. This review is based on a lecture note on scale Invariance vs conformal Invariance, on which the author gave lectures at Taiwan Central University for the 5th Taiwan School on Strings and Fields.
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zoology of heterotic supercurrent supermultiplets in d 2
arXiv: High Energy Physics - Theory, 2013Co-Authors: Yu NakayamaAbstract:We present various (0,2) heterotic supercurrent supermultiplets in (1+1) dimensional quantum field theories. From the minimal supercurrent supermultiplets, we deduce conditions on symmetry enhancement such as Lorentz Invariance, (chiral) dilatation Invariance, R-Invariance, (chiral) conformal Invariance and their various combinations. Our construction covers many interesting and/or exotic possibilities such as Lifshitz supersymmetry and warped superconformal algebra. We also discuss the corresponding supergravity by gauging the supercurrent supermultiplet. In particular, we propose a novel class of heterotic supergravity based on the virial supercurrent.
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Scale Invariance vs conformal Invariance
arXiv: High Energy Physics - Theory, 2013Co-Authors: Yu NakayamaAbstract:In this review article, we discuss the distinction and possible equivalence between scale Invariance and conformal Invariance in relativistic quantum field theories. Under some technical assumptions, we can prove that scale invariant quantum field theories in $d=2$ dimension necessarily possess the enhanced conformal symmetry. The use of the conformal symmetry is well appreciated in the literature, but the fact that all the scale invariant phenomena in $d=2$ dimension enjoy the conformal property relies on the deep structure of the renormalization group. The outstanding question is whether this feature is specific to $d=2$ dimension or it holds in higher dimensions, too. As of January 2014, our consensus is that there is no known example of scale invariant but non-conformal field theories in $d=4$ dimension under the assumptions of (1) unitarity, (2) Poincar\'e Invariance (causality), (3) discrete spectrum in scaling dimension, (4) existence of scale current and (5) unbroken scale Invariance in the vacuum. We have a perturbative proof of the enhancement of conformal Invariance from scale Invariance based on the higher dimensional analogue of Zamolodchikov's $c$-theorem, but the non-perturbative proof is yet to come. As a reference we have tried to collect as many interesting examples of scale Invariance in relativistic quantum field theories as possible in this article. We give a complementary holographic argument based on the energy-condition of the gravitational system and the space-time diffeomorphism in order to support the claim of the symmetry enhancement. We believe that the possible enhancement of conformal Invariance from scale Invariance reveals the sublime nature of the renormalization group and space-time with holography.
