Three-dimensional Lorentz group and harmonic analysis of the scattering amplitude

Toller, M.

doi:10.1007/bf02749860

Cited by 186 publications

(26 citation statements)

References 13 publications

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“…Here the ω-dependent factor (k < /k > ) ω can be directly interpreted as an s-channel threshold factor [15] in properly defined Toller variables [16].…”

Section: Improved Next-to-leading Expansionmentioning

confidence: 99%

The BFKL equation at next-to-leading level and beyond

1999

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On the basis of a renormalization group analysis of the kernel and of the solutions of the BFKL equation with subleading corrections, we propose and calculate a novel expansion of a properly defined effective eigenvalue function. We argue that in this formulation the collinear properties of the kernel are taken into account to all orders, and that the ensuing next-to-leading truncation provides a much more stable estimate of hard Pomeron and of resummed anomalous dimensions.PACS 12.38.Cy †

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“…Here the ω-dependent factor (k < /k > ) ω can be directly interpreted as an s-channel threshold factor [15] in properly defined Toller variables [16].…”

Section: Improved Next-to-leading Expansionmentioning

confidence: 99%

The BFKL equation at next-to-leading level and beyond

1999

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“…The variable (-III() (Toller, 1965) of Bali,Chew and Pignotti (19·67). Dependence upon the To~ier variable was often assumed to be absent in early studies of the multiRegge limit and the Veneziano model was among the first to predict a definite dependence on this variable.…”

Section: _147-mentioning

confidence: 99%

Review of Recent Work on Narrow Resonance Models

Sivers

Yellin

1971

Rev. Mod. Phys.

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“…The conformal partial-wave expansion can be traced back to work of [82][83][84][85][86][87][88] and has been carried out more recently in a series of papers by Dolan and Osborn [1][2][3]. Application of partialwave expansions for non-compact group has had a long history [45,73,[89][90][91][92][93]. Recent works on these expansions have been carried out exclusively in an Euclidean framework, and Minkowski results are obtained via careful analytic continuation.…”

Section: Minkowski Conformal Blocksmentioning

confidence: 99%

“…Let us now turn to functions which grow with w. To deal with functions which grow with w as a power, it is possible to enlarge the Hilbert space [91,93], and, for the class of functions which are polynomially bounded F (w) = O(w L0 ), the region of analyticity forf + ( ) gets pushed out to the right. In other words, L 0 < Re < ∞.…”

Section: Bfkl-dglap Equationmentioning

confidence: 99%

Minkowski conformal blocks and the Regge limit for Sachdev-Ye-Kitaev-like models

Raben¹,

Tan²

2018

Phys. Rev. D

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We discuss scattering in a CFT via the conformal partial-wave analysis and the Regge limit. The focus of this paper is on understanding an OPE with Minkowski conformal blocks. Starting with a t-channel OPE, it leads to an expansion for an s-channel scattering amplitude in terms of t-channel exchanges. By contrasting with Euclidean conformal blocks we see a precise relationship between conformal blocks in the two limits without preforming an explicit analytic continuation. We discuss a generic feature for a CFT correlation function having singular F (M ) (u, v) ∼ u −δ , δ > 0, in the limit u → 0 and v → 1. Here, δ = ( ef f − 1)/2, with ef f serving as an effective spin and it can be determined through an OPE. In particular, it is bounded from above, ef f ≤ 2, for all CFTs with a gravity dual, and it can be associated with string modes interpolating the graviton in AdS. This singularity is historically referred to as the Pomeron. This bound is nearly saturated by SYK-like effective d = 1 CFT, and its stringy and thermal corrections have piqued current interests. Our analysis has been facilitated by dealing with Wightman functions. We provide a direct treatment in diagonalizing dynamical equations via harmonic analysis over physical scattering regions. As an example these methods are applied to the SYK model.

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Three-dimensional Lorentz group and harmonic analysis of the scattering amplitude

Cited by 186 publications

References 13 publications

The BFKL equation at next-to-leading level and beyond

The BFKL equation at next-to-leading level and beyond

Review of Recent Work on Narrow Resonance Models

Minkowski conformal blocks and the Regge limit for Sachdev-Ye-Kitaev-like models

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