Semi-group approach to multiperipheral dynamics

Ferrara, S.; Mattioli, G.; Rossi, G.C.; Toller, M.

doi:10.1016/0550-3213(73)90451-3

Cited by 15 publications

(4 citation statements)

References 26 publications

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“…We remark that the Jiti-contraction semigroup of the preceding example was introduced under another guise in [6] as a tool to aid in the study of certain physical problems in multiperipheral dynamics. Certain properties of this semigroup and its representations are established there.…”

Section: Let G Be a Hermitian Simple Lie Algebra Let Gc Be A Connectmentioning

confidence: 98%

Semigroups of Ol'shanskiĭ type

Lawson¹

1995

Semigroups in Algebra, Geometry and Analysis

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This article surveys major developments in the structure theory of an important class of semigroups called Ol'shanskii semigroups. Such semigroups admit a characteristic polar decomposition and other interesting types of decompositions. The important special case of complex Ol'shanskii semigroups receives special consideration. Particular attention is also devoted to maximal Ol'shanskii semigroups and their properties. Important examples of Ol'shanskii semigroups are presented, particularly semigroups of contractions and semigroups of compressions of an open domain.

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Section: Let G Be a Hermitian Simple Lie Algebra Let Gc Be A Connectmentioning

confidence: 98%

Semigroups of Ol'shanskiĭ type

Lawson¹

1995

Semigroups in Algebra, Geometry and Analysis

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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%

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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“…It follows that every element in the interior of ® can be parametrized in the form (4.4). In fact ®° is just the interior of ® and is itself a semigroup [17].…”

Section: A Semigroupmentioning

confidence: 99%

“…In the present paper we use it to analytically continue a contractive representation of a maximal open semigroup S° C © SO(5,1) to a unitary representation of the universal covering group ©* of SO (4,2). Contractive representations of S~ can be obtained in a heuristic manner from unitary representations of (5 by splitting the representation space as in [17], and then analytically continuing in the continuous Casimir invariant. This idea will be further developed elsewhere [2].…”

Section: (λ)ψ -T(u)ψ\\-»0 Whenever A-^ueu Through Values In S~ [To See This Define λ' = U-l λ€<And and Note That \\T(λ)ψ -T(u)ψ\\ = \\ T(mentioning

confidence: 99%

Global conformal invariance in quantum field theory

1975

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Suppose that there is given a Wightman quantum field theory (QFT) whose Euclidean Green functions are invariant under the Euclidean conformal group (5~SO e (5, 1). We show that its Hubert space of physical states carries then a unitary representation of the universal (oo-sheeted) covering group (5* of the Minkowskian conformal group SO e (4, 2)/Z 2 . The Wightman functions can be analytically continued to a domain of holomorphy which has as a real boundary an oo-sheeted covering M of Minkowski-space M 4 . It is known that 05* can act on this space M and that M admits a globally @*-invariant causal ordering; M is thus the natural space on which a globally (5*-invariant local QFT could live. We discuss some of the properties of such a theory, in particular the spectrum of the conformal Hamiltonian H = i(P° + K°).As a tool we use a generalized Hille-Yosida theorem for Lie semigroups. Such a theorem is stated and proven in Appendix C. It enables us to analytically continue contractive representations of a certain maximal subsemigroup 6 of (5 to unitary representations of (5*.

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Semi-group approach to multiperipheral dynamics

Cited by 15 publications

References 26 publications

Semigroups of Ol'shanskiĭ type

Semigroups of Ol'shanskiĭ type

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

Global conformal invariance in quantum field theory

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