Local Commutativity and the Analytic Continuation of the Wightman Function

1963 ◽  
Vol 4 (10) ◽  
pp. 1240-1252 ◽  
Author(s):  
Yukio Tomozawa
Keyword(s):  
Analytic Continuation ◽  
Wightman Function ◽  
Local Commutativity

scholarly journals PCT theorem, Wightman axioms and conformal bootstrap

2021 ◽  
Vol 36 (11) ◽  
pp. 2150072
Author(s):  
Jnanadeva Maharana
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Analytic Continuation ◽  
Crucial Role ◽  
Point Function ◽  
Bootstrap Equation ◽  
Conformal Field ◽  
Local Commutativity ◽  
Conformal Bootstrap ◽  
Wightman Axioms

The axiomatic Wightman formulation for nonderivative conformal field theory is adopted to derive conformal bootstrap equation for the four-point function. The equivalence between PCT theorem and weak local commutativity, due to Jost plays a very crucial role in axiomatic field theory. The theorem is suitably adopted for conformal field theory to derive the desired equations in CFT. We demonstrate that the two Wightman functions are analytic continuation of each other.

scholarly journals Distributions in CFT. Part II. Minkowski space

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Petr Kravchuk ◽  
Jiaxin Qiao ◽  
Slava Rychkov
Keyword(s):  
Minkowski Space ◽  
Statistical Physics ◽  
Minimal Set ◽  
Local Commutativity ◽  
Classic Result ◽  
Lorentzian Signature ◽  
Open Question ◽  
Wightman Axioms ◽  
Euclidean Signature ◽  
3D Ising Model

Abstract CFTs in Euclidean signature satisfy well-accepted rules, such as the convergent Euclidean OPE. It is nowadays common to assume that CFT correlators exist and have various properties also in Lorentzian signature. Some of these properties may represent extra assumptions, and it is an open question if they hold for familiar statistical-physics CFTs such as the critical 3d Ising model. Here we consider Wightman 4-point functions of scalar primaries in Lorentzian signature. We derive a minimal set of their properties solely from the Euclidean unitary CFT axioms, without using extra assumptions. We establish all Wightman axioms (temperedness, spectral property, local commutativity, clustering), Lorentzian conformal invariance, and distributional convergence of the s-channel Lorentzian OPE. This is done constructively, by analytically continuing the 4-point functions using the s-channel OPE expansion in the radial cross-ratios ρ, $$ \overline{\rho} $$ ρ ¯ . We prove a key fact that |ρ|, $$ \left|\overline{\rho}\right| $$ ρ ¯ < 1 inside the forward tube, and set bounds on how fast |ρ|, $$ \left|\overline{\rho}\right| $$ ρ ¯ may tend to 1 when approaching the Minkowski space.We also provide a guide to the axiomatic QFT literature for the modern CFT audience. We review the Wightman and Osterwalder-Schrader (OS) axioms for Lorentzian and Euclidean QFTs, and the celebrated OS theorem connecting them. We also review a classic result of Mack about the distributional OPE convergence. Some of the classic arguments turn out useful in our setup. Others fall short of our needs due to Lorentzian assumptions (Mack) or unverifiable Euclidean assumptions (OS theorem).

scholarly journals Analytic continuation of the harmonic sums for the 3-loop anomalous dimensions

2005 ◽  
Vol 614 (1-2) ◽  
pp. 53-61 ◽  
Author(s):  
Johannes Blümlein ◽  
Sven-Olaf Moch
Keyword(s):  
Analytic Continuation ◽  
Anomalous Dimensions

scholarly journals Spectral Inclusion and Analytic Continuation

1999 ◽  
Vol 31 (6) ◽  
pp. 722-728 ◽  
Author(s):  
A. Atzmon ◽  
A. Eremenko ◽  
M. Sodin
Keyword(s):  
Analytic Continuation ◽  
Spectral Inclusion

Analytic continuation of quantum systems and their temporal evolution

1993 ◽  
Vol 47 (6) ◽  
pp. 2602-2614 ◽  
Author(s):  
E. C. G. Sudarshan ◽  
Charles B. Chiu
Keyword(s):  
Analytic Continuation ◽  
Temporal Evolution ◽  
Quantum Systems

Analytic continuation of Matsubara Green's functions

1998 ◽  
Vol 63 (1-3) ◽  
pp. 655-657 ◽  
Author(s):  
E.G. Klepfish ◽  
C.E. Creffield ◽  
E.R. Pike
Keyword(s):  
Analytic Continuation ◽  
Green's Functions ◽  
Green’S Functions
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