scholarly journals Solving the Bethe-Salpeter equation for scalar theories in Minkowski space

1995 ◽  
Vol 51 (12) ◽  
pp. 7026-7039 ◽  
Author(s):  
Kensuke Kusaka ◽  
Anthony G. Williams
Keyword(s):  
Minkowski Space ◽  
Scalar Theories

scholarly journals Solving the Bethe - Salpeter Equation in Minkowski Space: Scalar Theories and Beyond

1997 ◽  
Vol 50 (1) ◽  
pp. 147 ◽  
Author(s):  
K. Kusaka ◽  
A. G. Williams ◽  
K. M. Simpson
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Vertex Function ◽  
Bound States ◽  
Spectral Representation ◽  
Ladder Approximation ◽  
Wick Rotation ◽  
Space Solution ◽  
Scalar Theories ◽  
Scattering Kernel

The Bethe–Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional approach, where the BSE is solved in Euclidean space after a Wick rotation. For all but the lowest-order (i.e. ladder) approximation to the scattering kernel, the naive Wick rotation is invalid. Our approach generates the vertex function and Bethe–Salpeter amplitude for the entire allowed range of momenta, whereas these cannot be directly obtained from the Euclidean space solution. Our method is quite general and can be applied even in cases where the Wick rotation is not possible.

scholarly journals Preface: Quarks, hadrons and nuclei

1997 ◽  
Vol 50 (1) ◽  
pp. I
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Vertex Function ◽  
Bound States ◽  
Spectral Representation ◽  
Ladder Approximation ◽  
Wick Rotation ◽  
Space Solution ◽  
Scalar Theories ◽  
Scattering Kernel

The Bethe–Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional approach, where the BSE is solved in Euclidean space after a Wick rotation. For all but the lowest-order (i.e. ladder) approximation to the scattering kernel, the naive Wick rotation is invalid. Our approach generates the vertex function and Bethe–Salpeter amplitude for the entire allowed range of momenta, whereas these cannot be directly obtained from the Euclidean space solution. Our method is quite general and can be applied even in cases where the Wick rotation is not possible.

scholarly journals Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space

1997 ◽  
Vol 56 (8) ◽  
pp. 5071-5085 ◽  
Author(s):  
Kensuke Kusaka ◽  
Ken Simpson ◽  
Anthony G. Williams
Keyword(s):  
Minkowski Space ◽  
Bound States ◽  
Scalar Theories

On generalized partially null Mannheim curves in Minkowski space-time

2016 ◽  
Vol 46 (1) ◽  
pp. 159-170 ◽  
Author(s):  
Emilija Nešović ◽  
Milica Grbović
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Minkowski Space Time

scholarly journals Quantum volume and length fluctuations in a midi-superspace model of Minkowski space

2015 ◽  
Vol 32 (5) ◽  
pp. 055009
Author(s):  
Jeremy Adelman ◽  
Franz Hinterleitner ◽  
Seth Major
Keyword(s):  
Minkowski Space ◽  
Quantum Volume

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).

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