General Principles of Quantum Field Theory

Bogolyubov, N. N.; Oksak, A. I.; Todorov, Ivan; Logunov, A. A.; Gould, Glenn

doi:10.1007/978-94-009-0491-0

Cited by 279 publications

(24 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To derive a dispersion formula for the S-matrix, one needs to amputate the external lines and analytically continue k 2 i to the mass-shell. In the process of analytically continuing, anomalous thresholds can move onto the physical sheet and the dispersion integral may be deformed into the complex plane [59,62]. In this work we are interested in correlation functions and will study dispersion formulas inside the primitive domain D, where we have analyticity in the entire cut t-plane.…”

Section: Jhep05(2021)098mentioning

confidence: 99%

“…Section 3 will then largely be a review on how these off-shell dispersion formulas are derived. To our knowledge, the main new results in this section is the expression for the five-point dispersion formula in terms of a double advanced product 6 and the method used to relate momentum space discontinuities to causal commutators, at general n-points, using the axiomatic definitions of the time-ordered and causal products [62,79].…”

Section: Jhep05(2021)098mentioning

confidence: 99%

“…We will use a different approach and, following [62,79], define the time-ordered product using a set of physically well-motivated conditions. For simplicity, we restrict to real, scalar operators.…”

Section: Operator Orderingsmentioning

confidence: 99%

“…The terms on the right-hand side of (2.7) can be factorized by inserting a complete set of states between the pairs of ordered operators. For theories with an S-matrix, one can use the LSZ prescription to go from (2.7) to the standard S-matrix unitarity condition S † S = 1 [62,89]. In appendix B, we review how to use (2.7) to derive the AdS cutting rules.…”

Section: Jhep05(2021)098mentioning

confidence: 99%

“…properties of scattering amplitudes [9,59,61,62]. The simplest amplitude to study is a 2 → 2 scattering amplitude, M (s, t), for identical scalars of mass m > 0.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Dispersion formulas in QFTs, CFTs and holography

Meltzer

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n-points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.

show abstract

Section: Jhep05(2021)098mentioning

confidence: 99%

Section: Jhep05(2021)098mentioning

confidence: 99%

Section: Operator Orderingsmentioning

confidence: 99%

Section: Jhep05(2021)098mentioning

confidence: 99%

“…properties of scattering amplitudes [9,59,61,62]. The simplest amplitude to study is a 2 → 2 scattering amplitude, M (s, t), for identical scalars of mass m > 0.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations