Integral-Darstellung kausaler Kommutatoren

Jost, Rossana Cristine Floriano; Lehmann, Hans‐Albert

doi:10.1007/bf02856049

Cited by 209 publications

(105 citation statements)

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“…We consider the retarded two-point function in the forward limit 37) which is related to the function M µµ (k) introduced in eq. (B.10) in infinite volume through a Wick rotation…”

Section: B1 Analyticity Propertiesmentioning

confidence: 99%

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Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions

Lucini

Patella

Ramos

et al. 2016

J. High Energ. Phys.

177

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In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C boundary conditions. In particular we learn that a certain class of electricallycharged states can be constructed in a fully consistent fashion without relying on gauge fixing and without peculiar complications. This class includes single particle states of most stable hadrons. We also calculate finite-volume corrections to the mass of stable charged particles and show that these are much smaller than in non-local formulations of QED.

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“…We consider the retarded two-point function in the forward limit 37) which is related to the function M µµ (k) introduced in eq. (B.10) in infinite volume through a Wick rotation…”

Section: B1 Analyticity Propertiesmentioning

confidence: 99%

“…The analyticity properties of the modified retarded commutator can be exposed by means of the Jost-Lehmann-Dyson (JLD) representation [37,38],…”

Section: Jhep02(2016)076mentioning

confidence: 99%

Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions

Lucini

Patella

Ramos

et al. 2016

J. High Energ. Phys.

177

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“…Jost and Lehmann [42] obtained an integral presentation for the matrix element of the causal commutator. This is a very powerful result.…”

Section: The Jost-lehmann-dyson Representationmentioning

confidence: 99%

“…Indeed, the Jost-Lehmann-Dyson representation is very crucial for deriving Lehmann's result. We remind the reader the two equations representing F (s, t), (42) and (43). Since we consider scattering of equal mass identical particles, the kinematics is simplified.…”

Section: D-dimensional Derivation Of Lehmann's Ellipsesmentioning

confidence: 99%

Analyticity properties and asymptotic behavior of scattering amplitude in higher dimensional theories

Maharana

2017

Journal of Mathematical Physics

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The properties of the high energy behavior of the scattering amplitude of massive, neutral and spinless particles in higher dimensional field theories are investigated. The axiomatic formulation of Lehmann, Symanzik and Zimmermann is adopted. The analyticity properties of the causal, the retarded and the advanced functions associated with the four point elastic amplitudes are studied. The analog of the Lehmann-Jost-Dyson representation is obtained in higher dimensional field theories. The generalized J-L-D representation is utilized to derive the t-plane analyticity property of the amplitude. The existence of an ellipse analogous to the Lehmann ellipse is demonstrated. Thus a fixed-t dispersion relation can be written down with finite number of subtractions due to the temperedness of the amplitudes. The domain of analyticity of scattering amplitude in s and t variables is extended by imposing unitarity constraints. A generalized version of Martin's theorem is derived to prove the existence of such a domain in D-dimensional field theories. It is shown that the amplitude can be expanded in a power series in t which converges for |t| < R; R being sindependent. The positivity properties of absorptive amplitudes are derived to prove the t-plane analyticity of amplitude. In the extended analyticity domain dispersion relations are written with two subtractions. The bound on the total cross section is derived from LSZ axioms without any extra ad hoc assumptions.

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“…based on the theory of many complex variables, and by the work of Jost & Lehmann ( 9 ) and of Dyson, (lO) based on more familiar but still tricky mathematics.…”

Section: Ucrl-8670mentioning

confidence: 99%

The Pion-Nucleon Interaction and Dispersion Relations

Chew¹

1959

Annu. Rev. Nucl. Sci.

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Integral-Darstellung kausaler Kommutatoren

Cited by 209 publications

References 0 publications

Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions

Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions

Analyticity properties and asymptotic behavior of scattering amplitude in higher dimensional theories

The Pion-Nucleon Interaction and Dispersion Relations

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