The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz

Babujian, H.; Foerster, Angela; Karowski, M.

doi:10.3842/sigma.2006.082

Cited by 27 publications

(70 citation statements)

References 48 publications

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“…There are two complementary approaches to obtaining local observables in integrable models. The first of them, known as the form factor program [1,2], aims at constructing point-local quantum fields Φ(x) directly. 1 Their n-point functions are expanded in a series by inserting a basis of intermediate asymptotic states, for example for n = 2, Ω, Φ(x)Φ(y)Ω = ∞ m=0 dθ 1 · · · dθ m (2π) m Ω|Φ(0)|θ 1 , .…”

Section: Introductionmentioning

confidence: 99%

Towards an Explicit Construction of Local Observables in Integrable Quantum Field Theories

Bostelmann

Cadamuro

2019

Ann. Henri Poincaré

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We present a new viewpoint on the construction of pointlike local fields in integrable models of quantum field theory. Rather than exhibiting their n-point functions and verifying the Wightman axioms, we aim to establish them as closed operators affiliated with a net of local von Neumann algebras, which is defined indirectly via wedge-local quantities. We also investigate whether these fields have the Reeh-Schlieder property, and in which sense they generate the net of algebras. For these results, we establish sufficient criteria that do not depend on details of the interaction, i.e., on the two-particle scattering matrix, and we complete the construction in the case of the massive Ising model.

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Section: Introductionmentioning

confidence: 99%

Towards an Explicit Construction of Local Observables in Integrable Quantum Field Theories

Bostelmann

Cadamuro

2019

Ann. Henri Poincaré

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“…a solution does not exist unless the function h(u, v, w) vanishes. 6 The extra contribution in this equation is given by…”

Section: The Off-shell Square With Three Excitationsmentioning

confidence: 99%

Cutting the cylinder into squares: the square form factor

Nieto

2019

J. High Energ. Phys.

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In this article we present a method for constructing two-point functions in the spirit of the hexagon proposal, which leads us to propose a "square form factor". Since cutting the square gives us two squares, we can write a consistency condition that heavily constrains such form factors. In particular, we are able to use this constraint to reconstruct the Gaudin through the forest expansion of the determinant appearing in its definition. We also use this procedure to compute the norm of off-shell Bethe states for some simple cases.

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“…Conventionally, one starts from a classical Lagrangian, derives the two-particle scattering function S from there, and then constructs local operators (quantum fields) by their matrix elements in asymptotic scattering states; this is the form factor programme [Smi92,BFK06]. A more recent, alternative approach [SW00,Lec08] starts from the function S as its input, then constructs quantum field localized in spacelike wedges (rather than at spacetime points), and uses these to abstractly obtain observables localized in bounded regions.…”

Section: Integrable Modelsmentioning

confidence: 99%

Negative energy densities in integrable quantum field theories at one-particle level

Bostelmann

Cadamuro

2016

Phys. Rev. D

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We study the phenomenon of negative energy densities in quantum field theories with selfinteraction. Specifically, we consider a class of integrable models (including the sinh-Gordon model) in which we investigate the expectation value of the energy density in one-particle states. In this situation, we classify the possible form of the stress-energy tensor from first principles. We show that one-particle states with negative energy density generically exist in non-free situations, and we establish lower bounds for the energy density (quantum energy inequalities). Demanding that these inequalities hold reduces the ambiguity in the stress-energy tensor, in some situations fixing it uniquely. Numerical results for the lowest spectral value of the energy density allow us to demonstrate how negative energy densities depend on the coupling constant and on other model parameters.

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The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz

Cited by 27 publications

References 48 publications

Towards an Explicit Construction of Local Observables in Integrable Quantum Field Theories

Towards an Explicit Construction of Local Observables in Integrable Quantum Field Theories

Cutting the cylinder into squares: the square form factor

Negative energy densities in integrable quantum field theories at one-particle level

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