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Bosonic-type S-Matrix, Vacuum Instability and CDD Ambiguities

Mussardo, G, Pascal Simon

Published Mar 10, 1999• 49 citations
OpenAlex

Abstract

We consider the simplest bosonic-type S-matrix which is usually regarded as unphysical due to the complex values of the finite volume ground state energy. While a standard quantum field theory interpretation of such a scattering theory is precluded, we argue that the physical situation described by this S-matrix is of a massive Ising model perturbed by a particular set of irrelevant operators. The presence of these operators drastically affects the stability of the original vacuum of the massive Ising model and its ultraviolet properties. This scenario is supported by a numerical calculation of the energy levels of the model on a finite geometry which shows a level crossing of the two lowest energy eigenvalues.

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Kinks in finite volume

Timothy R. Klassen, Ezer Melzer

A (1+1)-dimensional quantum field theory with a degenerate vacuum (in finite volume) can contain particles, known as kinks, which interpolate between different vacua and have non-trivial restrictions on their multi-particle Hilbert space. Assuming such a theory to be integrable, we show how to calculate the multi-kink energy levels in finite volume given its factorizable S-matrix. In massive theories this can be done exactly up to contributions due to off-shell and tunneling effects that fall off exponentially with volume. As a first application we compare our analytical predictions for the kink scattering theories conjectured to describe the sub-leading thermal and magnetic perturbations of the tricritical Ising model with numerical results from the truncated conformal space approach. In particular, for the sub-leading magnetic perturbation our results allow us to decide between the two different S-matrices proposed by Smirnov and Zamolodchikov.

arXiv:hep-th/9202034•Nuclear Physics B•Sep 1, 1992•28 citations

On The S-Matrix of Ising Field Theory in Two Dimensions

Barak Gabai, Xi Yin

We explore the analytic structure of the non-perturbative S-matrix in arguably the simplest family of massive non-integrable quantum field theories: the Ising field theory (IFT) in two dimensions, which may be viewed as the Ising CFT deformed by its two relevant operators, or equivalently, the scaling limit of the Ising model in a magnetic field. Our strategy is that of collider physics: we employ Hamiltonian truncation method (TFFSA) to extract the scattering phase of the lightest particles in the elastic regime, and combine it with S-matrix bootstrap methods based on unitarity and analyticity assumptions to determine the analytic continuation of the 2 to 2 S-matrix element to the complex s-plane. Focusing primarily on the "high temperature" regime in which the IFT interpolates between that of a weakly coupled massive fermion and the E8 affine Toda theory, we will numerically determine 3-particle amplitudes, follow the evolution of poles and certain resonances of the S-matrix, and exclude the possibility of unknown wide resonances up to reasonably high energies.

arXiv:1905.00710•May 2, 2019•2 citations

On the S-matrix of Ising field theory in two dimensions

Barak Gabai, Xi Yin

Abstract We explore the analytic structure of the non-perturbative S-matrix in arguably the simplest family of massive non-integrable quantum field theories: the Ising field theory (IFT) in two dimensions, which may be viewed as the Ising CFT deformed by its two relevant operators, or equivalently, the scaling limit of the Ising model in a magnetic field. Our strategy is that of collider physics: we employ Hamiltonian truncation method (TFFSA) to extract the scattering phase of the lightest particles in the elastic regime, and combine it with S-matrix bootstrap methods based on unitarity and analyticity assumptions to determine the analytic continuation of the 2 → 2 S-matrix element to the complex s-plane. Focusing primarily on the “high temperature” regime in which the IFT interpolates between that of a weakly coupled massive fermion and the E8 affine Toda theory, we will numerically determine 3-particle amplitudes, follow the evolution of poles and certain resonances of the S-matrix, and exclude the possibility of unknown wide resonances up to reasonably high energies.

Journal of High Energy Physics•Oct 26, 2022•22 citations

A toy model of bosonic non-canonical quantum field

Marek Czachor, Monika Syty

A harmonic oscillator is an indefinite-frequency one if the parameter $ω$ is replaced by an operator. An ensemble of $N$ such oscillators may be regarded as a toy model of a bosonic quantum field. All the possible frequencies associated with a given problem are present already in a single oscillator and $N$ can be finite. Due to the operator character of $ω$ the resulting algebra of creation-annihilation operators is non-canonical. In the limit of large $N$ one recovers perturbation theory formulas of the canonical quantum field theory but with form factors automatically built in. Vacuum energy of the ensemble is finite, a fact discussed in the context of the cosmological constant problem. Space of states is given by a vector bundle with Fock-type fibers. Interactions of the field with 2-level systems, including Rabi oscillations and spontaneous emission, are discussed in detail.

arXiv:hep-th/0112011•Dec 2, 2001•2 citations

BOUNDARY S MATRIX FOR THE TRICRITICAL ISING MODEL

LEUNG CHIM

The tricritical Ising model perturbed by the subleading energy operator [Formula: see text] was known to be an integrable scattering theory of massive kinks,14 and in fact it preserves supersymmetry. We consider here the model defined on the half-plane with a boundary and compute the associated factorizable boundary S matrix. The conformal boundary conditions of this model are identified and the corresponding S matrices are found. We also show how some of these S matrices can be perturbed and generate “flows” between different boundary conditions.

arXiv:hep-th/9510008•International Journal of Modern Physics A•Oct 10, 1996•73 citations

1D Hubbard model elementary objects scattering

J. M. P. Carmelo, Pedro D Sacramento

In terms of electron processes, the 1D Hubbard model is a nonperturbative problem. That renders the description in terms of electron scattering of the microscopic processes that control the model properties a very difficult task. In this paper we study the corresponding scattering processes of the elementary objects whose occupancy configurations generate the energy eigenstates from the electron vacuum. Due to the related occurrence of an infinite set of conservation laws associated with the model integrability, such objects are found to undergo only zero-momentum forward-scattering collisions. The description of the model dynamical properties in terms of such elementary objects scattering events then drastically simplifies. The corresponding 1D Hubbard model scattering theory refers to arbitrary values of the densities and finite repulsive interaction U>0. Each ground-state - excited-state transition is associated with a well defined set of elementary zero-momentum forward-scattering events. The elementary-object scatterers dressed S matrix is expressed as a commutative product of S matrices, each corresponding to a two-object scattering event. This commutative factorization is stronger than the factorization associated with Yang-Baxter equation for the original spin-1/2 electron bare S matrix. The power-law singularities exponents in the finite-energy correlation-functions of the metallic phases of a wide class of 1D integrable and non-integrable systems are momentum dependent. In the present exactly solvable model such an exponent momentum dependence is controlled by the phase shifts and corresponding dressed S matrix considered in this paper.

arXiv:1211.6073•Nov 22, 2012•1 citation
We consider the simplest bosonic-type S-matrix which is usually regarded as unphysical due to the complex values of the finite volume ground state energy. While a standard quantum field theory interpretation of such a scattering theory is precluded, we argue that the physical situation described by this S-matrix is of a massive Ising model perturbed by a particular set of irrelevant operators. The presence of these operators drastically affects the stability of the original vacuum of the massive Ising model and its ultraviolet properties. This scenario is supported by a numerical calculation of the energy levels of the model on a finite geometry which shows a level crossing of the two lowest energy eigenvalues.
A (1+1)-dimensional quantum field theory with a degenerate vacuum (in finite volume) can contain particles, known as kinks, which interpolate between different vacua and have non-trivial restrictions on their multi-particle Hilbert space. Assuming such a theory to be integrable, we show how to calculate the multi-kink energy levels in finite volume given its factorizable S-matrix. In massive theories this can be done exactly up to contributions due to off-shell and tunneling effects that fall off exponentially with volume. As a first application we compare our analytical predictions for the kink scattering theories conjectured to describe the sub-leading thermal and magnetic perturbations of the tricritical Ising model with numerical results from the truncated conformal space approach. In particular, for the sub-leading magnetic perturbation our results allow us to decide between the two different S-matrices proposed by Smirnov and Zamolodchikov.
We explore the analytic structure of the non-perturbative S-matrix in arguably the simplest family of massive non-integrable quantum field theories: the Ising field theory (IFT) in two dimensions, which may be viewed as the Ising CFT deformed by its two relevant operators, or equivalently, the scaling limit of the Ising model in a magnetic field. Our strategy is that of collider physics: we employ Hamiltonian truncation method (TFFSA) to extract the scattering phase of the lightest particles in the elastic regime, and combine it with S-matrix bootstrap methods based on unitarity and analyticity assumptions to determine the analytic continuation of the 2 to 2 S-matrix element to the complex s-plane. Focusing primarily on the "high temperature" regime in which the IFT interpolates between that of a weakly coupled massive fermion and the E8 affine Toda theory, we will numerically determine 3-particle amplitudes, follow the evolution of poles and certain resonances of the S-matrix, and exclude the possibility of unknown wide resonances up to reasonably high energies.
Abstract We explore the analytic structure of the non-perturbative S-matrix in arguably the simplest family of massive non-integrable quantum field theories: the Ising field theory (IFT) in two dimensions, which may be viewed as the Ising CFT deformed by its two relevant operators, or equivalently, the scaling limit of the Ising model in a magnetic field. Our strategy is that of collider physics: we employ Hamiltonian truncation method (TFFSA) to extract the scattering phase of the lightest particles in the elastic regime, and combine it with S-matrix bootstrap methods based on unitarity and analyticity assumptions to determine the analytic continuation of the 2 → 2 S-matrix element to the complex s-plane. Focusing primarily on the “high temperature” regime in which the IFT interpolates between that of a weakly coupled massive fermion and the E8 affine Toda theory, we will numerically determine 3-particle amplitudes, follow the evolution of poles and certain resonances of the S-matrix, and exclude the possibility of unknown wide resonances up to reasonably high energies.
A harmonic oscillator is an indefinite-frequency one if the parameter ωωω is replaced by an operator. An ensemble of NNN such oscillators may be regarded as a toy model of a bosonic quantum field. All the possible frequencies associated with a given problem are present already in a single oscillator and NNN can be finite. Due to the operator character of ωωω the resulting algebra of creation-annihilation operators is non-canonical. In the limit of large NNN one recovers perturbation theory formulas of the canonical quantum field theory but with form factors automatically built in. Vacuum energy of the ensemble is finite, a fact discussed in the context of the cosmological constant problem. Space of states is given by a vector bundle with Fock-type fibers. Interactions of the field with 2-level systems, including Rabi oscillations and spontaneous emission, are discussed in detail.
The tricritical Ising model perturbed by the subleading energy operator [Formula: see text] was known to be an integrable scattering theory of massive kinks,14 and in fact it preserves supersymmetry. We consider here the model defined on the half-plane with a boundary and compute the associated factorizable boundary S matrix. The conformal boundary conditions of this model are identified and the corresponding S matrices are found. We also show how some of these S matrices can be perturbed and generate “flows” between different boundary conditions.
In terms of electron processes, the 1D Hubbard model is a nonperturbative problem. That renders the description in terms of electron scattering of the microscopic processes that control the model properties a very difficult task. In this paper we study the corresponding scattering processes of the elementary objects whose occupancy configurations generate the energy eigenstates from the electron vacuum. Due to the related occurrence of an infinite set of conservation laws associated with the model integrability, such objects are found to undergo only zero-momentum forward-scattering collisions. The description of the model dynamical properties in terms of such elementary objects scattering events then drastically simplifies. The corresponding 1D Hubbard model scattering theory refers to arbitrary values of the densities and finite repulsive interaction U>0. Each ground-state - excited-state transition is associated with a well defined set of elementary zero-momentum forward-scattering events. The elementary-object scatterers dressed S matrix is expressed as a commutative product of S matrices, each corresponding to a two-object scattering event. This commutative factorization is stronger than the factorization associated with Yang-Baxter equation for the original spin-1/2 electron bare S matrix. The power-law singularities exponents in the finite-energy correlation-functions of the metallic phases of a wide class of 1D integrable and non-integrable systems are momentum dependent. In the present exactly solvable model such an exponent momentum dependence is controlled by the phase shifts and corresponding dressed S matrix considered in this paper.