THE S-MATRIX, CURRENTS, AND CROSSING SYMMETRY

1975 ◽  
pp. 229-246
Author(s):  
YU.V. NOVOZHILOV
Keyword(s):  
Crossing Symmetry ◽  
S Matrix

Chern–Simons theories with fundamental matter: A brief review of large N results including Fermi–Bose duality and the S-matrix

2016 ◽  
Vol 31 (32) ◽  
pp. 1630052 ◽  
Author(s):  
Spenta R. Wadia
Keyword(s):  
String Theory ◽  
Gauge Fields ◽  
Duality Symmetry ◽  
Large N ◽  
Fundamental Matter ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Symmetry Relations ◽  
Aharonov Bohm ◽  
Chern Simons

We begin with a few words about Salam’s contribution to the growth of String Theory in India. In the technical talk we review results in [Formula: see text] Chern–Simons plus vector matter theories in 2[Formula: see text]+[Formula: see text]1 dim in the large [Formula: see text] limit. The dressing of charged matter by Chern–Simons gauge fields leads to anyons that interpolate between fermions and bosons and lead to a duality symmetry between fermionic and bosonic theories. The S-matrix (defined in the large [Formula: see text] limit) besides exhibiting this duality, also exhibits novel properties due to the presence of anyons. The S-matrix is not analytic, like in Aharonov–Bohm scattering, and satisfies modified crossing symmetry relations.

scholarly journals Dual S-matrix bootstrap. Part I. 2D theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Andrea L. Guerrieri ◽  
Alexandre Homrich ◽  
Pedro Vieira
Keyword(s):  
Optimization Theory ◽  
Scattering Matrix ◽  
Dual Approach ◽  
Physical Systems ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Primal Formulation ◽  
Rigorous Bounds ◽  
Duality In Optimization ◽  
Stable Particles

Abstract Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We then explain how to optimize such bounds numerically, and prove that they provide the same bounds obtained from the usual primal formulation of the S-matrix Bootstrap, at least once convergence is attained from both perspectives. These techniques are then applied to the study of a gapped system with two stable particles of different masses, which serves as a toy model for bootstrapping popular physical systems.

Dynamic Form of Static Dispersion Relations and Projective Spaces

1997 ◽  
Vol 12 (01) ◽  
pp. 249-254 ◽  
Author(s):  
V. A. Meshcheryakov
Keyword(s):  
Dispersion Relation ◽  
Global Analysis ◽  
Projective Spaces ◽  
Analytical Continuation ◽  
Physical Sheet ◽  
System Of Difference Equations ◽  
Static Limit ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Dynamic Form

The S-matrix in the static limit of a dispersion relation has a finite order N and is a matrix of meromorfic functions of energy ω in the plane with cuts (-∞, -1],[+1, = ∞). In the elastic case it reduces to N functions Si(ω) conncted by the crossing symmetry matrix A. The problem of analytical continuation of Si(ω) from the physical sheet to unphysical ones can be treated as a nonlinear system of difference equations. It is shown that a global analysis of this system can be carried out effectively in projective spaces PN and PN+1. The connection between spasec PN and PN+1 is discussed.

scholarly journals ON THE S MATRIX OF THE SUBLEADING MAGNETIC DEFORMATION OF THE TRICRITICAL ISING MODEL IN TWO DIMENSIONS

1992 ◽  
Vol 07 (21) ◽  
pp. 5281-5305 ◽  
Author(s):  
F. COLOMO ◽  
G. MUSSARDO ◽  
A. KOUBEK
Keyword(s):  
Ising Model ◽  
Finite Size ◽  
Numerical Data ◽  
Two Dimensions ◽  
Conformal Space ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Space Approach ◽  
Good Agreement

We compute the S matrix of the tricritical Ising model perturbed by the subleading magnetic operator using Smirnov’s RSOS reduction of the Izergin-Korepin model. The massive model contains kink excitations which interpolate between two degenerate asymmetric vacua. As a consequence of the different structure of the two vacua, the crossing symmetry is implemented in a nontrivial way. We use finite-size techniques to compare our results with the numerical data obtained by the truncated conformal space approach and find good agreement.

scholarly journals BOUNDARY S MATRIX AND BOUNDARY STATE IN TWO-DIMENSIONAL INTEGRABLE QUANTUM FIELD THEORY

1994 ◽  
Vol 09 (21) ◽  
pp. 3841-3885 ◽  
Author(s):  
SUBIR GHOSHAL ◽  
ALEXANDER ZAMOLODCHIKOV
Keyword(s):  
Field Theory ◽  
Two Dimensional ◽  
Boundary State ◽  
Integrable Field Theory ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Boundary Analog ◽  
Sine Gordon Model ◽  
Integrable Quantum Field Theory ◽  
Integrable Field

We study integrals of motion and factorizable S matrices in two-dimensional integrable field theory with boundary. We propose the "boundary cross-unitarity equation," which is the boundary analog of the crossing-symmetry condition of the "bulk" S matrix. We derive the boundary S matrices for the Ising field theory with boundary magnetic field and for the boundary sine–Gordon model.

MODULAR CONSTRUCTIONS OF QUANTUM FIELD THEORIES WITH INTERACTIONS

2000 ◽  
Vol 12 (02) ◽  
pp. 301-326 ◽  
Author(s):  
B. SCHROER AKEROYD ◽  
H.-W. WIESBROCK
Keyword(s):  
Fourier Transforms ◽  
Double Cone ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Cone Algebra ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Modular Method ◽  
Quantum Localization

We extend the previously introduced constructive modular method to nonperturbative QFT. In particular the relevance of the concept of "quantum localization" (via intersection of algebras) versus classical locality (via support properties of test functions) is explained in detail, the wedge algebras are constructed rigorously and the formal aspects of double cone algebras for d=1+1 factorizing theories are determined. The well-known on-shell crossing symmetry of the S-Matrix and of formfactors (cyclicity relation) in such theories is intimately related to the KMS properties of new quantum-local PFG (one-particle polarization-free) generators of these wedge algebras. These generators are "on-shell" and their Fourier transforms turn out to fulfill the Zamolodchikov–Faddeev algebra. As the wedge algebras contain the crossing symmetry information, the double cone algebras reveal the particle content of fields. Modular theory associates with this double cone algebra two very useful chiral conformal quantum field theories which are the algebraic versions of the light ray algebras.

scholarly journals Unitarity, crossing symmetry and duality of the S-matrix in large N Chern-Simons theories with fundamental matter

2015 ◽  
Vol 2015 (4) ◽  
Author(s):  
Sachin Jain ◽  
Mangesh Mandlik ◽  
Shiraz Minwalla ◽  
Tomohisa Takimi ◽  
Spenta R. Wadia ◽  
...  
Keyword(s):  
Large N ◽  
Fundamental Matter ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Chern Simons

POLES OF S-MATRIX: 1D WELL/BARRIER POTENTIAL

2018 ◽  
Author(s):  
Alexandre Drinko ◽  
Fabiano M. Andrade
Keyword(s):  
Barrier Potential ◽  
S Matrix

1H NMR characterisation of the diffusional properties of methanogenic granular sludge

1999 ◽  
Vol 39 (7) ◽  
pp. 187-194 ◽  
Author(s):  
P. Lens ◽  
F. Vergeldt ◽  
G. Lettinga ◽  
H. Van As
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Bacterial Cell ◽  
Granular Sludge ◽  
T2 Relaxation ◽  
Self Diffusion ◽  
Diffusion Analysis ◽  
S Matrix ◽  
Granular Matrix ◽  
Pfg Nmr

The diffusive properties of mesophilic methanogenic granular sludge have been studied using diffusion analysis by relaxation time separated pulsed field gradient nuclear magnetic resonance (DARTS PFG NMR) spectroscopy. NMR measurements were performed at 22°C with 10 ml granular sludge at a magnetic field strength of 0.5 T (20 MHz resonance frequency for protons). Spin-spin relaxation (T2) time measurements indicate that three 1H populations can be distinguished in methanogenic granular sludge beds, corresponding to water in three different environments. The T2 relaxation time measurements clearly differentiate the extragranular water (T2 ≈ 1000 ms) from the water present in the granular matrix (T2 = 40-100 ms) and bacterial cell associated water (T2 = 10-15 ms). Self-diffusion coefficient measurements at 22°C of the different 1H-water populations as the tracer show that methanogenic granular sludge does not contain one unique diffusion coefficient. The observed distribution of self-diffusion coefficients varies between 1.1 × 10−9 m2/s (bacterial cell associated water) and 2.1 × 10−9 m2/s (matrix associated water).

Sign in / Sign up

Export Citation Format

Share Document