This thesis considers massive field theories in 1+1 dimensions known as
affine Toda quantum field theories. We first consider the boundary sine-Gordon
model, deriving a complete picture of the boundary bound state structure for
general integrable boundary conditions, and then more general ATFTs in the
bulk, discovering a "generalised bootstrap" equation which explicitly encodes
the Lie algebra into the S-matrix. This last is related to a number of S-matrix
identities, as well as a generalisation of the idea that the conserved charges
of the theory form an eigenvector of the Cartan matrix.Comment: Ph.D. thesis, Durham, LaTeX, 112 pages, 6 eps figures, uses
  fancyheadings.st

Mattsson, Peter

English

arXiv

In this thesis, we consider the massive field theories in 1+1 dimensions known as affine Toda quantum field theories. These have the special property that they possess an infinite number of conserved quantities, a feature which greatly simplifies their study, and makes extracting exact information about them a tractable problem. We consider these theories both in the full space (the bulk) and in the half space bounded by an impenetrable boundary at x = 0. In particular, we consider their fundamental objects: the scattering matrices in the bulk, and the reflection factors at the boundary, both of which can be found in a closed form. In Chapter 1, we provide a general introduction to the topic before going on, in Chapter 2, to consider the simplest ATFT—the sine-Gordon model—with a boundary. We begin by studying the classical limit, finding quite a clear picture of the boundary structure we can expect in the quantum case, which is introduced in Chapter 3. We obtain the bound-state structure for all integrable boundary conditions, as well as the corresponding reflection factors. This structure turns out to be much richer than had hitherto been imagined. We then consider more general ATFTs in the bulk. The sine-Gordon model is based on a(^(1))(_1), but there is an ATFT for any semi-simple Lie algebra. This underlying structure is known to show up in their S-matrices, but the path back to the parameters in the Lagrangian is still unclear. We investigate this, our main result being the discovery of a "generalised bootstrap" equation which explicitly encodes the Lie algebra into the S-matrix. This leads to a number of new S-matrix identities, as well as a generalisation of the idea that the conserved charges of the theory form an eigenvector of the Cartan matrix. Finally our results are summarised in Chapter 5, and possible directions for further study are highlighted

Mattsson, Peter Aake

Durham e-Theses

A remark on the coupling dependence in affine Toda field theories,

Absence of particle production and factorization of the S-matrix in 1+1 dimensional models,

Affine Toda field theory and exact S-matrices,

All possible symmetries of the S-matrix,

Bound State Boundary S-Matrix of the sine-Gordon Model,

Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions,

Boundary breathers in the sinh-Gordon model,

Boundary S matrix and boundary state in two-dimensional integrable quantum field theory.

Boundary Sine-Gordon Interactions at the Free Fermion Point.

Boundary spectrum in the sine-Gordon model with Dirichlet boundary conditions,

Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states,

Deformations of W-algebras associated to simple Lie algebras.

Dynkin TBA's,

Elastic S-matrices in (l-hl) dimensions and Toda field theories.

Essentially nonlinear one-dimensional model of classical field theory Theor.

Exact Conductance through Point Contacts in the v

Exact S-matrices for NonsimplyLaced Affine Toda Theories,

Exact S-matrices,

Exact solutions of the Korteweg-de Vries equation for multiple collisions ofsolitons,

Exact two-particle matrix elements in S-matrix preserving deformation of integrable QFTs,

Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models,

Factorized Scattering in the Presence of Reflecting Boundaries,

Factorizing particles on a half line and root systems,

Generalisations of the Coleman-Thun mechanism and boundary reflection factors,

In &quot;Interface Between Physics and Mathematics&quot;

Integrable boundary conditions for classical sine-Gordon theory,

Integrable field theory with boundary conditions. Talks given at the workshop Frontiers in Quantum Field Theory, held in Urumqi, Xinjiang Uygur Autonomous Region. People's Republic of China,

Integrable systems away from criticality: the Toda field theory and S-matrix of the tricritical Ising model,

Integrals of motion in scaling 3-state Potts-model fieldtheory Int.

Lectures given at the TMR Montpellier Summer School Recent advances and applications of Conformal Field Theory held in Sete,

Lectures on non perturbative field theory and quantum impurity problems,

Method for solving the Korteweg-deVries equation,

Oeuvres Completes, Gauthier-Villars,

On a Generalised Bootstrap Principle,

On duality and reflection factors for the sinh-Gordon model, Int.J.Mod.Phys.

On the mass spectrum of affine Toda field theory Phys.

On the Prosaic Origin of the Double Poles in the Sine-Gordon S-matrix,

On the universal representation of the scattering matrix of affine Toda field theory Nucl. Phys.

Particle reflection amplitudes in al^^ Toda field theories,

Purely elastic scattering theories and their ultraviolet limits,

q-deformed Coxeter element in non-simply-laced affine Toda field theory

QKZ equation with \q\ = 1 and correlation functions of the XXZ model in the gapless regime,

Quantum S-matrix of the (l-hl)-dimensional Todd chain,

Recent developments in affine Toda quantum field theory, Invited lectures at the CRM-CAP Summer School 'Particles and Fields 94'

Root systems and purely elastic S-matrices,

S-matrices and bi-linear sum rules of conserved charges in affine Toda field theories,

S-matrix identities in affine Toda field theories,

Simple Groups of Lie Type,

The Analytic S-matrix,

The Analytic Smatrix,

The boundary sine-Gordon theory: classical and semi-classical analysis,

The hitch hiker's guide to the galaxy Pan,

The Quantum Theory of Fields,

The structure of semi-simple Lie algebras,

The Theory of the Double Gamma Function, Phil. Trans. Roy Soc. A196

Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas, Phys. Rev,

Two-dimensional generalized Toda lattice,

What is the use of a book', thought Alice, 'without pictures or conversations?'&quot;

Integrable quantum field theories, in the bulk and with a boundary

In this thesis, we consider the massive field theories in 1+1 dimensions known as affine Toda quantum field theories. These have the special property that they possess an infinite number of conserved quantities, a feature which greatly simplifies their study, and makes extracting exact information about them a tractable problem. We consider these theories both in the full space (the bulk) and in the half space bounded by an impenetrable boundary at x 0. In particular, we consider their fundamental objects: the scattering matrices in the bulk, and the reflection factors at the boundary, both of which can be found in a closed form. In Chapter 1, we provide a general introduction to the topic before going on, in Chapter 2, to consider the simplest ATFT - the sine-Gordon model - with a boundary. We begin by studying the classical limit, finding quite a clear picture of the boundary structure we can expect in the quantum case, which is introduced in Chapter 3. We obtain the bound-state structure for all integrable boundary conditions, as well as the corresponding reflection factors. This structure turns out to be much richer than had hitherto been imagined. We then consider more general ATFTs in the bulk. The sine-Gordon model is based on a_1&quot;(&quot;1&quot;) but there is an ATFT for any semi-simple Lie algebra. This underlying structure is known to show up in their S-matrices, but the path back to the parameters in the Lagrangian is still unclear. We investigate this, our main result being the discovery of a 'generalised bootstrap' equation which explicitly encodes the Lie algebra into the S-matrix. This leads to a number of new S-matrix identities, as well as a generalisation of the idea that the conserved charges of the theory form an eigenvector of the Cartan matrix. Finally, our results are summarised in Chapter 5, and possible directions for further study are highlighted. (author)SIGLEAvailable from British Library Document Supply Centre-DSC:DXN042845 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Mattsson, P.A.

OpenGrey Repository

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.263.961

Integrable Quantum Field Theories, in the Bulk and with a Boundary

Integrable Quantum Field Theories, in the Bulk and with a Boundary

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