Excited state g-functions from the Truncated Conformal Space

In this paper we consider excited state g-functions, that is, overlaps between boundary states and excited states in boundary conformal field theory. We find a new method to calculate these overlaps numerically using a variation of the truncated conformal space approach. We apply this method to the Lee-Yang model for which the unique boundary perturbation is integrable and for which the TBA system describing the boundary overlaps is known. Using the truncated conformal space approach we obtain numerical results for the ground state and the first three excited states which are in excellent agreement with the TBA results. As a special case we can calculate the standard g-function which is the overlap with the ground state and find that our new method is considerably more accurate than the original method employed by Dorey et al.Comment: 21 pages, 6 figure

The Political Rhetoric and Oratory of Margaret Thatcher

The aim of this book is to assess the construction of the political persona of Margaret Thatcher and within this the rhetorical devices and oratorical methods that she used to justify Thatcherism. The study of political persona, rhetoric and oratory and its impact upon the political process is an emerging area of academic research, and Thatcher constitutes a high profile and controversial figure to use as a case study. By doing so, the book will provide an insight into the persuasive abilities (and limitations) of Thatcher, and the extent to which the personalisation of her leadership was core to the narrative(s) of Thatcherism. The book will revolve around two sections. The first section evaluates how the political persona of Thatcher was established and embedded by examining her approach, arguments and effects in three different arenas: first, at parliamentary debate; second, in set piece speeches, most notably party conferences; and third, in interviews and press conferences. The second section will examine her rhetoric and oratory by considering her use of ethos or her character to justify political positions; her exploitation of pathos or emotion as a means of justification, and the extent to which her communication was informed by logos (evidence and logic) as a means of persuasion. The second section also broadens the analysis out to consider her communicative style in terms of the Olmsted criteria: when was it deliberative (considered); when was it judicial (reflective and forensic) and to what extent was it epideitic (based around drama and performance). By the analytical approaches identified above the book will offer a new and distinctive interpretation of the leadership of Margaret Thatcher and the politics of Thatcherism. It will also offer a framework for analysis that can be applied to other political elites

Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime

A generic PT-symmetric Hamiltonian is assumed tridiagonalized and truncated to N dimensions, and its up-down symmetrized special cases with J=[N/2] real couplings are considered. In the strongly non-Hermitian regime the secular equation gets partially factorized at all N. This enables us to reveal a fine-tuned alignment of the dominant couplings implying an asymptotically sharply spiked shape of the boundary of the J-dimensional quasi-Hermiticity domain in which all the spectrum of energies remains real and observable.Comment: 28 pp., 4 tables, 1 figur

Finite size effects in perturbed boundary conformal field theories

We discuss the finite-size properties of a simple integrable quantum field theory in 1+1 dimensions with non-trivial boundary conditions. Novel off-critical identities between cylinder partition functions of models with differing boundary conditions are derived.Comment: 7 pages, 11 figures, JHEP proceedings style. Uses epsfig, amssymb. Talk given at the conference `Nonperturbative Quantum Effects 2000', Pari

Oscillons in gapless theories

We show that large scale oscillons, i.e., quasiperiodic, long-living particlelike solutions, may exist in massless theories, too. Their existence is explained using an effective (smeared) mass threshold which takesinto account nonlinear (finite) perturbations

Instanton Calculus and SUSY Gauge Theories on ALE Manifolds

We study instanton effects along the Coulomb branch of an N=2 supersymmetric Yang-Mills theory with gauge group SU(2) on Asymptotically Locally Euclidean (ALE) spaces. We focus our attention on an Eguchi-Hanson gravitational background and on gauge field configurations of lowest Chern class.Comment: 15 pages, LaTeX file. Extended version to be published in Physical Review

Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics

In a recent paper it was shown that if a Hamiltonian H has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT. The inner product with respect to CPT is associated with a positive norm and the quantum theory built on the associated Hilbert space is unitary. In this paper it is shown how to construct the operator C for the non-Hermitian PT-symmetric Hamiltonian $H={1\over2}p^2+{1\over2}x^2 +i\epsilon x^3$ using perturbative techniques. It is also shown how to construct the operator C for $H={1\over2}p^2+{1\over2}x^2-\epsilon x^4$ using nonperturbative methods

Does the complex deformation of the Riemann equation exhibit shocks?

The Riemann equation $u_t+uu_x=0$, which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time. This equation is \cP\cT symmetric. A one-parameter \cP\cT-invariant complex deformation of this equation, $u_t-iu(iu_x)^\epsilon= 0$ ($\epsilon$ real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless $\epsilon$ is an odd integer.Comment: latex, 8 page

Reflectionless Potentials and PT Symmetry

Large families of Hamiltonians that are non-Hermitian in the conventional sense have been found to have all eigenvalues real, a fact attributed to an unbroken PT symmetry. The corresponding quantum theories possess an unconventional scalar product. The eigenvalues are determined by differential equations with boundary conditions imposed in wedges in the complex plane. For a special class of such systems, it is possible to impose the PT-symmetric boundary conditions on the real axis, which lies on the edges of the wedges. The PT-symmetric spectrum can then be obtained by imposing the more transparent requirement that the potential be reflectionless.Comment: 4 Page

Effect of retardation on dynamical mass generation in two-dimensional QED at finite temperature

The effect of retardation on dynamical mass generation in is studied, in the imaginary time formalism. The photon porarization tensor is evaluated to leading order in 1/N (N is the number of flavours), and simple closed form expressions are found for the fully retarded longitudinal and transverse propagators, which have the correct limit when T goes to zero. The resulting S-D equation for the fermion mass (at order 1/N) has an infrared divergence associated with the contribution of the transverse photon propagator; only the longitudinal contribution is retained, as in earlier treatments. For solutions of constant mass, it is found that the retardation reduces the value of the parameter r (the ratio of twice the mass to the critical temperature) from about 10 to about 6. The gap equation is then solved allowing for the mass to depend on frequency. It was found that the r value remained close to 6. Possibilities for including the transverse propagator are discussed.Comment: 26 pages 8 figure