Thermodynamics of $T \Tbar$ perturbations of some single particle field theories

We study the Thermodynamic Bethe Ansatz (TBA) equations for pure $T\Tbar$ perturbations of some simple integrable quantum field theories with a single bosonic or fermionic particle, in particular the massive sinh-Gordon model and its ultraviolet (UV) limit which is a deformation of the conformally invariant free massless boson. Whereas the TBA equations for $T\Tbar$ deformations of massive theories are in principle known, the TBA equations we propose for the deformations of conformal field theories (CFT's) are relatively new and require a special factorization in rapidity variables of the CDD factor for the scattering of the massless particles. The latter TBA equations can be solved exactly and reproduce the known results for the ground state energy on a cylinder of circumference $R$ which were previously obtained using different methods based for instance on the Burgers differential equation. Special attention is paid to the c-theorem in this context which is discussed in some detail. For positive infra-red (IR) central charge $c_{IR}$, for flows consistent with the c-theorem the ground state energy develops a (previously known) square-root singularity towards the UV, which strongly suggests the theories are UV incomplete in these physically important cases. We suggest that the singularity indicates a tachyonic vacuum instability. Other cases with $c_{IR} < 0$ do not have this singularity are interpreted as being UV complete with $c_{UV} = 0$. We extend our results to a continuously variable $c_{IR}$ by introducing a chemical potential and suggest this as a possible toy model for the $T\Tbar$ perturbed Liouville theory.

Massless Composite Bosons Formed by the Coupled Electron-Positron Pairs and Two-Photon Angular Correlations in the Colliding Beam Reaction e-e+→Bγγ with Emission of the Massless Boson

The approach in which the electron and positron are treated as ordinary, different particles, each being characterized by the complete set of the Dirac plane waves, is examined. This completely symmetric representation that is beyond the standard QED makes it necessary to choose another solution of the Dirac equation for the free particle propagator as compared to that used currently. The Bethe-Salpeter equation with these particle propagators is solved in the ladder approximation. A new solution has been found represented by the massless composite bosons formed by the coupled electron-positron pairs with the coupling equal to the fine structure constant. It has been demonstrated that (1) the massless boson states have normalizable complex wave functions which are transversely compressed plane waves; (2) the transverse radius of the wave functions diverges as the boson energy goes to zero; that is, the composite bosons cannot be at rest; (3) increasing the boson energy results in an extension of the transverse wave function in the momentum space and a corresponding contraction of the real space coordinate wave function. The new reaction e-e+→Bγγ is investigated with the products composed of the massless composite boson and two photons. The cross-section of this reaction is derived for nonrelativistic colliding beams of spin-polarized electrons and positrons. In this case the 2γ angular correlation spectrum is characterized by a narrow peak with the full-width-at-half-maximum not exceeding 0.2 mrad. It is shown that in order to distinguish between the conventional annihilation of the singlet electron-positron pair with the two-photon emission and the new examined reaction yielding the three particles, experiments are proposed with the extremely nonrelativistic colliding beams.

RESONANCES FOR A HYDROGENIC SYSTEM OR A HARMONIC OSCILLATOR STRONGLY COUPLED TO A FIELD

We calculate resonances which are formed by a particle in a potential which is either Coulombian or quadratic when the particle is strongly coupled to a massless boson, taking only two energy levels into consideration. From these calculations we derive how the moving away of the particle from its attraction center goes together with the energy lowering of hybrid states that this particle forms with the field. We study the width of these states and we show that stable states may also appear in the coupling.

MARINARI–PARISI AND SUPERSYMMETRIC COLLECTIVE FIELD THEORY

A field theoretic formulation of the Marinari–Parisi supersymmetric matrix model is established and shown to be equivalent to a recently proposed supersymmetrization of the bosonic collective string field theory. It also corresponds to a continuum description of super-Calogero models. The perturbation theory of the model is developed and, in this approach, an infinite sequence of vertices is generated. A class of potentials is identified for which the spectrum is that of a massless boson and Majorana fermion. For the harmonic oscillator case, the cubic vertices are obtained in an oscillator basis. For a rather general class of potentials it is argued that one cannot generate from Marinari–Parisi models a continuum limit similar to that of the d = 1 bosonic string.

CHARGE SCREENING AND SPACE DIMENSION

We consider two static “charges” interacting through the exchange of massless boson “photon” and study the screening which arises when the medium, into which the system is placed, gives a non-vanishing effective mass to the boson. We investigate how the functional form of screening depends on the space dimensions of the problem using a generalized Debye-Hückel formalism and calculate, in particular, the screened form of the linearly rising potential in a three dimensional space.