Thermodynamics of the massive Thirring model: Weak sine-Gordon coupling regime

The thermodynamics of the massive Thirring model is formulated in the weak sine-Gordon coupling regime. In particular, the breather problem is discussed and the exact classical theory is reproduced. The soliton mass and the breather mass at finite temperature are also found.     

On the supersymmetric sine-Gordon model

The basic model in a new trend in supersymmetry and soliton theory is presented. Exact soliton-like solutions of the supercovariant coupled equations of motion are obtained. From this a bag model is constructed.Talk given at the ldSymposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.     

On the conformal transformations in the massless Thirring model

On the basis of solutions for the massless scalar field in two space-time dimensions obtained in a previous paper, the field satisfying the renormalized Thirring equation is constructed. Both infinitesimal and global transformations with respect to the two-dimensional conformal group for these field is obtained. The latter do not coincide with the standard ones. The renormalized Thirring equation is proved to be covariant under infinitesimal conformal transformations as well as under the global transformations belonging to the representations of the universal covering of the conformal group.     

On the equivalence between magnetic-field-induced phase transitions in the integer quantum Hall effect

Magnetic-field-induced phase transitions in the two-dimensional electron system in a AlGaAs/InGaAs/GaAs heterostructure are studied. Two kinds of magnetic-field-induced phase transitions, plateau-plateau (P-P) and insulator-quantum Hall conductor (I-QH) transitions, are observed in the integer quantum Hall effect regime at high magnetic fields. In the P-P transition, both the semicircle law and the universality of critical conductivities are broken and we do not observe the universal scaling. However, the P-P transition can still be mapped to the I-QH transition by the Landau-level addition transformation, and as the temperature decreases the critical points of these two transitions appear at the same temperature. Our observations indicate that the equivalence between P-P and I-QH transitions can be found by the suitable analysis even when some expected universal properties are invalid.     

Normal products in the Thirring model

The short-distance behavior of products of fields is studied in the Thirring model of a self-interacting, massless, spinor field in two dimensions. One is able to construct normal products which share most of the convenient properties of the free-field Wick products. A modified form of Wilson's expansion formula is verified. The original formulation of Wilson's hypothesis is seen to hold to every finite order in the coupling constant, but fails in the exact solution of the model for sufficiently strong coupling.Research supported by the Banco Nacional do Desenvolvimento Econômico and the Conselho Nacional de Pesquisas.     

Non-equivalence between Heisenberg XXZ spin chain and Thirring model

The Bethe ansatz equations for the spin 1/2 Heisenberg XXZ spin chain are numerically solved, and the energy eigenvalues are determined for the antiferromagnetic case. We examine the relation between the XXZ spin chain and the massless Thirring model, and show that the spectrum of the XXZ spin chain has a gapless excitation while the regularized Thirring model calculated with the Bogoliubov transformation method has a finite gap. This finite gap spectrum is also confirmed by the Bethe ansatz solution of the massless Thirring model.Received: 28 October 2004, Published online: 21 January 2005PACS: 10.Kk, 03.70. + k, 11.30.-j, 11.30.Rd     

On the super sigma models and super sine-Gordon model

A study of theO(3) invariant sigma model, theCP ¹ model and the sine-Gordon model in view of their equivalence in the Bose and Fermi-Bose cases is given, using the modern mathematical language of differential forms. On the basis of complex supersymmetry the central charges are shown to exist and interesting properties of complex supersymmetry are studied.     

Strong coupling expansion in the massive Thirring model

A strong coupling expansion of the Green functions in the massive Thirring model is formulated. Expressions obtained for the fundamental fermion mass and theβ function agree with the known qualitative features of these physical quantities.     

Boson-soliton scattering in the sine-Gordon model

In this paper we calculate the boson-soliton scattering amplitudes for various processes in the sine-Gordon model to obtain results in agreement with the prediction of no-particle production and equality of ingoing and outgoing sets of momenta.     

On the relation between the Abelian Higgs model and the spontaneously broken massless scalar electrodynamics

An analysis is made of the connection between the “massless” field theories, in the presence of the Coleman-Weinberg phenomenon and the corresponding models with a “negative mass” term as origin of the spontaneous breakdown. For the very interesting case of an Abelian gauge theory, i.e. the Higgs model, we find the conditions for the parameters of the theory which make it equivalent to the spontaneously broken scalar massless electrodynamics. The properties of the effective potential in this limit are studied.     

Gauss law commutator in the chirally gauged Wess-Zumino-Witten model

We evaluate the commutator of the Gauss law constraints starting from the chirally gauged Wess-Zumino-Witten action. The calculations are done at tree level, i.e. by evaluating corresponding Poisson brackets. The results are compared with commutators obtained by others directly from the gauged fermionic theory, and with Faddeev's results based on cohomology.     

Thermal activation rates in the chirally asymmetric Gross-Neveu model

We address the problem of how to incorporate quantum effects into the calculation of finite-temperature decay rates for a metastable state of a quantum field theory. To do this, we consider the Gross-Neveu model with an explicit chiral symmetry breaking term, which allows for a metastable state. This theory can be shown to have a “critical bubble” which is a solution to the exact equations of motions (i.e. to all orders in perturbation theory, including all higher derivative, quantum and thermal corrections). This configuration mediates the thermal activation of the metastable vacuum to the true ground state, with a decay rate Γ∞ exp(−F_c/T), where F_c is the free energy of the critical bubble. We then compare this exact calculation to various approximations that have been used in previous work. We find that these approximations all overestimate the activation rate. Furthermore, we study the effect of finite baryon number upon the bubble profile and the activation barriers. We find that beyond a critical baryon number the activation barriers disappear altogether.     

Commensurate-incommensurate phase transition in one-dimensional quantum sine-Gordon model based on a lattice massive thirring model

The commensurate-incommensurate (C-IC) phase transition in the one dimensional quantum sine-Gordon model at zero temperature is exactly solved with the use of the Bethe ansatz technique for the lattice massive Thirring model. The energy difference between C and IC phases is derived based on the same ground state which is valid in the whole parameter region. It is due to the fact that there is no change in the ground state of the lattice massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model. It is proved in the whole parameter region that the IC phase can be realized with the soliton density proportional to (E _s : formation energy of soliton), whenE _s becomes negative.     

On the equivalence between the wave-packet phase space representation (WPPSR) and the phase space generated by the squeezed states

We show that the parametrized Wave-Packet Phase Space representation, which has been studied earlier by one of the authors, is equivalent to a Squeezed States Phase Space Representation of quantum mechanics.     

Numerical study of self-couplings in the broken phase of the lattice Ising model

A Monte Carlo study of a one-component scalar Φ⁴ model was made on a 10⁴ hypercubic lattice in its Ising limit. We measured the renormalized mass and coupling of the three-point vertex in the spontaneously broken phase. By measuring them at non-zero momenta, we successfully settled problems caused by the finite vacuum expectation value of the scalar field. To suppress artificial fluctuation of observables, a uniform source was introduced. Our results are in good agreement with the one-loop relation between the vacuum expectation value, mass and the three-point coupling.     

Thirring model partition functions and harmonic differentials

The partition function of the Thirring model on a Riemann surface is calculated using the representation of the model as a fermion interacting with an auxiliary vector potential. The Hodge decomposition of the potential is used and the integral over the harmonic forms is shown to reproduce exactly the soliton sum in the bosonic version of the theory.