Dimensional Field Theoretic Models Research Articles

The Tomonaga–Luttinger liquid with quantum impurity revisited: Critical line and phase diagram

We revisit the (1+1) dimensional field theoretical model, which describes the Tomonaga–Luttinger liquid (TLL), interacting with a static impurity at the origin of the half line. Applying the Fermi–Bose equivalence and finite conformal transformations only, we map the model onto the Schmid model. Some details of the bosonization procedure have been given. The critical line and the phase diagram of the model follow from the renormalization group analysis of the Schmid model. The obtained critical line of the model is a hyperbola in the parameter space of the two couplings of the TLL.

Dynamical effects in (2+1)-dimensional theories with four-fermion interaction

The critical behavior of some of the simplest (2+1) -dimensional field-theoretic models with four-fermion interaction at nonzero temperature, chemical potential, and external gauge fields is studied. It is shown that an external magnetic field catalyzes spontaneous symmetry breaking. The chromomagnetic gluon condensate in QCD 3 can also spontaneously break chiral symmetry. The thermodynamics of these effects is studied in detail. The conditions under which superconducting phase transitions and also dynamical generation of a Chern–Simons term are possible in three-dimensional models of the Gross–Neveu type are derived.

Construction of (1+1)-Dimensional Field Models with Exactly Solvable Fluctuation Equations about Classical Finite-Energy Configurations

A systematic construction of (1+1)-dimensional field theoretic models with exactly solvable excitation spectrum about its classical static finite-energy configuration is presented. The approach is based on the concept of shape-invariant potentials in supersymmetric quantum mechanics. Stable and unstable field models are taken into account. In the case of stable models two new field potentials are found, which give rise to exactly solvable fluctuation equations about their topologically non-trivial classical solutions. In the case of unstable models two new families of field potentials with fractional powers and one with a logarithmic term are found.

Berry phase and induced fractional fermion number on vaccum

We show that, in four dimensional field-theoretical model containing fermion field and background isovector scalar field, an induced magnetic monopole field emerges as a result of adiabatical evolution of the scalar field. For the corresponding Dirac Hamiltonian the degenerate eigenmodes of the vacuum are known to exist. The effective system is then shown to give fractional fermion number on vacuum. In the present approach the magnetic monopole field is not quite essentially given as a topologically non-trivial external field but induced as the result of adiabatic evolution of a scalar field.

Sphalerons and instantons in two-dimensional field theory

In this paper the decay amplitudes of sphalerons in a non-relativistic (1 + 1)-dimensional field theoretical model are discussed within the framework of instanton physics. The Morse theory describing the topology of the configuration space as given by the critical point structure of some functional is developed by constructing the Witten-Smale complex in terms of a related supersymmetric model. The link between both models is shown to be stochastic quantization. A careful analysis about how supersymmetry breaking is related with the stochastic quantization of a topological field theory is offered.

Superconductivity in the (2+1)-dimensional nonlinear sigma model.

A (2+1)-dimensional field-theoretical model is constructed that shows magnetic-induced superconductivity. The model consists of the O(3) nonlinear {sigma} model interacting via a Yukawa coupling with Dirac fermions.

Dynamical breakdown of supersymmetry and chiral symmetry in 1+1 dimensions

Dynamical breakdown of supersymmetry and chiral symmetry is studied through a 1+1 dimensional field theoretical model in the large-N limit in 1/N expansion. The study is based on the calculation of bilinear field condensates in an effective potential approach. It is shown that the condition for supersymmetry breaking is related to the values of the parameters in the model and chiral symmetry breaking exists in most cases.

Lattice study of solitons with half-integral fermionic charge in a (1 + 1)-dimensional field theoretical model

A (1+1)-dimensional field theoretical model of interacting Higgs field, fermions and abelian gauge bosons with spontaneous symmetry breaking is studied on the lattice using the local hamiltonian Monte Carlo method. Solitons with half-integral fermionic charge are found in this model. The electromagnetic properties of the solitons are studied by gauging the global charge and by introducing an electric background field. The solitons become confined except for the background field value θ= π 2 . We introduce an expectation value 〈 S〉 to measure the appearance of liberated fractionally charged solitons on the lattice.

XIII. Exact S-matrices and form factors in 1 + 1 dimensional field theoretic models with soliton behaviour

A review is given of the derivation of exact S-matrices in field theoretic models with soliton behaviour, that means models obeying infinitely many conservation laws which imply the factorization of the S-matrix. Form factors of various operators are calculated exactly by means of Watson's theorem. The exact value of the finite Sine-Gordon wave function renormalization constant is determined.

Exact form factors in (1 + 1)-dimensional field theoretic models with soliton behaviour

A system of equations is derived which must be satisfied by multiparticle matrix elements of any local operator in field theories with soliton behaviour. Form factors of various operators of interest are calculated exactly by means of the known exact S-matrices in the sine-Gordon, massive Thirring, non-linear σ −, and Gross-Neveu models. The finite sine-Gordon wave function renormalization constant is determined exactly.