Perturbative and nonperturbative studies in light-front field theory and operator solutions of some two-dimensional models

Ľubomı́r Martinovic̆ (BLTP and Institute of Physics, Slovak Academy of Sciences, Bratislava)

The present doctoral thesis is devoted to a few perturbative and non-perturbative results obtained in the framework of quantum field theory (QFT), formulated in terms of light-front (LF) variables (”light front field theory”). This (mostly hamiltonian) form of QFT is not as widely used as the conventional one (called ”space-like” (SL) here), but it offers us a framework with considerable advantages, related first of all to its vacuum ”triviality”: vacuum state of an interacting theory is equal to the free-theory vacuum.

Our perturbative results clarify relationship between the ”infinite momentum” and genuine LF approaches in the continuum and finite-volume theory, and deal with the existence of vacuum bubbles in the LF perturbation theory. The non-perturbative analyses include a semiclassical description of spontaneous symmetry breaking in the LF theory using a unitary operator that shifts the scalar field by a constant, mechanisms that give structure to the LF Fock vacuum (which naively appears to be the true physical LF vacuum) like the gauge-field zero mode and fermionic zero modes. Properties of quantum kinks are studied by means of a numerical diagonalization of an interacting scalar-field Hamiltonian in two dimen- sions. In the second part of the thesis several aspects of solvable two-dimensional models are addressed in both the LF and conventional field theory. In the former case, the notorious problem of massless LF field in two dimensions is solved and LF operator solutions of the Thirring and Thirring-Wess models are given for the first time. Relationship of the quantized massless LF fields to conformal field theory is established. In the latter case, the correct choice of the field variables and of the Hamiltonian is pointed out. Physical vacuum state of the Thirring model is derived along with a generalized operator solution of the model. The axial anomaly is studied non-perturbatively in the Thirring-Wess and Schwinger model based on analogous operator solutions. A few representative results in more details include:

• Demonstration of the efficiency of the LF perturbation theory and its relationship to the ”infinite momentum” and ”near-light cone” schemes in both the continuum and discretized (finite-volume) formulations at the one-loop level in self-interacting scalar models. The LF amplitudes cannot be obtained as limits of SL amplitudes calculated ”close” to the light front. The continuum limit of the LF scattering amplitudes computed in the finite volume reproduces the covariant results.
• Gauge-field zero mode is shown to be responsible for the vacuum degeneracy in the LF massive Schwinger model. The unitary operator that implements the residual ”large” gauge symmetry of the LF Hamiltonian also leads to the fermionic structure of the family of vacuum states that make up the gauge invariant θ-vacuum.
• A generalization of the Klaiber’s operator solution (i.e. explicit solution of the field equations) of the SL Thirring model is found and the physical ground state, neglected in the previous studies, of the bosonized Hamiltonian is found by means of a Bogoliubov transformation.
• Two-dimensional massless LF fields (scalar and fermion) are correctly quantized as the massless limits of the corresponding massive fields. The LF version of bosonization is formulated and the LF operator solutions of the Thirring and Thirring-Wess models is derived based on the above quantization scheme. Going over to the imaginary time in the LF field operators, the correlation functions between components of the energy-momentum tensor as well as the Virasoro algebra of the conformal field theory are obtained in a natural way.

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(Based on the research topics of the doctoral (Doctor of Science) thesis)