Two-dimensional Gauge Model Research Articles

Quantum field theory as effective BV theory from Chern–Simons

The general procedure for obtaining explicit expressions for all cohomologies of Berkovits' operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern–Simons-like theory (Witten's OSFT-like theory) reproduces BV version of two-dimensional gauge model at the level of effective action. This model contains gauge field, scalars, fermions and some other fields. We prove that this model is an example of “singular” point from the perspective of the suggested method for cohomology evaluation. For arbitrary “regular” point the same technique results in AKSZ (Alexandrov, Kontsevich, Schwarz, Zaboronsky) version of Chern–Simons theory (BF theory) in accord with [N. Berkovits, Covariant quantization of the superparticle using pure spinors, JHEP 0109 (2001) 016, hep-th/0105050; N. Berkovits, ICTP lectures on covariant quantization of the superstring, hep-th/0209059; M. Movshev, A. Schwarz, On maximally supersymmetric Yang–Mills theories, Nucl. Phys. B 681 (2004) 324, hep-th/0311132; M. Movshev, A. Schwarz, Algebraic structure of Yang–Mills theory, hep-th/0404183].

Restrictions over two-dimensional gauge models with Thirring-like interaction

Some years ago, it was shown how fermion self-interacting terms of the Thirring-type impact the usual structure of massless two-dimensional gauge theories [1]. In that work only the cases of pure vector and pure chiral gauge couplings have been considered and the corresponding Thirring term was also pure vector and pure chiral respectively, such that the vector (or chiral) Schwinger model should not lose its chirality structure due to the addition of the quartic interaction term. Here we extend this analysis to a generalized vector and axial coupling both for the gauge interaction and the quartic fermionic interactions. The idea is to perform quantization without losing the original structure of the gauge coupling. In order to do that we make use of an arbitrariness in the definition of the Thirring-like interaction.

NONINTEGRABLE PHASE DYNAMICS IN TWO-DIMENSIONAL GAUGE MODELS

In two-dimensional gauge models the nonintegrable phases of the line Wilson integrals are the only physical gauge field degrees of freedom, providing the gauge field diminishes rather rapidly at spatial infinities. We construct a “physical” quantum Hamiltonian in terms of the physical degrees of freedom for the Schwinger model and the chiral Schwinger model. We show that in the latter case the physical quantum picture can be formulated in two equivalent ways: either in terms of the fermionic matter degrees of freedom moving in a linearly rising background electric field, or in terms of matter fields with exotic statistics.

MINIMAL QUANTIZATION OF ANOMALOUS TWO-DIMENSIONAL GAUGE MODELS

Two-dimensional gauge models with chiral anomalies — "left-handed" QED and the chiral Schwinger model are consistently quantized in the frames of the minimal quantization method. The choice of the cone time as a physical time for the system of quantization is motivated. The well-known mass spectrum is found but with a fixed value of the regularization parameter a = 2. Such a unique solution is obtained due to the strong requirement of self-consistency of the minimal quantization method that is reflected in the physically motivated choice of the time axis.

Two-Dimensional Gauge Model with Vector U(1) and Axial-Vector U(1) Symmetries

Two-Dimensional Gauge Model with Vector U(1) and Axial-Vector U(1) Symmetries

Two-dimensional gauge model with vector U(1) and axial-vector U(1) symmetries

We have succeeded in constructing a two-dimensional gauge model with both vector U(1) and axial-vector U(1) symmetries. This model is exactly solvable. The Schwinger term vanishes in this model as a consequence of the above symmetries, and negative-norm states appear. However, the norms of physical states are always positive semidefinite due to the gauge symmetries.

Nonconservation of the fermion number in the decay of a heavy fermion in a two-dimensional gauge model

Nonconservation of the fermion number in the decay of a heavy fermion in a two-dimensional gauge model

Nonconservation of the fermion number and the limiting density of fermionic matter (two-dimensional gauge model)

Thus, at the present time there are two possible ways for instability to develop in gauge theories at high fermion density. In the four-dimensional Abelian model considered in [1] there is ultimately formed an anomalous state characterized by zero density of the real fermions, zero scalar condensate, and large gauge field condensate. In the two-dimensional model considered in the present paper, the effects of the complicated vacuum structure have the consequence that the system undergoes a transition to a normal state with low fermion density above a topologically nontrivial vacuum, this transition being accompanied by nonconservation of the fermion number. It is of undoubted interest to clarify which of these possibilities is realized in realistic non-Abelian four-dimensional theories (for example, in the standard model of electroweak interactions), i. e., to consider the existence of stable anomalous states in such theories. This question will be considered in later papers.

On the renormalization of the theories with $$\gamma _{5^ - } $$ anomalies(*).

We investigate the\(\gamma _{5^ - } \)anomalous two-dimensional gauge model (the generalized Schwinger model). We show that there are at least three ways to restore the gauge invariance.

Classical relativistic string as an exactly solvable sector of the SO(1, 1) × SO(2) gauge model

It is shown that the classical relativistic string in four-dimensional space-time is described by a closed exactly solvable sector of the SO(1, 1) × SO(2) two-dimensional gauge model.

Perturbation theory for two-dimensional gauge models

Euclidean symmetric integration, previously proposed for the SU(N) Yang-Mills theory in the limit of large N, is used to study the propagators in the Schwinger model and the massive vector-meson model in two dimensions. The result of summing the perturbation series agrees with the exact solution in each case. Therefore, perturbation theory is here capable of dealing with non-analytic behaviour in the coupling constant.

Quark fragmentation function in inclusive hadron scattering: Universality

We extract from 16-GeV/c and 32-GeV/c data on ${K}^{+}p\ensuremath{\rightarrow}{K}^{0}X$ and ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\overline{K}}^{0}X$ the strange-quark fragmentation function ${D}_{s}^{\overline{\mathrm{k}}0}(x)$. We show that it has the right properties expected for such a function. This is in agreement with predictions on the universality of quark fragmentation functions obtained in two-dimensional gauge models, and also with what is suggested in some dual models.