Exact solution of the multiflavor gross-neveu model

The Bethe-ansatz solution is presented for the multiflavor model arising in the Polyakov-Wiegmann fermionization of the SU(2) principal chiral field, i.e. the O(4) σ model. The vacuum and excitations with finite energy and momentum are constructed. The assumption that massive particles of the σ model are in the vector representation of O(4) is not corroborated. The renormalization-group β function agrees with a one-charge solution in perturbation theory.     

Schwinger model in the light-cone representation

Light-cone quantization of gauge field theory is considered. With a careful treatment of the relevant degrees of freedom and where they must be initialized, the results obtained in equal-time quantization are recovered, in particular the Mandelstam-Leibbrandt form of the gauge field propagator. Some aspects of the discretized light-cone quantization of gauge fields are discussed.     

Schwinger model in temporal gauge

Acta Physica Hungarica - Exact solution of the zero-mass Schwinger model is given in temporal gauge in the presence of arbitrary background charge density. The structure of the Hilbert space is...     

Physics of the Schwinger model

The Coulomb gas of massless fermions (Schwinger model) is solved in a one-dimensional space of finite lengthL using the boson representation of fermions. Special attention is paid to boundary effects and global degrees of freedom. It is shown that the mean current is not conserved, but oscillates. The theory is constructed in all charge sectors. The Wightman functions are calculated and the limitL is discussed.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

Light-cone gauge Schwinger model

Nakawaki's Coulomb gauge solution to the Schwinger model is transformed to light-cone gauge. Various options for maintaining the gauge invariance necessary to satisfy the equations of motion are discussed. Satisfactory light-cone gauge solutions are found and are used to study light-cone quantization, the calculation of the dynamical operators and properties of the vacua in the light-cone representation. The solutions found here can be used to justify previous light-cone Tamm-Dancoff calculations performed by others.     

Chiral Schwinger model in curved space-time

We extend the method of path integrals to obtain the solution of the chiral Schwinger model in curved space-time and compare it with the flat space-time solution.     

Gauge invariant green function in the Schwinger model

In two-dimensional quantum electrodynamics with massless fermions (Schwinger model), the gauge invariant one-particle fermion Green function is computed. It is shown that this Green function is independent of the choice of integration contour in the gauge exponential, and coincides with the free fermionic propagator.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 49–52, December, 1984.The authors are deeply grateful to V. B. Belyaev and N. B. Skachkov for their stimulating interest in this work and useful comments.     

Higher derivative operators in the noncommutative Schwinger model

A study of the noncommutative Schwinger model is presented. It is shown that the Schwinger mass is not modified by the noncommutativity of spacetime till the first nontrivial order in the noncommutative parameter. Instead, a higher derivative kinetic term is dynamically generated by the lowest-order vacuum polarization diagrams. We argue that in the framework of the Seiberg–Witten map the feature of non-unitarity for a field theory with spacetime noncommutativity is characterized by the presence of higher derivative kinetic terms. The θ-expanded version of a unitary theory will not generate the lowest-order higher derivative quadratic terms.     

Physical particles of the massive Schwinger model

The massive Schwinger model is considered in the infinite momentum frame. By assuming its physical particles consist of two fermion bound states, we compute a spectrum. For fermions with large bare masses, the method is reliable. For low-mass fermions, we find we must include states of higher fermion number to adequately describe excited states of the fundamental boson of the theory. We do this for the scalar state in the limit of small bare fermion mass. This representation of the theory provides a unified treatment of both the weak and strong coupling limits, remaining in the fermion representation throughout. We have checked our numerical results with exact calculations wherever possible, and find good agreement.     

Operator product expansions in the massless Schwinger model

The known operator solution of the massless Schwinger model is used to calculate exactly, in three operator product expansions, the coefficient functions of the first few operators of low dimension which contribute when vacuum matrix elements are to be taken. A comparison of the results provides a test of the procedure used by M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov [Nucl. Phys. B147 (1979), 385–447] in their study of QCD. It is found that the shift in vacua does not affect the calculation of coefficient functions. The vacuum insertion approximation yields somewhat misleading estimates of vacuum expectation values of some composite operators; however, the standard method used to estimate the errors of vacuum insertion indicates that the approximation is unreliable in this model.