Instantons and vacuum expectation values in the Schwinger model

Vacuum expectation values for the Schwinger model are computed within the path integral formalism for an instanton vacuum. The calculations are done in flat Euclidean space and use the wellknown anomaly result. It can be demonstrated that the instanton vacuum is absolutely necessary to obtain a consistent quantization. At last the results are compared to a similar treatment on the sphere and to the operator solution of the Schwinger model.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Projekt Nr. P8444-TEC     

Instantons and the infrared behavior of the fermion propagator in the Schwinger model

The fermion propagator of the Schwinger model is revisited from the point of view of its infrared behavior. The values of the anomalous dimensions are found in arbitrary covariant gauge and in all contributing instanton sectors. In the case of a gauge invariant, but path dependent propagator, the exponential dependence, instead of a power law one, is established for the special case when the path is a straight line. The leading behavior is almost identical in any sector, differing only by the slowly varying, algebraic prefactors. The other kind of gauge invariant function, which is the amplitude of the dressed Dirac fermions, may be reduced, by an appropriate choice of the dressing, to the gauge variant one, if the Landau gauge is imposed. PACS  11.10.Kk; 11.15.-q     

Instantons in spherical model thermodynamics

The instanton thermodynamics of a spherical model analogous to the soliton thermodynamics of one-dimensional sine-Gordon and ⁴-models is constructed. Decomposition of the system phase volume integral into a sum of contributions corresponding to the thermal fluctuations above the basic and instanton vacua is obtained and all the components of this sum are found. It appears that fluctuations above instanton vacua are Gaussian at all temperature. It is shown that the phase transition temperature in the spherical model can be found from the Kosterlitz-Thouless criterion: in the high-temperature phase the instanton configurations become thermodynamically favorable. The obtained results are exact and are naturally formulated in terms of singularity 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.     

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     

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...     

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.     

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.