Fixed point action for the massless lattice Schwinger model

We determine non-perturbatively the fixed-point action for fermions in the two-dimensional U(1) gauge (Schwinger) model. This is done by iterating a block spin transformation in the background of non-compact gauge field configurations sampled according to the (perfect) Gausian measure. The resulting action has 123 independent couplings, is bilinear in the Grassmann fields, gauge invariant by the compact gauge transporters considered, and localized within a 7 × 7 lattice centered around one of the fermions. We then simulate the model at various values of β and compare with results obtained with the Wilson fermion action. We find excellent improvement for the observables studied (propagators and masses).     

Operator solutions of the bosonized chiral Schwinger model

Starting from the modified Lagrangian of the bosonized chiral Schwinger model, operator solutions are obtained under three types of gauge fixing conditions. We show that the physical spectrum consists of a massive free boson and a massless excitation. We emphasize that the “longitudinal” component of the gauge field must be treated properly.     

Operator product expansions in conformally covariant quantum field theory

Operator products in quantum field theory on two-dimensional Minkowski space are expanded into a series of local operators by means of the tensor product decomposition theorem for representations of the conformal group. The Thirring model is used as an explicit example. Two types of expansions result. If the operator product acts on the vacuum state, we obtain strictly covariant expansions. In general however, each term in the expansion is only semicovariant.     

Operator product expansions on the vacuum in conformal quantum field theory in two spacetime dimensions

Let ₁(x) and ₂(y) be two local fields in a conformal quantum field theory (CQFT) in two dimensional spacetime. It is then shown that the vector-valued distribution ₁(x)₂(y)|0 is a boundary value of a vectorvalued holomorphic function which is defined on a large conformally invariant domain. By group theoretical arguments alone it is proved that ₁(x)₂(y)|0 can be expanded into conformal partial waves. These have all the properties of a global version of Wilson's operator product expansions when applied to the vacuum state |0. Finally, the corresponding calculations are carried out more explicitly in the Thirring model. Here, a complete set of local conformally covariant fields is found, which is closed under vacuum expansion of any two it its elements (a vacuum expansion is an operator product expansion applied to the vacuum).Work supported by Deutsche Forschungsgemeinschaft     

Operator product expansions and composite field operators in the general framework of quantum field theory

The short distance behavior of field operator products is analyzed. It is shown that under certain conditions operator product expansions can be derived which give complete information on the short distance behavior and lead to the construction of composite field operators.Suported in parts by funds from the National Science Foundation Grant No. GP-25609.     

Operator expansions for critical dynamics

We derive the operator expansion method for dynamical one-particle-irreducible renormalization-group generators and apply the technique by calculating the exponents z and η to order ε² for selected time-dependent Ginzburg-Landau models.     

On epsilon expansions of four-loop non-planar massless propagator diagrams

We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter ϵ=(4−d)/2 up to transcendentality weight twelve, using a recently developed method of one of the present coauthors (R.L.). We observe only multiple zeta values in our results.     

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.