Klaus Fredenhagen

Locality and the structure of particle states

Starting from the principle of locality of observables we derive localization properties of massive particle states which hold in all models of relativistic quantum theory, including gauge theories. It turns out that particles may always be regarded as well localized distributions of matter, although their mathematical description might require the introduction of non-local (unobservable) fields, which are assigned to infinite string-like regions. In spite of the non-locality of these fields one can show that such particles obey Bose- or Fermi (para) statistics, that to each particle there exists an antiparticle and that collision states of particles exist. A selfcontained exposition of the underlying physical ideas is given in the Introduction, and some perspectives for the structure of field-theoretic models arising from our analysis are discussed in the Conclusions.

CAUSAL PERTURBATION THEORY IN TERMS OF RETARDED PRODUCTS, AND A PROOF OF THE ACTION WARD IDENTITY

In the framework of perturbative algebraic quantum field theory a local construction of interacting fields in terms of retarded products is performed, based on earlier work of Steinmann. In our formalism the entries of the retarded products are local functionals of the off shell classical fields, and we prove that the interacting fields depend only on the action and not on terms in the Lagrangian which are total derivatives, thus providing a proof of Storas Action Ward Identity. The theory depends on free parameters which flow under the renormalization group. This flow can be derived in our local framework independently of the infrared behavior, as was first established by Hollands and Wald. We explicitly compute non-trivial examples for the renormalization of the interaction and the field.

Charged states in ℤ2 gauge theories

Charged translation covariant states with finite energy are constructed in the Higgs phase of the ℤ2 gauge theory coupled to a ℤ2 matter field.

Local algebras of observables and pointlike localized fields

We present a method to recover Wightman fields from a Haag-Kastler theory of local observables. This may provide a basis for the comparison of different theories and for an algebraic description of high energy behaviour.

The Master Ward Identity and Generalized Schwinger-Dyson Equation in Classical Field Theory

AbstractIn the framework of perturbative quantum field theory a new, universal renormalization condition (called Master Ward Identity) was recently proposed by one of us (M.D.) in a joint paper with F.-M. Boas. The main aim of the present paper is to get a better understanding of the Master Ward Identity by analyzing its meaning in classical field theory. It turns out that it is the most general identity for classical local fields which follows from the field equations. It is equivalent to a generalization of the Schwinger-Dyson Equation and is closely related to the Quantum Action Principle of Lowenstein and Lam. nAs a byproduct we give a self-contained treatment of Peierls’ manifestly covariant definition of the Poisson bracket.n

On the existence of antiparticles

Without assuming the existence of interpolating fields, it is shown that any particle in a massive quantum field theory possesses a unique antiparticle and carries parastatistics of finite order. This closes a gap in the hitherto existing theoretical argument leading to particle statistics and to the existence of antiparticles.

Dilations and interaction

As a consequence of the geometrical features of dilations massless particles do not interact in a local, dilationally invariant quantum theory. This result also holds in models in which dilations are only a asymmetry of the S matrix.

Long range correlations in random number generators and their influence on Monte Carlo simulations

Abstract Random number generators based on the congruence method have long range correlations which can severely influence Monte Carlo simulations of lattice theories, especially in critical regions. We investigate the nature of these correlations both theoretically and in test simulations. We propose practical ways to avoid that random number correlations affect the simulation results.

Charges in spacelike cones

Starting from a conserved current, operators are defined which measure the charge in certain unbounded stringlike regions which are possible localization regions of charged fields in gauge theories.

Line of second-order phase transitions in the four-dimensional Z2 gauge theory with matter fields

Strong evidence is presented that the phase transition between the free-charge and the screening region of the four-dimensional Z 2 lattice gauge theory with Z 2 matter fields is second order with mean field exponents. The quantity best suited for the analysis is an order parameter that tests the existence of charged states. Both its scaling and finite-size scaling properties are determined by performing a Monte Carlo simulation.