Lothar Schülke

UNIVERSALITY AND SCALING IN SHORT-TIME CRITICAL DYNAMICS

Abstract The short-time scaling behaviour of the critical dynamics for the two-dimensional Ising model and Potts model are investigated with both the heat-bath and the Metropolis algorithm. Special attention is drawn to universality. We observed that the microscopic time scale t mic after which the universal scaling behaviour appears is not always negligibly small. Taking carefully the effect of t mic into account, the critical exponents are extracted from the power law behaviour of the observables in the beginning of the time evolution. All the results are consistent and therefore universality and scaling are confirmed.

BETA DECAY THEORY USING EXACT ELECTRON RADIAL WAVE FUNCTIONS. IV. INDUCED EFFECTS

Abstract Beta decay formulae derived in previous papers are re-interpreted on the basis of a quite general V-A interaction which takes into account all effects induced by the strong interaction. As an example of application the induced pseudoscalar interaction is investigated in some detail.

Kℓ3 form factors and the algebra of charges

Starting from the algebra of vector and axial vector charges, we obtain information about the Kl3 form factors by approximating the commutation relations with the one particle intermediate states. We assume a once subtracted dispersion relation for the weak form factors appearing in the calculation. The subtraction constants can then be uniquely determined as a function of the weak decay constants ƒπ, ƒK and ƒK of the mesons contributing in the intermediate states. The momentum transfer dependence of the Kl3 form factors is characterized by the particle masses, the above mentioned decay constants and the two additional constants gπKκ and ƒK∗gπKK∗, where gπKκ∗ and gπKK∗ are strong coupling constants, and ƒK∗ is the weak decay constant of the K∗ meson. Assuming unsubtracted dispersion relations for the various form factors, we are able to make some numerical predictions.

Nuclear β-decay. II

A general expression for the beta-decay transition amplitude is evaluated, using the decomposition of the nuclear current matrix element into beta-decay form factors as obtained in the previous paper. For the electron radial wave functions the finite nuclear size is taken into account. Formulas for the spectrum shape factor and the polarisation are calculated.

On the segregation phenomenon in complex Langevin simulation

In the numerical simulation of certain field theoretical models, the complex Langevin simulation has been believed to fail due to the violation of ergodicity. We give a detailed analysis of this problem based on a toy model with one degree of freedom (S = −s cos θ). We find that the failure is not due to the defect of the complex Langevin simulation itself, but rather to the way one treats the singularity appearing in the drift force. An effective algorithm is proposed by which one can simulate the 1/s behaviour of the expectation value 〈cos θ〉 in the small s limit.

Bavkground field method in stochastic quantization two-loop renormalization of a dynamical Yang-Mills field in Zwanziger gauge☆

Abstract Two-loop renormalization of the dynamical Yang-Mills theory in the Zwanziger gauge has been performed by applying the background field method to stochastic quantization. It enables us to determine most of the renormalization group functions of the theory up to two-loop order. As expected, the gauge coupling β-function coincidence with that of the conventional Yang-Mills theory. We also prove that all gauge-invariant correlation functions are independent of the background gauge field.

Subtractions and off-shell continuation of weak form factors

The dependence of the weak form factors on the mass variables is studied in the one-particle approximation, taking the Kl3 form factors as an example. The off-shell continuation considered is the same as in soft-pion calculations. The off-shell dependence is obtained in terms of the subtraction constants of the matrix elements of the axial vector current Aπo and strong coupling constants. Under the assumption of unsubtracted dispersion relations the correction to the soft-pion result is estimated to be small.

Renormalization and renormalization group behaviour of the O(N) non-linear sigma-model in stochastic quantization☆

Abstract The renormalization and renormalization group behaviour of the two-dimensional O( N ) non-linear sigma-model has been discussed in the framework of stochastic quantization. For this purpose the path integral representation of the generating functional of the extended stochastic correlation function for constrained systems has been given. The renormalization is formulated by use of the stochastic effective action which can be defined from this generating functional. The renormalization group behavior of the correlation function with different fictitious time arguments has also been investigated. It reduces to the normal one if all external fictitious times are taken to be equal.

The proton-antiproton annihilation at rest as predicted by theSU6-covariantS-matrix formalism and byW-spin analysis

The proton-antiproton annihilation at rest into two mesons is calculated by two methods: (i) on the basis of theSU6 -covariantS-matrix formalism recently proposed byRothleitner andStech, and (ii) by assuming the additional invariance under the group (SU6)W proposed byLipkin andMeshkov. In the first case the calculations give only few relations between transition amplitudes, whereas the larger symmetry group (SU6)W actually determines all amplitudes up to a common factor. While agreement with experiment seems to be poor in some cases for the (SU6)W, so far there are no experimental data available to test the relations of case (i).

Predictions for the weak leptonic baryon form factors from the hybrid groupSU3⊗SU3⊗U1

AbstractRelations between the form factors of the weak leptonic baryon interaction are obtained from invariance under the groupSU3⊗SU3⊗U1. The weak interaction operatorVμ −Aμ is assumed to behave like the corresponding components of representations35 ofSU6 with different parities. One gets the result that the well-known predictions of the staticSU6 theory, viz., pureF-coupling for the vector- and 3D+2F-coupling for the axial-vector part, are only valid in the limit of vanishing momentum transfer. In the same limit the resultCA/CV=−n