Heinz J. Rothe

Classical and quantum dynamics of constrained Hamiltonian systems

Singular Lagrangians and Local Symmetries Hamiltonian Approach. The Dirac Formalism Symplectic Approach to Constrained Systems Local Symmetries within the Dirac Formalism The Dirac Conjecture BFT Embedding of Second Class Systems Hamilton-Jacobi for Constrained Systems Operator Quantization of Second Class Systems Functional Quantization of Second Class Systems Dynamical Gauges. BFV Functional Quantization Field-Antifield Quantization

Hamiltonian approach to Lagrangian gauge symmetries

Abstract We reconsider the problem of finding all local symmetries of a Lagrangian. Our approach is completely Hamiltonian without any reference to the associated action. We show that the restrictions on the gauge parameters entering in the definition of the generator of gauge transformations follow from the commutativity of a general gauge variation with the time derivative operation.

Master equation for lagrangian gauge symmetries

Using purely Hamiltonian methods we derive a simple differential equation for the generator of the most general local symmetry transformation of a Lagrangian. The restrictions on the gauge parameters found by earlier approaches are easily reproduced from this equation. We also discuss the connection with the purely Lagrangian approach. The general considerations are applied to the Yang-Mills theory.

Batalin-Fradkin-Tyutin embedding of a self-dual model and the Maxwell-Chern-Simons theory

Abstract We convert the self-dual model of Townsend, Pilch, and Nieuwenhuizen to a first-class system using the generalized canonical formalism of Batalin, Fradkin, and Tyutin and show that gauge-invariant fields in the embedded model can be identified with observables in the Maxwell-Chem-Simons theory as well as with the fundamental fields of the self-dual model. We construct the phase-space partition function of the embedded model and demonstrate how a basic set of gauge-variant fields can play the role of either the vector potentials in the Maxwell-Chern-Simons theory or the fundamental fields of the self-dual model by appropriate choices of gauge.

Equivalence of the Maxwell-Chern-Simons theory and a self-dual model.

We study the connection between the Green functions of the Maxwell-Chern-Simons theory and a self-dual model by starting from the phase-space path-integral representation of the Deser-Jackiw master Lagrangian. Their equivalence is established modulo time-ordering ambiguities.

LEPTONIC DECAYS OF BARYONS

Formulae are obtained for the differential decay rate, lepton spectrum, and partial lifetime for the leptonic decays of baryons, which cover effects down to the order of one percent. A weak, linearq2-dependence of the form factors is included, which should be a sufficiently good approximation in the physicalq2-range allowed in the decays. The one percent discrepancy arises as a consequence of the above-mentioned approximation to the form factors, whose value and slope atq2=0 are left open in the formulae;SU(3) symmetry, CVC, and PCAC yield an estimate for these parameters.

Field quantization on the surface X2 = constant

Abstract In analogy to non-relativistic quantum field theory where the Galilei invariant plane t = const. is used for a description of bound (and scattering) states we take the hyperboloid x2 = const. which is invariant under homogeneous Lorentz transformations. We give the appropriate complete set of basis functions for the expansion of any scalar and spin 1 2 field on the hyperboloid. The free Klein Gordon and Dirac fields are discussed in detail. In this formulation a multi-particle system can be described by a Lorentz covariant wave function.

Hamiltonian embedding of the self-dual model and equivalence with Maxwell-Chern-Simons theory

Following systematically the generalized Hamiltonian approach of Batalin and Fradkin, we demonstrate the equivalence of a self-dual model with the Maxwell-Chern-Simons theory by embedding the former second-class theory into a first-class theory. {copyright} {ital 1997} {ital The American Physical Society}

The Axial anomaly in lattice QED: A Universal point of view

Abstract We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absence of species doubling. They hold for Wilson fermions as well as for realizations of the Dirac operator that satisfy the Ginsparg–Wilson relation. The proof is based on the lattice power counting theorem.

Recursive construction of the generator for Lagrangian gauge symmetries

We obtain, for a subclass of structure functions characterizing a first-class Hamiltonian system, recursive relations from which the general form of the local symmetry transformations can be constructed in terms of the independent gauge parameters. We apply this to a non-trivial Hamiltonian system involving two primary constraints, as well as two secondary constraints of the Nambu-Goto type. We also illustrate for a pure Chern-Simons theory how this formalism can be extended to a system with first- and second-class constraints.