Klaus D. 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.

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.

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.

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}

On the exact gauge invariant calculation of the fermion determinant in massless two-dimensional QCD

Abstract Using heat-kernel methods, we show that factorization of the Dirac operator in two-dimensional QCD allows one to calculate exactly the corresponding functional determinant in an arbitrary gauge for any unitary Lie group. The possibility of achieving this is presented in the form of a theorem on functional determinants which covers a wide class of factorizable operators. In particular we recover in the light-cone gauge a result recently obtained by Polyakov and Wiegmann.

Study of a two-dimensional model with axial-current-pseudoscalar derivative interaction

Abstract A detailed study is made of a massive pseudoscalar field interacting via derivative coupling with massless fermions in two-dimensional space-time. The model provides an example of a soluble renormalizable theory with an anomalous axial-vector current and a zero-mass particle interpretation for the fermion. Except for a finite mass and wavefunction renormalization, the boson remains free in the presence of the interaction. The canonical fermion field exhibits an anomalous dimension that is found to be in agreement with the asymptotic Callan-Symanzik equation. The connection between the Wilson expansion for defining operator products in this model and the Dyson equations of renormalized perturbation theory is discussed, and agreement with second-order perturbation theory is verified by explicit calculation.

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.

On the Hamilton-Jacobi equation for second-class constrained systems

Abstract We discuss a general procedure for arriving at the Hamilton–Jacobi equation of second-class constrained systems, and illustrate it in terms of a number of examples by explicitely obtaining the respective Hamilton principal function, and verifying that it leads to the correct solution to the Euler–Lagrange equations.