arXiv subjects

H B Geyer

Publications and source records attributed to H B Geyer.

5 recordsLinked to original sources

arXiv2006

Operator equations and Moyal products -- metrics in quasi-hermitian quantum mechanics

The Moyal product is used to cast the equation for the metric of a non-hermitian Hamiltonian in the form of a differential equation. For Hamiltonians of the form $p^2+V(ix)$ with $V$ polynomial this is an exact equation. Solving this equation in perturbation theory recovers known results. Explicit criteria for the hermiticity and positive definiteness of the metric are formulated on the functional level.

quant-ph↗

arXiv1997

Factored coset models: A unifying approach to different bosonization schemes

We discuss various bosonization schemes from a path integral perspective. Our analysis shows that the existence of different bosonization schemes, such as abelian bosonization of non-abelian models and non-abelian bosonization of fermions with colour and flavour indices, can be understood as different ways of factoring out a dynamically trivial coset which contains the fermions. From this perspective follows the importance of the coset model in ensuring the correct superselection rules on the bosonic level.

hep-th↗

arXiv1997

Bosonization in d=2 from finite chiral determinants with a Gauss decomposition

We show how to bosonize two-dimensional non-abelian models using finite chiral determinants calculated from a Gauss decomposition. The calculation is quite straightforward and hardly more involved than for the abelian case. In particular, the counterterm $A\bar A$, which is normally motivated from gauge invariance and then added by hand, appears naturally in this approach.

hep-th↗

arXiv1996

Boson-fermion mapping and dynamical supersymmetry in fermion models

We show that a dynamical supersymmetry can appear in a purely fermionic system. This ``supersymmetry without bosons" is constructed by application of a recently introduced boson-fermion Dyson mapping from a fermion space to a space comprised of collective bosons and ideal fermions. In some algebraic fermion models of nuclear structure, particular Hamiltonians may lead to collective spectra of even and odd nuclei that can be unified using the dynamical supersymmetry concept with Pauli correlations exactly taken into account.

nucl-th↗

arXiv1994

Boson-fermion Dyson mapping and supersymmetry in fermion systems

We demonstrate that exact supersymmetry can emerge in a purely fermionic system. This "supersymmetry without bosons" is unveiled by constructing a novel boson-fermion Dyson mapping from a fermion space to a space comprised of collective bosons and ideal fermions. In a nuclear structure context the collective spectra of even and odd nuclei can then be unified in a supersymmetric description with Pauli correlations still exactly taken into account.

nucl-th↗