The choice of test functions in gauge quantum field theories

We discuss the problem of the choice of test functions in gauge quantum field theories. Analysis of explicitly soluble models suggests that the test function spaces which are suitable for local and covariant formulation of gauge theories are the Gelfand and Shilov spaces , +>1. We also discuss a possible generalization of the spectral condition.     

The Bohm-Aharonov effect: A seven-dimensional structural group

We realize a nonfaithful representation of a seven-dimensional Lie algebra, the extension of which to its universal enveloping algebra contains most of the observables of the scattering Aharonov-Bohm effect, as essentially self-adjoint operators: the scattering Hamiltonian, the total and kinetic angular momenta, the positions and the kinetic momenta. By restriction, we obtain the model introduced in Lett. Math. Phys. 1 (1976), 155–163.     

Scattering theory for a model of an atom in a quantized field

We compute the scattering operator for a simplified model of an atom interacting a with a quantized field. The field is restricted to the vacuum and one-particle sectors, and the atom has only two states. We also solve the inverse scattering problem for the same model. The methods used rely on the particular form of the interaction, which is chosen to mimic the interaction between radiation and matter.This work was partially supported by NSF Grant DMS-8922941.     

A stochastic posterior Schrödinger equation for counting nondemolition measurement

A stochastic model of the continuous counting nondemolition measurement of photons emitted by an excited atom in a quantum electromagnetic field is given. It is proved that the posterior dynamics of such an atom is described by a new nonlinear stochastic wave equation showing the relaxation of the atom to its ground state due to the photon emission.     

Towards a generalized distribution formalism for gauge quantum fields

We prove that the distributions defined on the Gelfand-Shilov spacesS with < 1 and, hence, more singular than hyperfunctions, retain the angular localizability property. Specifically, they have uniquely determined support cones. This result enables one to develop a distribution-theoretic technique suitable for the consistent treatment of quantum fields with arbitrarily singular ultraviolet and infrared behavior. The proof covering the most general and difficult case = 0 is based on the use of the theory of plurisubharmonic functions and Hörmander'sL ²-estimates.This work was supported in part by a Soros Humanitarian Foundation Grant awarded by the American Physical Society.     

Quasi-quantum groups as internal symmetries of topological quantum field theories

We show that every topological quantum field theory (understood as a functor) has an associated quasi-quantum group of internal symmetries.     

Avoided level crossings and pair production in strong Coulomb fields

Generalising previous work on static strong Coulomb fields to the time-dependent case, we propose an alternative e ⁺ e ^- -pair production mechanism relying on avoided crossing transitions between positive and negative energy states. The resulting essential independence on the details of the collision process nicely matches experimental findings.     

Local quantum field theories involving the U(1) current algebra on the circle

The OPE algebra Q=Q(g ² ) generated by a pair of oppositely charged currents (z,±g)(|z|=1) of spin is specified by the leading terms in the small distance expansions of (z ₁,g)(z ₂, -g) and (z ₁,g)(z ₂,g). The current (z,g) splits into a product of a U(1)-Thirring field and a Zamolodchikov-Fattev parafermionic current. The quasilocal(i.e.single-or double-valued) representations of Q are classified. The level k states involve 2(k+1) (ks–k+1) lowest weights (dimensions). The results can be viewed as an extension of the (known) representation theory of the SU(2) current algebra in the bosonic case corresponding to even values of g ² and of the N=2 extended superconformal algebra in the fermionic case corresponding to odd g ².     

Stochastic quantisation of a gauge field in the spatial axial gauge

The stochastic quantisation method of Nelson can be applied to quantise an Abelian gauge field in the spatial axial gauge.     

Commutators of Schrödinger Hamiltonians and applications in scattering theory

We give results on the behaviour at infinity of commutators of the form [(H), f(Q)], where H is a Schrödinger operator and Q denotes the position operator in [(H),f(Q)]. These results are applied to obtain propagation properties and asymptotic completeness below the three-body threshold for N-body systems.     

C *-algebraic quantization and the origin of topological quantum effects

Concepts from the theory of abstract operator algebras are used to solve the problem of quantizing a particle moving on an arbitrary locally compact homogeneous space. Inequivalent quantizations are identified with inequivalent irreducible representations of the corresponding C ^*-algebra. Topological terms in the action (or Hamiltonian) are found to be representation-dependent, and are automatically induced by the quantization procedure. Known charge quantization conditions turn out to be identically satisfied. Several examples are considered, among them the Dirac monopole and the Aharonov-Bohm effect.     

On the dynamics and the temperature states of the spin-boson model

Recently, the finite temperature states of the spin-boson model were studied. Here with different techniques in the case of level-splitting zero, the explicit expressions for both the dynamics and the equilibrium states are derived, namely Trotter's product formula and analyticity methods from perturbation theory are used.     

When does Lorentz invariance imply wedge duality?

This Letter deals with the theory of local observables in the vacuum sector. We will give necessary and sufficient conditions which imply that the wedge duality is a consequence of the Lorentz covariance of this theory.     

Existence of bound states in quantum waveguides under weak conditions

The existence of bound states in a plane quantum waveguide is proved under weak conditions: Within a bounded set a more general shape than a curved parallel strip is admitted and the curvature of the reference curve need not be differentiable. Furthermore, no upper bound for the width of the strip is required.     

The Green function for the Duffin–Kemmer–Petiau equation

We present a calculation of the Green function for the Duffin–Kemmer–Petiau equation in the case of scalar and vectorial particles interacting with a square barrier potential, and relate it to that of the Klein–Gordon equation. A formal Hamiltonian of the Duffin–Kemmer–Petiau theory is first developed using the Feshbach–Villars analogy and the Sakata and Taketani decomposition. The coefficients of reflection and transmission are deduced.     

Unitarizable scalar multipoles

We show that the scalar multipole ( +m ²) ⁿ = 0 forn odd and all massesm0 allows a Gupta-Bleuler-type quantization with a unitary space of physical states.Feodor-Lynen fellow of the Humboldt foundation. On leave from Institut für Theoretische Physik, TU Clausthal, Leibnizstr. 10, D3392 Clausthal-Zellerfeld, W. Germany.     

Field quantization in non-archimedean field theory

A formulation of field quantization of bosonic and fermionic fields defined on the disconnected field of p-acid numbers Q _p is given. We introduce a canonical quantization procedure and exhibit the properties of the nonlocal operators present in the action. Its relevance to string theory on Q _p is also discussed.