Conformal covariance and the probability interpretation of wave equations

The Dirac and the Schrödinger fields are singled out among all other fields by their conformal dimension $\text{l = ?}\text{3}\text{2}$, a necessary condition for the field to have also a probability interpretation as a wave function. The correct dimension of the Schrödinger field comes about by an intricate contraction of the conformal group to the Schrödinger group.     

New theory of positronium decay and relativistic wave function corrections

The positronium decay rate is calculated directly from the scattering amplitude by analytic continuation to the bound-state singularities. Relativistic wave function corrections are obtained which improve the agreement between theory and experiment.     

New “Coherent” States associated with non-compact groups

Generalized Coherent States are the eigenstates of the lowering and raising operators of non-compact groups. In particular the discrete series of representations ofSO (2, 1) are studied in detail: the resolution of the identity and the connection with the Hilbert spaces of entire functions of growth (1, 1). Also discussed are the application to the evaluation of matrix elements of finite group elements and the contraction to the usual coherent states.Supported in part by the Air Force Office of Scientific Research under Grant AF-AFOSR-30-67.On leave from Istituto di Fisica dell'Universitá, Parma and Istituo Nazionale di Fisica Nucleare, Sezione di Milano (Italy).     

De Rham currents,extended singularities of fields and magnetic monopoles

We apply De Rham's concept of “currents” to the treatment of extended singularities or discontinuities of physical fields in a coordinate independent way. In particular, we obtain a generalization of the theory of magnetic monopoles when applied to the electromagnetic field.     

Criterion for and the physical interpretation of minimal and nonminimal interactions

A classification of currents for finite- and infinite-component wave equations is proposed depending on their algebraic and convective nature. Algebraic terms with a consistent one-particle interpretation constitute the minimal interactions. The nonminimal interactions are interpreted as effective c-number currents describing many particle effects and/or composite structures. A number of applications are treated.     

Massive narrow resonance solutions of strongly coupled relativistic particles: a mechanism of mass generation

By explicit solutions of the relativistic wave equation corresponding to strong singular (nonrenormalizable) magnetic dipole interactions, we show how very massive almost stable reonances, as well as normalizable stable states, can be formed from light or massless fermionic constituents.     

Matrix elements of representations of non-compact groups in a continuous basis

Explicit formulas are obtained by a simple algebraic method for the representations of the finite group transformations ofO(2,1) in a continuous basis when a non-compact generator is diagonalized. Compact and non-compact cases are treated in a unified form and the nature of analytic continuation is determined. The transformation function between the discrete and the continuous bases is also given. These explicit formulas have not been obtained in the literature before.Supported in part by the Air Force Office of Scientific Research, Office of Aerospace Research, U.S. Air Force, under Grant No. AF-AFOSR- 30–67.     

Optimal learning for sequential sampling with non-parametric beliefs

We propose a sequential learning policy for ranking and selection problems, where we use a non-parametric procedure for estimating the value of a policy. Our estimation approach aggregates over a set of kernel functions in order to achieve a more consistent estimator. Each element in the kernel estimation set uses a different bandwidth to achieve better aggregation. The final estimate uses a weighting scheme with the inverse mean square errors of the kernel estimators as weights. This weighting scheme is shown to be optimal under independent kernel estimators. For choosing the measurement, we employ the knowledge gradient policy that relies on predictive distributions to calculate the optimal sampling point. Our method allows a setting where the beliefs are expected to be correlated but the correlation structure is unknown beforehand. Moreover, the proposed policy is shown to be asymptotically optimal.     

Theory of Nucleon-Nucleon Scattering

We present a new study of kinematical problems of relativistic nucleon-nucleon interactions, more complete than the previous studies. Two-component spinor formalism is used throughout. Several choices of spinor bases, their relations, crossing relations in all channels, helicity amplitudes, partial-wave amplitudes, the absence of kinematical singularities, and unitarity are discussed. The contributions of arbitrary intermediate states J in the unitarity are summed and the Regge forms for all five scalar amplitudes are obtained.