Local Current Operators for Arbitrary Spin Particles

Free current operators are constructed for massive particles with arbitrary spin $j$. Such current operators are related to representations of the U(N,N) type groups and are covariant under the (extended) Poincar\'{e} group and charge conjugation, where the charge conjugation operation is defined as an automorphism on U(N,N) elements. The currents are also required to satisfy current conservation, hermiticity, and locality. The condition that the currents be local is shown to be equivalent to certain integral constraints on form factors. These constraints are satisfied by writing the currents in terms of free local spin $j$ fields. It is shown that there are $(2j+1)$ different local currents for a spin $j$ particle, each with an arbitrary form factor, generalizing the Dirac and Pauli currents for spin 1/2 particles. Static properties of the various currents are also given.Comment: 25 page

Point Form Electrodynamics and the Gupta-Bleuler Formalism

The Gupta-Bleuler formalism for photons is derived from induced representation theory. The representation for the little group for massless particles, the two dimensional Euclidian group, is chosen to be the four dimensional nonunitary representation obtained by restricting elements of the Lorentz group to the Euclidian group. Though the little group representation is nonunitary, it is shown that the representation of the Poincar\'{e} group is unitary. As a consequence of the four dimensional representation, the polarization vector, which connects the four-vector potential with creation and annihilation operators, is given in terms of boosts, coset representatives of the Lorentz group with respect to the Euclidian group. Several polarization vectors (boost choices) are worked out, including a front form polariation vector. The different boost choices are shown to be related by the analogue of Melosh rotations, namely Euclidian group transformations.Comment: 15 page

Constructing Point Form Mass Operators from Interaction Lagrangians

Starting from an interaction Lagrangian formed out of local fields, an interacting four-momentum operator is constructed by integrating the interaction Lagrangian over the forward hyperboloid. Such a four-momentum operator has the property that the components commute among themselves; however, when the Fock space on which the four-momentum operator acts is truncated, the components no longer commute among themselves. By modifying matrix elements of the four-momentum operator on the truncated space, Bakamjian-Thomas mass operatorsare constructed which restore the Poincare relations. Examples for a simple Lagrangian are given.Comment: 15 page

Representations of U(2\infty) and the Value of the Fine Structure Constant

A relativistic quantum mechanics is formulated in which all of the interactions are in the four-momentum operator and Lorentz transformations are kinematic. Interactions are introduced through vertices, which are bilinear in fermion and antifermion creation and annihilation operators, and linear in boson creation and annihilation operators. The fermion-antifermion operators generate a unitary Lie algebra, whose representations are fixed by a first order Casimir operator (corresponding to baryon number or charge). Eigenvectors and eigenvalues of the four-momentum operator are analyzed and exact solutions in the strong coupling limit are sketched. A simple model shows how the fine structure constant might be determined for the QED vertex.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Synthesis and photophysics of light-converting lanthanide complexes

The work described in this thesis deals with the synthesis, characterization, and photophysical studies of luminescent lanthanide complexes that are based on m-terphenyl and calix[4]arene building blocks

Point form relativistic quantum mechanics and relativistic SU(6)

The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces

Covariant Hamiltonian Dynamics with Negative Energy States

A relativistic quantum mechanics is studied for bound hadronic systems in the framework of the Point Form Relativistic Hamiltonian Dynamics. Negative energy states are introduced taking into account the restrictions imposed by a correct definition of the Poincar\'e group generators. We obtain nonpathological, manifestly covariant wave equations that dynamically contain the contributions of the negative energy states. Auxiliary negative energy states are also introduced, specially for studying the interactions of the hadronic systems with external probes.Comment: 42 pages, submitted to EPJ

Point-form quantum field theory

We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form $x_\mu x^\mu = \tau^2$. This choice of quantization surface implies that all components of the 4-momentum operator are affected by interactions (if present), whereas rotation and boost generators remain interaction free -- a feature characteristic of Dirac's `` point-form\rq\rq of relativistic dynamics. Unlike previous attempts to quantize fields on space-time hyperboloids, we keep the usual plane-wave expansion of the field operators and consider evolution of the system generated by the 4-momentum operator. We verify that the Fock-space representations of the Poincar\'e generators for free scalar and spin-1/2 fields look the same as for equal-time quantization. Scattering is formulated for interacting fields in a covariant interaction picture and it is shown that the familiar perturbative expansion of the S-operator is recovered by our approach. An appendix analyzes special distributions, integrals over the forward hyperboloid, that are used repeatedly in the paper.Comment: 30 page