Bogoliubov transformations and exact isolated solutions for simple non-adiabatic Hamiltonians

We present a new method for finding isolated exact solutions of a class of non-adiabatic Hamiltonians of relevance to quantum optics and allied areas. Central to our approach is the use of Bogoliubov transformations of the bosonic fields in the models. We demonstrate the simplicity and efficiency of this method by applying it to the Rabi Hamiltonian.Comment: LaTeX, 16 pages, 1 figure. Minor additions and journal re

Relativistic Kinetic Equations for Electromagnetic, Scalar and Pseudoscalar Interactions

We derive the kinetic equations for both the covariant and equal-time Wigner functions of Dirac particles with electromagnetic, scalar and pseudoscalar interactions. We emphasize the constraint equations for the spinor components in the equal-time formulation.Comment: 12 pages, no figures, revte

On Hirschman and log-Sobolev inequalities in mu-deformed Segal-Bargmann analysis

We consider a deformation of Segal-Bargmann space and its transform. We study L^p properties of this transform and obtain entropy-entropy inequalities (Hirschman) and entropy-energy inequalities (log-Sobolev) that generalize the corresponding known results in the undeformed theory.Comment: 42 pages, 3 figure

Infinite spin particles

We show that Wigner's infinite spin particle classically is described by a reparametrization invariant higher order geometrical Lagrangian. The model exhibit unconventional features like tachyonic behaviour and momenta proportional to light-like accelerations. A simple higher order superversion for half-odd integer particles is also derived. Interaction with external vector fields and curved spacetimes are analyzed with negative results except for (anti)de Sitter spacetimes. We quantize the free theories covariantly and show that the resulting wave functions are fields containing arbitrary large spins. Closely related infinite spin particle models are also analyzed.Comment: 43 pages, Late

Analytic representations based on SU(1,1) coherent states and their applications

We consider two analytic representations of the SU(1,1) Lie group: the representation in the unit disk based on the SU(1,1) Perelomov coherent states and the Barut-Girardello representation based on the eigenstates of the SU(1,1) lowering generator. We show that these representations are related through a Laplace transform. A ``weak'' resolution of the identity in terms of the Perelomov SU(1,1) coherent states is presented which is valid even when the Bargmann index $k$ is smaller than one half. Various applications of these results in the context of the two-photon realization of SU(1,1) in quantum optics are also discussed.Comment: LaTeX, 15 pages, no figures, to appear in J. Phys. A. More information on http://www.technion.ac.il/~brif/science.htm

The Geometric Phase and Ray Space Isometries

We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or anti-unitary transformations on the Hilbert space. We suggest that the construction involved in Wigner's proof is best viewed as an use of the Pancharatnam connection to ``lift'' a ray space isometry to the Hilbert space.Comment: 17 pages, Latex file, no figures, To appear in Pramana J. Phy

Electromagnetic properties of non-Dirac particles with rest spin 1/2

We resolve a number of questions related to an analytic description of electromagnetic form factors of non-Dirac particles with the rest spin 1/2. We find the general structure of a matrix antisymmetric tensor operator. We obtain two recurrence relations for matrix elements of finite transformations of the proper Lorentz group and explicit formulas for a certain set of such elements. Within the theory of fields with double symmetry, we discuss writing the components of wave vectors of particles in the form of infinite continued fractions. We show that for $Q^{2} \leq 0.5$ (GeV/c)$^{2}$, where $Q^{2}$ is the transferred momentum squared, electromagnetic form factors that decrease as $Q^{2}$ increases and are close to those experimentally observed in the proton can be obtained without explicitly introducing an internal particle structure.Comment: 18 pages, 2 figure

Minisuperspace Examples of Quantization Using Canonical Variables of the Ashtekar Type: Structure and Solutions

The Ashtekar variables have been use to find a number of exact solutions in quantum gravity and quantum cosmology. We investigate the origin of these solutions in the context of a number of canonical transformations (both complex and real) of the basic Hamiltonian variables of general relativity. We are able to present several new solutions in the minisuperspace (quantum cosmology) sector. The meaning of these solutions is then discussed.Comment: 23 pages, latex, 3 figures (uuencoded, separate file

SU(2) and SU(1,1) algebra eigenstates: A unified analytic approach to coherent and intelligent states

We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states associated with a dynamical symmetry group. On the one hand, algebra eigenstates include different sets of Perelomov's generalized coherent states. On the other hand, intelligent states (which are squeezed states for a system of general symmetry) also form a subset of algebra eigenstates. We develop the general formalism and apply it to the SU(2) and SU(1,1) simple Lie groups. Complete solutions to the general eigenvalue problem are found in the both cases, by a method that employs analytic representations of the algebra eigenstates. This analytic method also enables us to obtain exact closed expressions for quantum statistical properties of an arbitrary algebra eigenstate. Important special cases such as standard coherent states and intelligent states are examined and relations between them are studied by using their analytic representations.Comment: LaTeX, 24 pages, 1 figure (compressed PostScript, available at http://www.technion.ac.il/~brif/abstracts/AES.html ). More information on http://www.technion.ac.il/~brif/science.htm