Bo-Sture Skagerstam

Coherent states : applications in physics and mathematical physics

This volume is a review on coherent states and some of their applications. The usefulness of the concept of coherent states is illustrated by considering specific examples from the fields of physics and mathematical physics. Particular emphasis is given to a general historical introduction, general continuous representations, generalized coherent states, classical and quantum correspondence, path integrals and canonical formalism. Applications are considered in quantum mechanics, optics, quantum chemistry, atomic physics, statistical physics, nuclear physics, particle physics and cosmology. A selection of original papers is reprinted.

On superdense superstring gases: A heretic string model approach

Abstract A simple model is proposed to describe a gas of free strings at very high energy density, particularly in connection with a recently discovered phase dominated by macroscopic strings. This phase appears at high energy density if open strings are forbidden. For oriented strings the probability density for strings in the energy interval (E, E + dE) is dE / E in this phase. If open strings are allowed no such phase appears. The model is compared with superstring calculations, and relevant quantities are shown to agree. The model gives a simple and intuitively appealing picture of dense, free string gases. The effective string tension is also discussed and shown to vanish at the critical temperature.

QED effective action at finite temperature and density

The QED effective action at finite temperature and density is calculated to all orders in an external homogeneous and time-independent magnetic field, in the weak coupling limit. The free energy, obtained explicitly, exhibits the expected de Haas--van Alphen oscillations. An effective coupling at finite temperature and density is derived in a closed form and is compared with renormalization group results.

Morse potential derived from first principles

We show that a direct connection can be drawn, based on fundamental quantum principles, between the Morse potential, extensively used as an empirical description for the atomic interaction in diatomic molecules, and the harmonic potential. This is conceptually achieved here through a non-additive translation operator, whose action leads to a perfect equivalence between the quantum harmonic oscillator in deformed space and the quantum Morse oscillator in regular space. In this way, our theoretical approach provides a distinctive first-principle rationale for anharmonicity, therefore revealing a possible quantum origin for several related properties as, for example, the dissociation energy of diatomic molecules and the deformation of cubic metals.

Real-time thermal propagators and the QED effective action for an external magnetic field

Abstract The thermal averaged real-time propagator of a Dirac fermion in a static uniform magnetic field B is derived. At nonzero chemical potential and temperature we find explicitly the effective action for the magnetic field, which is shown to be closely related to the Helmholtz free energy of a relativistic fermion gas, and it exhibits the expected de Haas-van Alphen oscillations. An effective QED coupling constant at finite temperature and density is derived, and compared with renormalization group results. We discuss some astrophysical implications of our results.

Electromagnetic fields in a thermal background

Abstract The one-loop effective action for a slowly varying electromagnetic field is computed at finite temperature and density using a real-time formalism. We discuss the gauge invariance of the result. Corrections to the Debye mass from an electric field are computed at high temperature and high density. The effective coupling constant, defined from a purely electric weak-field expansion, behaves at high temperature very differently from the case of a magnetic field, and does not satisfy the renormalization group equation. The issue of pair production in the real-time formalism is discussed and also its relevance for heavy-ion collisions.

On finite lattice corrections to gauge field thermodynamics

Abstract We consider the ideal gas limit of lattice Yang-Mills with fermions. Recently, such a system has been considered in great detail in the literature. We discuss possible finite lattice corrections to the energy density of the quarks and gluons due to the constraint of the quark-gluon gas being in colour singlet state. In the case of pure Yang-Mills theory at finite temperature, we find that Monte Carlo data agree very well with the asymptotically free gluon gas being a colour singlet. In the presence of quarks, in the quenched approximation, we find that Monte Carlo data seem to agree with a distribution where the quarks themselves form a colour singlet.

Condensation and magnetization of the relativistic Bose gas

Abstract We show that the relativistic charged scalar boson gas exhibits a genuine Meissner-Ochsenfeld effect of the Schafroth form at fixed supercritical density. As in the well-known non-relativistic case, this total expulsion of a magnetic field is caused by the condensation of the Bose gas at vanishing magnetic field. In the course of these considerations, we present alternative proofs of the absence of Bose-Einstein condensation of a relativistic scalar boson gas, in any finite local magnetic field in less than five dimensions. The results are discussed in the context of kaon condensation in neutron stars.We present a simple proof of the absence of Bose--Einstein condensation of a relativistic boson gas, in any finite local magnetic field in less than five dimensions. We show that the relativistic charged boson gas exhibit a genuine Meissner--Ochsenfeld effect of the Schafroth form at fixed supercritical density. As in the well--known non--relativistic case, this total expulsion of a magnetic field is caused by the condensation of the Bose gas at vanishing magnetic field. The result is discussed in the context of kaon condensation in neutron stars.

Generalized phase-space representation of operators

Introducing asymmetry into the Weyl representation of operators leads to a variety of phase-space representations and new symbols. Specific generalizations of the Husimi and the Glauber–Sudarshan symbols are explicitly derived.

Thermal versus vacuum magnetization in QED

The magnetized relativistic Fermi (spin-1/2) and Bose (spin-0) gases are studied at finite temperature and density. At high enough magnetic fields the renormalized, paramagnetic vacuum ({ital T}={mu}=0) contribution starts to dominate the magnetization in both cases. This happens when the thermal magnetization saturates in the Fermi case, and when the thermal magnetization changes from a diamagnetic to a paramagnetic behavior in the Bose case. For fermions at high temperatures, the nonlinear vacuum part of the effective action is completely canceled by terms in the thermal effective action, so that the effective action becomes quadratic in the field. In the Bose case such a cancellation does not occur. Furthermore, we find for the Bose gas that the effective coupling constant for a weak nonzero external magnetic field is a decreasing function of the temperature.