This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

Continuing the program developed in a previous paper, a "superconductive" solution describing the proton-neutron doublet is obtained from a nonlinear spinor field Lagrangian. We find the pions of finite mass as nucleon-antinucleon bound states by introducing a small bare mass into the Lagrangian which otherwise possesses a certain type of the ${\ensuremath{\gamma}}_{5}$ invariance. In addition, heavier mesons and two-nucleon bound states are obtained in the same approximation. On the basis of numerical mass relations, it is suggested that the bare nucleon field is similar to the electron-neutrino field, and further speculations are made concerning the complete description of the baryons and leptons.

https://link.aps.org/pdf/10.1103/PhysRev.124.246

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II

Continuing the program developed in a previous paper, a "superconductive" solution describing the protonneutron doublet is obtained from a nonlinear spinor field Lagrangian. The pions of finite mass are found as nucleonantinucleon bound states by introducing a small bare mass into the Lagrangian which otherwise possesses a certain type of the gamma /sub 5/ invariance. In addition, heavier mesons and two-nucleon bound states are obtained in the same approximation. On the basis of numerical mass relations, it is suggested that the bare nucleon field is similar to the electron-neutrino field, and further speculations are made concerning the complete description of the baryons and leptons. (auth)

Dynamical model of elementary particles based on an analogy with superconductivity. part ii

http://cds.cern.ch/record/503806/files/0106045.pdf

New developments in the Casimir effect

This article reviews quantum cluster theories, a set of approximations for infinite lattice models which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a mean-field approximation. These methods become exact when the cluster size diverges, and most recover the corresponding mean-field approximation when the cluster size becomes 1. Although quantum cluster theories were originally developed to treat disordered systems, they have more recently been applied to the study of ordered and disordered correlated systems, which will be the focus of this review. After a brief historical review, the authors provide detailed derivations of three cluster formalisms: the cluster perturbation theory, the dynamical cluster approximation, and the cellular dynamical mean-field theory. They compare their advantages and review their applications to common models of correlated electron systems.

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Quantum cluster theories

Ludwig Boltzmann: Recent Applications of Boltzmann's Theory (D. Rainer). Cycles of the Transition Processes as Basic Idea of Ludwig Boltzmann (V.I. Belinicher). Quantum Fluids: Recent Progress in the Theory of Highly Correlated Quantum Fluids (C.E. Campbell). Systematics and Numerics in Manybody Systems (M. Suzuki). Quantum Chemistry: Research of Appropriate Treatments of the Various Aspects of the Electron Correlation in Molecules and Their Interplay (J.P. Malrieu). A Coupled Cluster Approach to the Electron Correlation Problem Using a Correlated Reference State (D. Mukherjee). Nuclear Physics: Realistic Microscopic Calculations of Nuclear Structure (B.R. Barrett et al.). Microscopic Theories of Atomic and Nuclear Optical Potentials (C. Mahaux). Lattice Hamiltonians: Microscopic Theories of Quantum Lattice Systems (R.F. Bishop). A Nonperturbative Microscopic Theory of Hamiltonian Lattice Gauge Systems (R.F. Bishop et al.). Complex Systems: Complexity, Correlations, and Fluctuations in Manyparticle Systems (P.A. Carruthers). Solids: High Temperature Superconductors: A Review (E. Dagotto). Feenberg Medal Presentation: Pathways to the Quantum Realm (J.W. Clark). 28 additional articles. Index.

Recent Progress in MANY-BODY THEORIES

The equation ${\gamma_{\nu}}\frac{\partial}{{\partial{x_{\nu}}}}\psi\pm{l^2}{\gamma_{\mu}}{\gamma_5}\psi\left({\bar{\psi}{\gamma_{\mu}}{\gamma_5}\psi}\right)=0 $ is analysed with respect to the following consequences. In I the group theoretical structure of the equation is studied. The equation is invariant under a number of continous transformations: the inhomogeneous Lorentzgroup, the transformations of Pauli, Gursey and Touschek, and the scale transformation [x → η x orψ → η 3/2 ψ (x η, l η)]. The Pauli-Gursey group is used for the interpretation of the isospin; the γ 3-transformation of Touschek establishes a quantum number I N, and the scale transformation leads to a quantum number l N, which both are connected with the baryonic and the leptonic number. The strangeness s = l N - l Q is suggested to be connected with the discrete groups of the equation and could then be defined and conserved only modulo 4. Of the discrete groups only the well known transformations P, C and T and the reversal of l(l → - l) are briefly discussed. In II the vacuum expectation values of products of two field operators are studied. These values are considered to be only in a first approximation invariant under the Isospin-group. The deviations from the Pauli-Gursey symmetry in higher approximations are supposed to be due to the replacement of the state “vacuum” by an idealised state “world”, which possesses an infinite isospin; the strange particles are consequently interpreted as states which “borrow” an isospin 1/2 or 1 from the ground state “world”. The concept of “One particle-wavefunctions” is discussed in III. The fermions of finite mass belong to wavefunctions obeying a Klein-Gordon-spinor equation instead of a Dirac equation. The connection with the conventional formalism of the Dirac equation is treated in detail. The process of ^-conjugation springing from these discussions is used for a variation of the methods of approximation needed later on for the determination of mass values and the pion-nucleon coupling constant.

/pdf/zur-theorie-der-elementarteilchen-40vm6b8qln.pdf

Zur Theorie der Elementarteilchen

Recent Aspects of Quantum Fields

According to quantum electrodynamics the vacuum shows polarization properties because of the presence of virtual electron-positron pairs. These properties are investigated in the presence of an intense plane wave field, such as is produced by a laser. The laser wave is considered as an external prescribed field and its interaction with the electron-positron field is treated without reference to perturbation theory. The vacuum polarization tensor is computed to second order in the fine structure constant in the form of a double integral. For a Dyson equation for the photon propagator is solved by an eigenfunction expansion. For a plane laser wave of infinite extent and circular polarization the results are relatively simple and explicit. Analytical properties of the photon propagator are discussed. The effects of vacuum polarization on an additional weak wave field (a non-laser photon) can be described approximately by two complex indices of refraction.

https://iopscience.iop.org/article/10.1088/0305-4470/8/10/017/pdf

Vacuum polarization in laser fields

Die vorliegende Arbeit gibt die mathematische Ausarbeitung eines Programms, das mit zwei fruheren Arbeiten uber ein Modell einer Theorie der Elementarteilchen aufgestellt worden war. Im ersten Teil der Arbeit wird die Verbindung zu den ublichen Methoden der Integralgleichungen hergestellt, im zweiten die Krafte zwischen den Spinorteilchen berechnet und die Massen der Bose-Teilchen bestimmt. Im einzelnen umfast die Arbeit folgende Abschnitte: Einleitung: Die Axiomatik der neuen Quantisierungsmethode. 1. Beziehungen zwischen dem τ- Gleichungssystem und der Methode der Integralgleichungen. a) Ubergang von den τ-Gleichungen zu Integralgleichungen und Darstellung durch Graphen. b) Streuprobleme. c) Spinorteilchen. 2. Wechselwirkung und gebundene Zustande. a) Kraft zwischen zwei Spinorteilchen. b) Bose-Teilchen der Ruhmasse Null. c) Hohere Naherungen fur die Kraft zwischen zwei Spinorteilchen und Berechnung der „Feinstrukturkonstante“. d) Bose-Teilchen nichtverschwindender Ruhmasse. e) Die Integralgleichungen fur die Funktion SF. Das Eigenwertspektrum, das sich aus der einfachen Ausgangsgleichung ergibt, hat eine uberraschende Ahnlichkeit mit dem Massenspektrum der wirklichen Elementarteilchen. Insbesondere sind auch wesentliche Teile der Elektrodynamik in der Ausgangsgleichung enthalten.

Heinrich Mitter

Papers

Recent Progress in MANY-BODY THEORIES

Zur Theorie der Elementarteilchen

Recent Aspects of Quantum Fields

Vacuum polarization in laser fields

Zur Quantentheorie nichtlinearer Wellengleichungen III