27720621
Integrability and nonintegrability of quantum systems: Quantum integrability and dynamical symmetry.
In this paper we discuss the concepts of quantum integrability and nonintegrability. Based on the concept of a complete set of commuting observables and the Hilbert-space structure of a quantum system, the definitions are given for the quantum-dynamical degrees of freedom and quantum phase space from which the quantum integrability is defined. A criterion for quantum integrability then emerges; the system is integrable if it possesses dynamical symmetry. Breaking of dynamical symmetry is connected with the nonintegrability of systems and thus is the inherent mechanism of chaotic motion. A number of examples are discussed.
120753030
Coherent states: Theory and some Applications
In this review, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented. The result is that, for a given dynamical group, the coherent states are isomorphic to a coset space of group geometrical space. Thus the topological and algebraic structure of the coherent states as well as the associated dynamical system can be extensively discussed. In addition, a quantum-mechanical phase-space representation is constructed via the coherent-state theory. Several useful methods for employing the coherent states to study the physical phenomena of quantum-dynamic systems, such as the path integral, variational principle, classical limit, and thermodynamic limit of quantum mechanics, are described.
119531804
Light front dynamics and light front QCD
In this article we review the basic formulation of light-front field theory and light-front phenomena in strong interaction. We also explore various approaches to the understanding of these phenomena and the associated problems of hadronic bound states based on QCD (quantum chromodynamics) on the light-front.
41901069
Geometrical interpretation of SO(7): A critical dynamical symmetry.
Potential-energy surfaces are obtained for the three dynamical-symmetry chains of SO(8) within the fermion-dynamical-symmetry model. A remarkable feature is that the SO(7) dynamical symmetry is transitional and ..beta.. soft. The transitional or ''critical'' behavior of SO(7) is vividly demonstrated.
117753364
Quantum Heisenberg Antiferromagnets versus Nonlinear $\sigma$ Model Without the Large S Limit
In this letter, I develop a new topologically invariant coherent state path integral for spin systems, and apply it to the quantum Heisenberg model on a square lattice. As a result, the quantum nonlinear $\sigma$ model for arbitrary values of spin can be directly obtained. The effective coupling constant and spin wave velocity are modified by $g_s= {2\over S}\sqrt{d+{T_\Lambda\over 2SJ}}$ and $c_s=2JSa \sqrt{d+{T_\Lambda\over 2SJ}}$, where $T_\Lambda$ is a natural temperature scale for the reliability of the theory. The formulation can also be extended to other generalized coherent state path integrals.
296941
Influence of Dynamical Pauli Effect and Dynamical Symmetry Breaking to Quantum Chaos
In this paper, we study the influence of quantum effects to chaotic dynamics, especially the influence of Pauli effect and dynamical symmetry breaking to chaotic motions. We apply the semiquantal theory to the Sp(6) fermion symmetry model in nuclear collective motion. We demonstrate that quantum chaos appears when dynamical symmetry is broken. We further show that dynamical Pauli effect enhances quantum chaos.
34188098
Stochastic quantization and random surface approach to Polyakov string theory.
38262994
Derivation of anomalous commutator and Jacobian from very general conditions.
Using only the equation of motion and the canonical commutator of anomalous gauge theories, we show clearly the relation between the Schwinger-Jackiw-Johnson (SJJ) term, the anomalous Jacobian, and the current-divergence anomaly by obtaining both the SJJ term and the anomalous Jacobian from the current-divergence anomaly.
858386
Chiral symmetry, quark mass, and scaling of the overlap fermions
The chiral symmetry relation and scaling of the overlap fermions are studied numerically on the quenched lattices at 3 couplings with about the same physical volume. We find that the generalized Gell-Mann-Oakes-Renner relation is satisfied to better than 1% down to the smallest quark mass at m(0)a = 0.006. We also obtain the quark mass from the PCAC relation and the pseudoscalar masses. The renormalization group invariant quark mass is shown to be fairly independent of scale. The pi and rho masses at a fixed m(pi)/m(rho) ratio indicate small O(a(2)) corrections. It is found that the critical slowing down sets in abruptly at a very small quark mass close to those of the physical u and d quarks.
43009443
Thermodynamical properties and Coulomb instabilities in hot nuclear systems with the Gogny interaction.
The thermodynamical properties and Coulomb instability in hot nuclear system with Gogny interactions are studied by using the finite-temperature real-time Green{close_quote}s function method. The isotherms, critical temperature, limiting temperature, saturation density, and isothermal incompressibility for various temperatures and different asymmetric parameters are calculated. To illustrate the importance of the finite-range part and density-dependence part of the interaction, we have compared our results with that given by the Skyrme interaction and Brink-Boeker interaction. {copyright} {ital 1996 The American Physical Society.}
32394428
Thermodynamical fluctuations of meson fields for a quantum hadrodynamics model.
Using the real-time Green's-function method with a pair-cutoff approximation up to second order, the thermodynamical fluctuation effects of meson fields on the QHD-II model are studied. We find that the fluctuation effects of meson fields, in particular, the \ensuremath{\pi} meson field, on saturation energy, effective mass of nucleon, and pressure are remarkable in the low-density region and/or high-temperature region. The results given by the QHD-I and QHD-II models are compared. The value of the critical point of the liquid-gas phase transition for the QHD-II model is given.