Does there arise a significant enhancement of the dynamical quark mass in external magnetic field?

Recently, it was found in QED that the generation of a dynamical electron mass in a strong magnetic field is significantly enhanced by the perturbative electron mass. In the present Letter, the related question of a possible enhancement of the dynamical quark mass in an external magnetic field and with a bare mass term is investigated in the Nambu–Jona-Lasinio model.     

Electron mass operator in a strong magnetic field and dynamical chiral symmetry breaking

The electron mass operator in a strong magnetic field is calculated. The contribution of higher Landau levels of virtual electrons, along with the ground Landau level, is shown to be essential in the leading log approximation. The effect of the electron dynamical mass generation by a magnetic field is investigated. In a model with N charged fermions, it is shown that some critical number N(cr) exists for any value of the electromagnetic coupling constant alpha, such that the fermion dynamical mass is generated with a doublet splitting for NN(cr), thus leaving the chiral symmetry unbroken.     

The Effect of Bare Quark Mass on the Pion Properties in BS Formalism Containing a Confining Term

Using the SD equation and the covariant BS equation, we investigate dynamical chiral symmetry breaking in the presence of a bare quark mass in a QCD motivated model containing a confining interaction. The bare quark mass m₀ corresponding to the physical mass of the pion and corrections to the dynamical quark mass and the pion decay constant due to mo are calculated. The results are consistent with the notion of chiral perturbatiyn and predictions of the current algebra.     

Gauge independence and chiral symmetry breaking in a strong magnetic field

The gauge independence of the dynamical fermion mass generated through chiral symmetry breaking in QED in a strong, constant external magnetic field is critically examined. We present a (first, to the best of our knowledge) consistent truncation of the Schwinger-Dyson equations in the lowest Landau level approximation. We demonstrate that the dynamical fermion mass, obtained as the solution of the truncated Schwinger-Dyson equations evaluated on the fermion mass shell, is manifestly gauge independent.     

A microscopic formula for actinide masses

A fully microscopic actinide mass formula is derived using the fermion dynamical symmetry model approximation to the spherical shell model. A rich dynamical symmetry phase structure is confirmed, and the mass formula fits the masses of 322 nuclei with an RMS deviation of 0.34 MeV.     

Some analytical aspects in field theories with dynamical mass generation

The consequence of dynamical mass generation on the singularity structure of propagators is discussed. First the phenomena of dynamical mass generation is discussed in the framework of Euclidean gap equations, then a possible Minkowski solution is looked for. The examples are reviewed and studied for several models: Yukawa, QED, QCD and Wess-Zumino. It is argued that the absence of propagator pole goes hand in hand with the nontrivial solution for mass function. The consequences are discussed.     

Monte Carlo simulation of SU(2) Yang-Mills theory with light gluinos

In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with light dynamical gluinos the low energy features of the dynamics as confinement and bound state mass spectrum are investigated. The motivation is supersymmetry at vanishing gluino mass. The performance of the applied two-step multi-bosonic dynamical fermion algorithm is discussed. Received: 15 March 1999 / Published online: 22 October 1999     

Spontaneous symmetry breaking in QCD

We study dynamical chiral symmetry breaking in massless QCD by the use of the generalized Hartree-Fock method. As the order parameter of chiral symmetry we choose the dynamical quark mass in the zero momentum limit which we call low energy quark mass. We calculate the low energy mass to the second order of diagrammatic expansion around shifted perturbative vacuum. We then show that the mass is finite and renormalization group invariant. After the improvement of the result by the method of effective charges we estimate the mass in the true vacuum under the gap and stationarity conditions and demonstrate that both of them produce non-zero mass proportional to a conventional scale, which breaks down the chiral symmetry.     

The decoupling of second-order linear systems with a singular mass matrix

It was demonstrated in earlier work that a nondefective, linear dynamical system with an invertible mass matrix in free or forced motion may be decoupled in the configuration space by a real and isospectral transformation. We extend this work by developing a procedure for decoupling a linear dynamical system with a singular mass matrix in the configuration space, transforming the original differential-algebraic system into decoupled sets of real, independent, first- and second-order differential equations. Numerical examples are provided to illustrate the application of the decoupling procedure.     

A self consistent approach to the transport equation for moving atoms in interaction with laser fields

The transport equations for moving atoms in interaction with laser fields, are derived using the hamiltonian in terms of the quantum dynamical variables for the center of mass motion and by introducing suitably defined local density matrices. Use is also made of the phase space variables associated with the quantum dynamical variables of center of mass and the projection operator techniques.     

Chiral symmetry breaking in QCD

By applying bifurcation theory to a truncated Dyson-Schwinger equation for the quark propagator in massless QCD, we show that dynamical symmetry breaking occurs at a certain critical value of the coupling constant. Essential ingredients are (a) an effective dynamical mass for the gluon, and (b) a running coupling constant.     

A theoretical model for the charge equilibration in heavy ion collisions

We propose to treat the charge equilibration process as a collective high frequency mode and discuss the implications for the first stages of a heavy ion collision. We show how its dynamics can be treated by means of a quantal master equation. We solve numerically the dynamical equations for a two-dimensional model, using charge excess and mass asymmetry as dynamical degrees of freedom.     

Massive mesons in Weyl–Dirac theory

In order to study the mass generation of the vector fields in the framework of a conformal invariant gravitational model, the Weyl–Dirac theory is considered. The mass of the Weyl’s meson fields plays a principal role in this theory, it connects basically the conformal and gauge symmetries. We estimate this mass by using the large-scale characteristics of the observed universe. To do this we firstly specify a preferred conformal frame as a cosmological frame, then in this frame, we introduce an exact possible solution of the theory. We also study the dynamical effect of the massive vector meson fields on the trajectories of an elementary particle. We show that a local change of the cosmological frame leads to a Hamilton–Jacobi equation describing a particle with an adjustable mass. The dynamical effect of the massive vector meson field presents itself in the form of a correction term for the mass of the particle.     

On the critical behavior of (2 + 1)-dimensional QED

It is shown the analysis [1] for QED in (2 + 1) dimensions with N four-component fermions in the leading and next-to-leading orders of the 1/N expansion. As it was demonstrated in [1], the range of the admissible values N, where the dynamical fermion mass exists, decreases strongly with the increasing of the gauge charge. So, in Landau gauge the dynamical chiral symmetry breaking appears forN < 3.78, that is very close to the results of the leading order and in Feynman gauge dynamical mass is completely absent.     

Deconfinement phase transition in QCD with heavy quarks

Using the pseudo-fermion method to simulate QCD with dynamical quarks we investigate the effects of heavy dynamical quarks of 2 flavours on the deconfinement phase transition in the quenched QCD. As the mass of the quark is decreased the phase transition weakens as expected. Compared to the earlier results with leading order hopping parameter expansion, however, the weakening is less rapid. Our estimated upper bound on the critical mass where the transition becomes continuous is 1.5–2 times lower than earlier results.     

Cabibbo angles without scalars

A simple model of dynamical symmetry breaking is presented in which the mass matrices of the up and down quarks are related to a (ETC) vector-boson mass-matrix in the 10–100 TeV range. Realistic quark masses and Cabibbo angles can be obtained. The problem of flavour-changing neutral interactions in theories of dynamical symmetry breaking is discussed in the context of this model.     

Computer simulation of particles with position-dependent mass

In the present work a dynamical system is investigated, in which the particles’ mass depends on their position in space. The first case study is that of a single point-like particle in one dimension, whose Hamiltonian is numerically integrated with a first-order, energy-conserving algorithm; subsequently, the model is extended to a Lennard-Jones fluid in three dimensions. The features of both setups are examined, and a simple, exact method is devised to obtain, from a system of particles with position-dependent mass, the same equilibrium observables that would be measured in a conventional simulation. The properties of these dynamical systems are explored, with possible applications in the development of efficient sampling strategies.     

Isospin violating mass differences of baryons and hadronic loops

Isospin violating mass splittings of the ground state baryons are discussed within the frame-work of the unitarized quark model. It is shown that the long-distance, nonperturbative unitarity effects are important, and that a good agreement with the observed mass splittings can be retained. The importance of six mass sum rules which hold independently of dynamical assumptions is emphasized.     

Energy equilibration and anomalous mass drift in heavy ion collisions

The lack of mass drift towards symmetry observed in many Kr-induced reactions, and the excessive mass drift towards larger asymmetry in Ne, Ar-induced reactions, is explained in terms of a dynamical driving force towards larger mass asymmetries due to the attempt of the smaller fragment to contain its temperature gradient with respect to the heavy fragment.     

A microscopic study on shape transition and shape coexistence in superdeformed nuclei

Superdeformed nuclei at high-spin states in several mass regions are investigated within a microscopic approach using cranked Nilsson-Strutinsky formalism to explore the equilibrium deformations in the ground state and their evolution with spin. Shape transition from normal deformed to superdeformed states with increasing spin is studied and a clear picture of shape coexistence is provided. Detailed information on spin, rotational energy, dynamical moment of inertia, and rotational frequency of superdeformed rotational bands is presented and the general features of superdeformed bands in certain mass regions are outlined. Rotational energy and dynamical moment of inertia are compared with available experimental data and the impact of temperature and pairing on superdeformed configuration are discussed.