Random matrices, fermions, collective fields, and universality

We first relate the random matrix model to a Fokker-Planck Hamiltonian system, such that the correlation functions of the model are expressed as the vacuum expectation values of equal-time products of density operators. We then analyze the universality of the random matrix model by solving the Focker-Planck Hamiltonian system for large N. We use two equivalent methods to do this, namely the method of relating it to a system of interacting fermions in one space dimension and the method of collective fields for large N matrix quantum mechanics. The final result using both these methods is the same Hamiltonian system of chiral bosons on a circle, which manifestly exhibits the universality of the random matrix model.     

Chiral bands, dynamical spontaneous symmetry breaking, and the selection rule for electromagnetic transitions in the chiral geometry

A model for a special configuration in triaxial odd-odd nuclei is constructed which exhibits degenerate chiral bands with a sizable rotation, a manifestation of dynamical spontaneous symmetry breaking. A quantum number obtained from the invariance of the model Hamiltonian, which characterizes observable states, is given and selection rules for electromagnetic transition probabilities in chiral bands is derived in terms of this quantum number. The degeneracy of the lowest two bands is indeed obtained in the numerical diagonalization of the Hamiltonian at an intermediate spin range, over which electromagnetic transitions follow exactly the selection rule expected for the chiral geometry.     

H-particle in a chiral quark model

In this paper we discuss the binding energy of the H-particle using a chiral quark model, where pion exchange plays an important role to reproduce the mass difference between the nucleon and Δ resonance. Since the main source for the bound H-particle is believed to be the color magnetic interaction, which gives the nucleon and Δ mass difference, it is very interesting to investigate whether the chiral quark model gives rise to the bound H-particle or not. We employ an extended resonating group method in order to take into account the possibility of a change of baryon wave functions when two baryons interact with each other. We found that a change of baryon size together with the Hamiltonian which consists of gluon, pseudoscalar meson and sigma meson exchange potentials gives rise to the bound H-particle. The binding energy is found to be about 25 MeV in a hybrid chiral quark model. Differences between the ordinary gluon dominant model and chiral quark models are also investigated. It is found that a pure chiral model has no bound state when the widely used sigma-quark coupling strength is employed.     

Batalin-Tyutin quantization of the chiral Schwinger model

We quantize the chiral Schwinger model by using the Batalin-Tyutin formalism. We show that one can systematically construct the first-class constraints and the desired involutive Hamiltonian, which naturally generates all secondary constraints. Fora>1, this Hamiltonian gives the gauge invariant Lagrangian including the well-known Wess-Zumino terms, while fora=1 the corresponding Lagrangian has the additional new type of the Wess-Zumino terms, which are irrelevant to the gauge symmetry.     

Nucleon magnetic moments in an extended chiral constituent quark model

We present results for the nucleon magnetic moments in the context of an extended chiral constituent quark model based on the mechanism of the Goldstone boson exchange, as suggested by the spontaneous breaking of chiral symmetry in QCD. The electromagnetic charge-current operator is consistently deduced from the model Hamiltonian, which includes all force components for the pseudoscalar, vector and scalar meson exchanges. Thus, the continuity equation is satisfied for each piece of the interaction, avoiding the introduction of any further parameter. A good agreement with experimental values is found. The role of isoscalar two-body operators, not constrained by the continuity equation, is also investigated.     

Gauge invariant theories of the generalized chiral Schwinger model

The gauge invariant theories of the generalized chiral Schwinger model are constructed in terms of two schemes with and without Wess-Zumino terms, respectively. Following the former scheme, we calculate the Wess-Zumino term which cancels the gauge anomaly, and then constitute the gauge invariant theory by adding the Wess-Zumino term to the original Lagrangian of the model. According to the latter, we modify the original Hamiltonian by adding a term composed of constraints of the model. It is so designed that the theory described by the modified Hamiltonian and its corresponding first-order Lagrangian maintains gauge invariance. We show by the canonical Dirac method that each of the two gauge invariant theories has the same physical spectrum as that of the original gauge noninvariant formulation.     

Gauge invariant theories of the generalized chiral Schwinger model

The gauge invariant theories of the generalized chiral Schwinger model are constructed in terms of two schemes with and without Wess-Zumino terms, respectively. Following the former scheme, we calculate the Wess-Zumino term which cancels the gauge anomaly, and then constitute the gauge invariant theory by adding the Wess-Zumino term to the original Lagrangian of the model. According to the latter, we modify the original Hamiltonian by adding a term composed of constraints of the model. It is so designed that the theory described by the modified Hamiltonian and its corresponding first-order Lagrangian maintains gauge invariance. We show by the canonical Dirac method that each of the two gauge invariant theories has the same physical spectrum as that of the original gauge noninvariant formulation.     

Gauge invariant formulation of non-Abelian chiral gauge theories in two dimensions

We study the gauge invariant version of a chiral non-Abelian gauge theory. A local bosonic effective action is obtained and the covariant conservation of the gauge current is verified. A Hamiltonian analysis of the model and of its constraints is performed. We show that the constraints are first class and that no anomalous term appears in the commutators of the gauge group generators. The current algebra of the model is obtained and the gauge fixing is analyzed.     

Coupling Parameter in the Single-j Shell Model

We propose a modified formula which is used to determine the coupling parameter C in the Hamiltonian of the single-j shell. In comparison with the previously known formula, the new formula improves the agreement between the intruder single-j levels and the Nilsson ones. For studies of chiral bands within the particle rotor model, the new coupling parameter will considerably influence the energy splitting between the doublet bands.     

A gauge-invariant theory of chiral bosons: Wess-Zumino term,Hamiltonian and BRST formulations

The Wess-Zumino term for the gauge-non-invariant Srivastava model for single self-dual chiral bosons is constructed, and the Hamiltonian and BRST formulations of the resulting gauge-invariant theory (obtained by the inclusion of the Wess-Zumino term) are investigated.     

Spin hamiltonian for which the chiral spin liquid is the exact ground state

We construct a Hamiltonian that singles out the chiral spin liquid on a square lattice with periodic boundary conditions as the exact and, apart from the twofold topological degeneracy, unique ground state.     

Constant-cutoff approach to electric seagull terms in the soliton Hamiltonian

We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. Using the constant-cutoff approach, we then study theSU(2) soliton Hamiltonian, which does not contain the electric seagull terms, and show that if the fields are restricted to the collective subspace, the electric seagull terms are induced in the effective Hamiltonian similarly to the case of the complete Skyrme model. These terms are consistent with gauge invariance and leading-term predictions of the chiral perturbation calculation of the electric polarizability.     

Observing Majorana bound states in p-wave superconductors using noise measurements in tunneling experiments

The zero-energy bound states at the edges or vortex cores of chiral p-wave superconductors should behave like Majorana fermions. We introduce a model Hamiltonian that describes the tunneling process when electrons are injected into such states. Using a nonequilibrium Green function formalism, we find exact analytic expressions for the tunneling current and noise and identify experimental signatures of the Majorana nature of the bound states to be found in the shot noise. We discuss the results in the context of different candidate materials that support triplet superconductivity. Experimental verification of the Majorana character of midgap states would have important implications for the prospects of topological quantum computation.     

Origin of the anomalous long lifetime of ¹⁴C

We report the microscopic origins of the anomalously suppressed beta decay of 1?C to 1?N using the ab initio no-core shell model with the Hamiltonian from the chiral effective field theory including three-nucleon force terms. The three-nucleon force induces unexpectedly large cancellations within the p shell between contributions to beta decay, which reduce the traditionally large contributions from the nucleon-nucleon interactions by an order of magnitude, leading to the long lifetime of 1?C.     

Image restoration using the chiral Potts spin glass

We report on the image reconstruction (IR) problem by making use of the random chiral q-state Potts model, whose Hamiltonian possesses the same gauge invariance as the usual Ising spin glass model. We show that the pixel representation by means of the Potts variables is suitable for the gray-scale level image which cannot be represented by the Ising model. We find that the IR quality is highly improved by the presence of a glassy term, besides the usual ferromagnetic term under random external fields, as very recently pointed out by Nishimori and Wong. We give the exact solution of the infinite range model with q=3, the three-gray-scale-level case. In order to check our analytical result and the efficiency of our model, two-dimensional Monte Carlo simulations have been carried out on real-world pictures with three and eight gray-scale levels.     

Chiral State Conversion in a Levitated Micromechanical Oscillator with In Situ Control of Parameter Loops

Physical systems with gain and loss can be described by a non-Hermitian Hamiltonian, which is degenerated at the exceptional points(EPs).Many new and unexpected features have been explored in the non-Hermitian systems with a great deal of recent interest.One of the most fascinating features is that chiral state conversion appears when one EP is encircled dynamically.Here, we propose an easy-controllable levitated microparticle system that carries a pair of EPs and realize slow evolution of the H...     

Chiral-symmetry breaking and the QCD string

The Lorentz nature of the effective interquark interaction is investigated in a heavy-light quarkonium. The approach of the Dyson-Schwinger-type equation and the quantum-mechanical Hamiltonian method of the QCD string with quarks at the ends are employed to demonstrate that the effective scalar interaction, which appears owing to chiral-symmetry breaking, is responsible for the QCD-string formation. The Hamiltonian of the QCD string with quarks at the ends arises naturally if this effective scalar interaction dominates. If, on the contrary, chiral symmetry is manifest, the effective interquark interaction remains vectorial, and the corresponding bound-state equation is incompatible with the QCD-string Hamiltonian.We conclude therefore that the genuine Lorentz nature of the QCD string is scalar. The text was submitted by the authors in English.     

Can QCD Be a Perturbation Theory of Hadrons?

We have found that the S-matrix for atoms and hadrons depends on a gauge as the elementary particles are off mass-shell in the bound states. The S-matrix for bound states one should to construct by the projection of the Belinfante energy-momentum tensor on the Gauss equation solution for the time component with the time-axis chosen as the eigenvector of the bound state total momentum operator. We have shown that this QCD Hamiltonian determined in infrared region by the rising potential ansatz, besides the parton model in the specific gauge, contains also the nonrelativistic potential model for heavy quarkonia, the chiral Lagrangians for light quarkonia with their spectrum, the glueball physics, and the small effective coupling constant in the whole region of transversal momenta.