The Dirac equation serves as the basis for the relativistic description of atoms, nuclei and hadrons. In atoms the relevant potentials felt by the electron are Coulombic vector potentials. A Dirac Hamiltonian with a Coulomb potential exhibits a finestructure spectrum with characteristic two-fold degeneracy. Relativistic mean fields in nuclei generated by meson exchanges , and quark confinement ...

The world-line (Fock-Feynman-Schwinger) representation is used for quarks in arbitrary (vacuum and valence gluon) field to construct the relativistic Hamiltonian. After averaging the Green's function of the white q ¯ q system over gluon fields one obtains the relativistic Hamiltonian, which is matrix in spin indices and contains both positive and negative quark energies. The role of the latter ...

We construct the family of spin chain Hamiltonians, which have affine U q g guantum group symmetry. Their eigenvalues coincides with the eigenvalues of the usual spin chain Hamiltonians which have non-affine U q g 0 quantum group symmetry, but have the degeneracy of levels, corresponding to affine U q g. The space of states of these chaines are formed by the tensor product of the fully reducibl...

An argument is presented to explain the fact that the same mean-field results apply to several spin glass models, such as the 'random-energy' model and the large-p Potts glass model. The dilute simplest spin glass model is solved, yielding the same mean-field results. The argument is based on the fact that the symmetry of the discrete-spin system can be determined by the discrete-spin type or b...

We study the computational complexity of estimating the ground state energy and simulating the adiabatic evolution for the transverse field Ising model (TIM). It is shown that the ground state energy problem for TIM on a degree-3 graph is complete for the complexity class StoqMA. This is an extension of the classical class MA where the verifier can accept quantum states as a proof and apply cla...

Topological or deconfined phases of matter exhibit emergent gauge fields and quasiparticles that carry a corresponding gauge charge. In systems with an intrinsic conserved U(1) charge, such as all electronic systems where the Coulombic charge plays this role, these quasiparticles are also characterized by their intrinsic charge. We show that one can take advantage of the topological order fairl...

In this article, the second quantization method has been used to investigate some thermodynamic properties of spin-polarized metallic nanowire in the presence of magnetic field at zero temperature. We have been observed that in different magnetic field, the equilibrium energy of system increases as the density increases. The spin-polarization parameter corresponding to the equilibrium state of ...

We present a method for computing the non-perturbative mass-gap in the theory of Bosonic membranes in flat background spacetimes. The analysis is extended to the study of membranes coupled to background fluxes as well. The computation of mass-gaps is carried out using a matrix regularization of the membrane Hamiltonians. The mass gap is shown to be naturally organized as an expansion in a ’hidd...