Generalized Levy-Leblond equation with external potentials and effects of rest energy for non-relativistic Fermi fields

The generalized Levy-Leblond equation (GLL) is used to study the bound state problem for a non-relativistic Fermi field in pseudoscalar external potentials. Two spherically symmetrical external potentials, a pseudoscalar spherical well of finite depth and a pseudoscalar Coulomb potential, are considered. It is shown that the rest energy of the Fermi field affects non-trivially the bound state spectrum. The existence of bound states, their number and energies all depend on the value of the rest energy.Comment: References added, minor changes in Introduction, LaTex file, 32 pages, 6 figure

Non-Markovian source term for particle production by a self-interacting scalar field in the large-N approximation

The particle production in the self-interacting N-component complex scalar field theory is studied at large N. A non-Markovian source term that includes all higher order back-reaction and collision effects is derived. The kinetic amplitudes accounting for the change in the particle number density caused by collisions are obtained. It is shown that the production of particles is symmetric in the momentum space. The problem of renormalization is briefly discussed.Comment: minor changes, journal versio

Non-relativistic Fermi particle in one-dimensional pseudoscalar δ{\delta}-function potential

It is shown that a non-relativistic Fermi particle with a non-zero rest energy moving in a pseudoscalar ${\delta}$-function potential in one dimension can be confined for both signs of the coupling constant. The binding energies depend on the value of the particle's rest energy, and in the limit of vanishing rest energy only one of the bound states survives. The coefficients of reflection and transmission are determined, and the conditions for complete reflection and transmission are discussed.Comment: Minor changes in Discussion, LaTex file, 10 page

Poincare Algebra in Chiral QCD_2

For the chiral QCD_2 on a cylinder, we give a construction of a quantum theory consistent with anomaly. We construct the algebra of the Poincare generators and show that it differs from the Poincare one.Comment: LATEX file, 10 p

Berry phase in generalized chiral QED2QED_2

We consider the generalized chiral $QED_2$ on $S^1$ with a $U(1)$ gauge field coupled with different charges to both chiral components of a fermionic field. Using the adiabatic approximation we calculate the Berry phase and the corresponding ${\rm U}(1)$ connection and curvature for the vacuum and many particle Fock states. We show that the nonvanishing vacuum Berry phase is associated with a projective representation of the local gauge symmetry group and contributes to the effective action of the model.Comment: LATEX file, 17 pages; extended version of a talk given at Int. Colloquium on Group-Theoretical Methods in Physics, 15-20 July, 1996, Goslar, German

Generalised chiral QED2 : Anomaly and Exotic Statistics

We study the influence of the anomaly on the physical quantum picture of the generalized chiral Schwinger model defined on the circle. We show that the anomaly i) results in the background linearly rising electric field and ii) makes the spectrum of the physical Hamiltonian nonrelativistic without a massive boson. The physical matter fields acquire exotic statistics . We construct explicitly the algebra of the Poincare generators and show that it differs from the Poincare one. We exhibit the role of the vacuum Berry phase in the failure of the Poincare algebra to close. We prove that, in spite of the background electric field, such phenomenon as the total screening of external charges characteristic for the standard Schwinger model takes place in the generalized chiral Schwinger model, too.Comment: LATEX file, 36 pp., to appear in Phys.Rev.