1,342 research outputs found
Representations of U(2\infty) and the Value of the Fine Structure Constant
A relativistic quantum mechanics is formulated in which all of the
interactions are in the four-momentum operator and Lorentz transformations are
kinematic. Interactions are introduced through vertices, which are bilinear in
fermion and antifermion creation and annihilation operators, and linear in
boson creation and annihilation operators. The fermion-antifermion operators
generate a unitary Lie algebra, whose representations are fixed by a first
order Casimir operator (corresponding to baryon number or charge). Eigenvectors
and eigenvalues of the four-momentum operator are analyzed and exact solutions
in the strong coupling limit are sketched. A simple model shows how the fine
structure constant might be determined for the QED vertex.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Point form relativistic quantum mechanics and relativistic SU(6)
The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces
Bakamjian-Thomas mass operator for the few-nucleon system from chiral dynamics
We present an exploratory study consisting in the formulation of a
relativistic quantum mechanics to describe the few-nucleon system at low
energy, starting from the quantum field theoretical chiral Lagrangian involving
pions and nucleons. To this aim we construct a Bakamjian-Thomas mass operator
and perform a truncation of the Fock space which respects at each stage the
relativistic covariance. Such truncation is justified, at sufficiently low
energy, in the framework of a systematic chiral expansion. As an illustration
we discuss the bound state observables and low-energy phaseshifts of the
nucleon-nucleon and pion-nucleon scattering at the leading order of our scheme.Comment: 17 pages, 10 figures. Revised formulation, matches the journal
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