49,962 research outputs found
Normalization of the covariant three-body bound state vertex function
The normalization condition for the relativistic three nucleon Bethe-Salpeter
and Gross bound state vertex functions is derived, for the first time, directly
from the three body wave equations. It is also shown that the relativistic
normalization condition for the two body Gross bound state vertex function is
identical to the requirement that the bound state charge be conserved, proving
that charge is automatically conserved by this equation.Comment: 24 pages, 9 figures, published version, minor typos correcte
A comprehensive treatment of electromagnetic interactions and the three-body spectator equations
We present a general derivation the three-body spectator (Gross) equations
and the corresponding electromagnetic currents. As in previous paper on
two-body systems, the wave equations and currents are derived from those for
Bethe-Salpeter equation with the help of algebraic method using a concise
matrix notation. The three-body interactions and currents introduced by the
transition to the spectator approach are isolated and the matrix elements of
the e.m. current are presented in detail for system of three indistinguishable
particles, namely for elastic scattering and for two and three body break-up.
The general expressions are reduced to the one-boson-exchange approximation to
make contact with previous work. The method is general in that it does not rely
on introduction of the electromagnetic interaction with the help of the minimal
replacement. It would therefore work also for other external fields
Mastering the Master Field
The basic concepts of non-commutative probability theory are reviewed and
applied to the large limit of matrix models. We argue that this is the
appropriate framework for constructing the master field in terms of which large
theories can be written. We explicitly construct the master field in a
number of cases including QCD. There we both give an explicit construction
of the master gauge field and construct master loop operators as well. Most
important we extend these techniques to deal with the general matrix model, in
which the matrices do not have independent distributions and are coupled. We
can thus construct the master field for any matrix model, in a well defined
Hilbert space, generated by a collection of creation and annihilation
operators---one for each matrix variable---satisfying the Cuntz algebra. We
also discuss the equations of motion obeyed by the master field.Comment: 46 pages plus 11 uuencoded eps figure
Folds in 2D String Theories
We study maps from a 2D world-sheet to a 2D target space which include folds.
The geometry of folds is discussed and a metric on the space of folded maps is
written down. We show that the latter is not invariant under area preserving
diffeomorphisms of the target space. The contribution to the partition function
of maps associated with a given fold configuration is computed. We derive a
description of folds in terms of Feynman diagrams. A scheme to sum up the
contributions of folds to the partition function in a special case is suggested
and is shown to be related to the Baxter-Wu lattice model. An interpretation of
folds as trajectories of particles in the adjoint representation of
gauge group in the large limit which interact in an unusual way with the
gauge fields is discussed.Comment: 56 pages, latex, followed by epsf, 13 uuencoded epsf figure
Electromagnetic interactions for the two-body spectator equations
This paper presents a new non-associative algebra which is used to (i) show
how the spectator (or Gross) two-body equations and electromagnetic currents
can be formally derived from the Bethe-Salpeter equation and currents if both
are treated to all orders, (ii) obtain explicit expressions for the Gross
two-body electromagnetic currents valid to any order, and (iii) prove that the
currents so derived are exactly gauge invariant when truncated consistently to
any finite order. In addition to presenting these new results, this work
complements and extends previous treatments based largely on the analysis of
sums of Feynman diagrams.Comment: 44 pages, 14 figure
The stability of the spectator, Dirac, and Salpeter equations for mesons
Mesons are made of quark-antiquark pairs held together by the strong force.
The one channel spectator, Dirac, and Salpeter equations can each be used to
model this pairing. We look at cases where the relativistic kernel of these
equations corresponds to a time-like vector exchange, a scalar exchange, or a
linear combination of the two. Since the model used in this paper describes
mesons which cannot decay physically, the equations must describe stable
states. We find that this requirement is not always satisfied, and give a
complete discussion of the conditions under which the various equations give
unphysical, unstable solutions
Quark-Antiquark Bound States in the Relativistic Spectator Formalism
The quark-antiquark bound states are discussed using the relativistic
spectator (Gross) equations. A relativistic covariant framework for analyzing
confined bound states is developed. The relativistic linear potential developed
in an earlier work is proven to give vanishing meson decay
amplitudes, as required by confinement. The regularization of the singularities
in the linear potential that are associated with nonzero energy transfers (i.e.
) is improved. Quark mass functions that build chiral
symmetry into the theory and explain the connection between the current quark
and constituent quark masses are introduced. The formalism is applied to the
description of pions and kaons with reasonable results.Comment: 31 pages, 16 figure
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