80 research outputs found
The energy operator for infinite statistics
We construct the energy operator for particles obeying infinite statistics
defined by a q-deformation of the Heisenberg algebra.
(This paper appeared published in CMP in 1992, but was not archived at the
time.)Comment: 6 page
Scaling limit of a non-relativistic model
I calculate the structure function for scattering from the two-body bound
state in its lowest level in a non-relativistic model of confined scalar
``quarks'' of masses and . The scaling limit in exists and is non-vanishing only for the values
and which correspond to the fractions of
the momentum of the two-body system carried by each of the ``quarks.'' In the
scaling limit, the interference from scattering off of the two ``quarks''
vanishes. Thus the scaling limit of this model agrees with the parton picture.Comment: 10 pages, 3 figures not included, in LaTex, UMD 92-22
Conservation of Statistics and Generalized Grassmann Numbers
Conservation of statistics requires that fermions be coupled to Grassmann
external sources. Correspondingly, conservation of statistics requires that
parabosons, parafermions and quons be coupled to external sources that are the
appropriate generalizations of Grassmann numbers.Comment: 10 pages, late
Canonical Commutation Relations in The Schwinger Model
We give the first operator solution of the Schwinger model that obeys the
canonical commutation relations in a covariant guage.Comment: 7 page
Why is CPT fundamental?
G. L\"uders and W. Pauli proved the theorem based on
Lagrangian quantum field theory almost half a century ago. R. Jost gave a more
general proof based on ``axiomatic'' field theory nearly as long ago. The
axiomatic point of view has two advantages over the Lagrangian one. First, the
axiomatic point of view makes clear why is fundamental--because
it is intimately related to Lorentz invariance. Secondly, the axiomatic proof
gives a simple way to calculate the transform of any
relativistic field without calculating , and
separately and then multiplying them. The purpose of this
pedagogical paper is to ``deaxiomatize'' the theorem by
explaining it in a few simple steps. We use theorems of distribution theory and
of several complex variables without proof to make the exposition elementary.Comment: 17 pages, no figure
The Free Quon Gas Suffers Gibbs' Paradox
We consider the Statistical Mechanics of systems of particles satisfying the
-commutation relations recently proposed by Greenberg and others. We show
that although the commutation relations approach Bose (resp.\ Fermi) relations
for (resp.\ ), the partition functions of free gases are
independent of in the range . The partition functions exhibit
Gibbs' Paradox in the same way as a classical gas without a correction factor
for the statistical weight of the -particle phase space, i.e.\ the
Statistical Mechanics does not describe a material for which entropy, free
energy, and particle number are extensive thermodynamical quantities.Comment: number-of-pages, LaTeX with REVTE
Canonical Partition Functions for Parastatistical Systems of any order
A general formula for the canonical partition function for a system obeying
any statistics based on the permutation group is derived. The formula expresses
the canonical partition function in terms of sums of Schur functions. The only
hitherto known result due to Suranyi [ Phys. Rev. Lett. {\bf 65}, 2329 (1990)]
for parasystems of order two is shown to arise as a special case of our general
formula. Our results also yield all the relevant information about the
structure of the Fock spaces for parasystems.Comment: 9 pages, No figures, Revte
Hybrid Dirac Fields
Hybrid Dirac fields are fields that are general superpositions of the
annihilation and creation parts of four Dirac spin 1/2 fields,
, whose annihilation and creation parts obey the Dirac
equation with mass and mass . We discuss a specific case of such
fields, which has been called ``homeotic.'' We show for this case, as is true
in general for hybrid Dirac fields (except the ordinary fields whose
annihilation and creation parts both obey one or the other Dirac equation),
that (1) any interacting theory violates both Lorentz covariance and causality,
(2) the discrete transformations , and map the
pair and into fields that are not linear
combinations of this pair, and (3) the chiral projections of are
sums of the usual Dirac fields with masses and ; on these chiral
projections , and are defined in the usual way,
their interactions do not violate , and interactions of chiral
projections are Lorentz covariant and causal. In short, the main claims
concerning ``homeotic'' fields are incorrect.Comment: 10 pages, acknowledgement added, to appear in Phys. Lett.
Dynamical mapping method in nonrelativistic models of quantum field theory
The solutions of Heisenberg equations and two-particles eigenvalue problems
for nonrelativistic models of current-current fermion interaction and model are obtained in the frameworks of dynamical mapping method. The
equivalence of different types of dynamical mapping is shown. The connection
between renormalization procedure and theory of selfadjoint extensions is
elucidated.Comment: 14 page
COVARIANT SINGLE-TIME BOUND-STATE EQUATION
We derive a system of covariant single-time equations for a two-body bound
state in a model of scalar fields and interacting via
exchange of another scalar field . The derivation of the system of
equations follows from the Haag expansion. The equations are linear integral
equations that are explicitly symmetric in the masses, and , of the
scalar fields, and . We present an approximate analytic
formula for the mass eigenvalue of the ground state and give numerical results
for the amplitudes for a choice of constituent and exchanged particle masses.Comment: 8 pages latex; 4 figures uuencoded ps fil
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