29,798 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
The microcanonical thermodynamics of finite systems: The microscopic origin of condensation and phase separations; and the conditions for heat flow from lower to higher temperatures
Microcanonical thermodynamics allows the application of statistical mechanics
both to finite and even small systems and also to the largest, self-gravitating
ones. However, one must reconsider the fundamental principles of statistical
mechanics especially its key quantity, entropy. Whereas in conventional
thermostatistics, the homogeneity and extensivity of the system and the
concavity of its entropy are central conditions, these fail for the systems
considered here. For example, at phase separation, the entropy, S(E), is
necessarily convex to make exp[S(E)-E/T] bimodal in E. Particularly, as
inhomogeneities and surface effects cannot be scaled away, one must be careful
with the standard arguments of splitting a system into two subsystems, or
bringing two systems into thermal contact with energy or particle exchange. Not
only the volume part of the entropy must be considered. As will be shown here,
when removing constraints in regions of a negative heat capacity, the system
may even relax under a flow of heat (energy) against a temperature slope. Thus
the Clausius formulation of the second law: ``Heat always flows from hot to
cold'', can be violated. Temperature is not a necessary or fundamental control
parameter of thermostatistics. However, the second law is still satisfied and
the total Boltzmann entropy increases. In the final sections of this paper, the
general microscopic mechanism leading to condensation and to the convexity of
the microcanonical entropy at phase separation is sketched. Also the
microscopic conditions for the existence (or non-existence) of a critical
end-point of the phase-separation are discussed. This is explained for the
liquid-gas and the solid-liquid transition.Comment: 23 pages, 2 figures, Accepted for publication in the Journal of
Chemical Physic
An Exact Prediction of N=4 SUSYM Theory for String Theory
We propose that the expectation value of a circular BPS-Wilson loop in N=4
SUSYM can be calculated exactly, to all orders in a 1/N expansion and to all
orders in g^2 N. Using the AdS/CFT duality, this result yields a prediction of
the value of the string amplitude with a circular boundary to all orders in
alpha' and to all orders in g_s. We then compare this result with string
theory. We find that the gauge theory calculation, for large g^2 N and to all
orders in the 1/N^2 expansion does agree with the leading string theory
calculation, to all orders in g_s and to lowest order in alpha'. We also find a
relation between the expectation value of any closed smooth Wilson loop and the
loop related to it by an inversion that takes a point along the loop to
infinity, and compare this result, again successfully, with string theory.Comment: LaTeX, 22 pages, 3 figures. Argument corrected and two new sections
adde
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
Relativistic calculation of the triton binding energy and its implications
First results for the triton binding energy obtained from the relativistic
spectator or Gross equation are reported. The Dirac structure of the nucleons
is taken into account. Numerical results are presented for a family of
realistic OBE models with off-shell scalar couplings. It is shown that these
off-shell couplings improve both the fits to the two-body data and the
predictions for the binding energy.Comment: 5 pages, RevTeX 3.0, 1 figure (uses epsfig.sty
Calculating the Rest Tension for a Polymer of String Bits
We explore the application of approximation schemes from many body physics,
including the Hartree-Fock method and random phase approximation (RPA), to the
problem of analyzing the low energy excitations of a polymer chain made up of
bosonic string bits. We accordingly obtain an expression for the rest tension
of the bosonic relativistic string in terms of the parameters
characterizing the microscopic string bit dynamics. We first derive an exact
connection between the string tension and a certain correlation function of the
many-body string bit system. This connection is made for an arbitrary
interaction potential between string bits and relies on an exact dipole sum
rule. We then review an earlier calculation by Goldstone of the low energy
excitations of a polymer chain using RPA. We assess the accuracy of the RPA by
calculating the first order corrections. For this purpose we specialize to the
unique scale invariant potential, namely an attractive delta function potential
in two (transverse) dimensions. We find that the corrections are large, and
discuss a method for summing the large terms. The corrections to this improved
RPA are roughly 15\%.Comment: 44 pages, phyzzx, psfig required, Univ. of Florida preprint,
UFIFT-HEP-94
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