60 research outputs found
Invariance in linear systems
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32794/1/0000167.pd
Correlations in the Sine-Gordon Model with Finite Soliton Density
We study the sine-Gordon (SG) model at finite densities of the topological
charge and small SG interaction constant, related to the one-dimensional
Hubbard model near half-filling. Using the modified WKB approach, we find that
the spectrum of the Gaussian fluctuations around the classical solution
reproduces the results of the Bethe ansatz studies. The modification of the
collective coordinate method allows us to write down the action, free from
infra-red divergencies. The behaviour of the density-type correlation functions
is non-trivial and we demonstrate the existence of leading and sub-leading
asymptotes. A consistent definition of the charge-raising operator is
discussed. The superconducting-type correlations are shown to decrease slowly
at small soliton densities, while the spectral weight of right (left) moving
fermions is spread over neighboring "4k_F" harmonics.Comment: 12 pages, 3 eps figures, REVTEX; a discussion of fermions is adde
Light quarks masses and condensates in QCD
We review some theoretical and phenomenological aspects of the scenario in
which the spontaneous breaking of chiral symmetry is not triggered by a
formation of a large condensate . Emphasis is put on the resulting
pattern of light quark masses, on the constraints arising from QCD sum rules
and on forthcoming experimental tests.Comment: 23 pages, 12 Postscript figures, LaTeX, uses svcon2e.sty, to be
published in the Proceedings of the Workshop on Chiral Dynamics 1997, Mainz,
Germany, Sept. 1-5, 199
The staggered domain wall fermion method
A different lattice fermion method is introduced. Staggered domain wall
fermions are defined in 2n+1 dimensions and describe 2^n flavors of light
lattice fermions with exact U(1) x U(1) chiral symmetry in 2n dimensions. As
the size of the extra dimension becomes large, 2^n chiral flavors with the same
chiral charge are expected to be localized on each boundary and the full
SU(2^n) x SU(2^n) flavor chiral symmetry is expected to be recovered. SDWF give
a different perspective into the inherent flavor mixing of lattice fermions and
by design present an advantage for numerical simulations of lattice QCD
thermodynamics. The chiral and topological index properties of the SDWF Dirac
operator are investigated. And, there is a surprise ending...Comment: revtex4, 7 figures, minor revisions, 2 references adde
The Low Energy Amplitude to One and Two Loops
The low-energy amplitude is computed explicitly to two-loop accuracy
in the chiral expansion. It depends only on six independent (combinations of)
low-energy constants which are not fixed by chiral symmetry. Four of these
constants are determined {\it via} sum rules which are evaluated using
scattering data at higher energies. Dependence of the low-energy phase shifts
and of the threshold parameters on the remaining two constants (called
and ) are discussed and compared to the existing data from
experiments. Using generalised PT, the constants and are
related to fundamental QCD parameters such as the quark condensate and the quark mass ratio . It is shown
that forthcoming accurate low-energy data can be used to provide, for
the first time, experimental evidence in favour of or against the existence of
a large quark-antiquark condensate in the QCD vacuum.Comment: 61 pages, LaTeX, 10 figures in separate tarred, compressed and
uuencoded Postscript fil
Propagators in Noncommutative Instantons
We explicitly construct Green functions for a field in an arbitrary
representation of gauge group propagating in noncommutative instanton
backgrounds based on the ADHM construction. The propagators for spinor and
vector fields can be constructed in terms of those for the scalar field in
noncommutative instanton background. We show that the propagators in the
adjoint representation are deformed by noncommutativity while those in the
fundamental representation have exactly the same form as the commutative case.Comment: 28 pages, Latex, v2: A few typos correcte
The Hamiltonian limit of (3+1)D SU(3) lattice gauge theory on anisotropic lattices
The extreme anisotropic limit of Euclidean SU(3) lattice gauge theory is
examined to extract the Hamiltonian limit, using standard path integral Monte
Carlo (PIMC) methods. We examine the mean plaquette and string tension and
compare them to results obtained within the Hamiltonian framework of Kogut and
Susskind. The results are a significant improvement upon previous Hamiltonian
estimates, despite the extrapolation procedure necessary to extract
observables. We conclude that the PIMC method is a reliable method of obtaining
results for the Hamiltonian version of the theory. Our results also clearly
demonstrate the universality between the Hamiltonian and Euclidean formulations
of lattice gauge theory. It is particularly important to take into account the
renormalization of both the anisotropy, and the Euclidean coupling ,
in obtaining these results.Comment: 10 pages, 11 figure
Zero Modes and the Atiyah-Singer Index in Noncommutative Instantons
We study the bosonic and fermionic zero modes in noncommutative instanton
backgrounds based on the ADHM construction. In k instanton background in U(N)
gauge theory, we show how to explicitly construct 4Nk (2Nk) bosonic (fermionic)
zero modes in the adjoint representation and 2k (k) bosonic (fermionic) zero
modes in the fundamental representation from the ADHM construction. The number
of fermionic zero modes is also shown to be exactly equal to the Atiyah-Singer
index of the Dirac operator in the noncommutative instanton background. We
point out that (super)conformal zero modes in non-BPS instantons are affected
by the noncommutativity. The role of Lorentz symmetry breaking by the
noncommutativity is also briefly discussed to figure out the structure of U(1)
instantons.Comment: v3: 24 pages, Latex, corrected typos, references added, to appear in
Phys. Rev.
Hamiltonian Study of Improved Lattice Gauge Theory in Three Dimensions
A comprehensive analysis of the Symanzik improved anisotropic
three-dimensional U(1) lattice gauge theory in the Hamiltonian limit is made.
Monte Carlo techniques are used to obtain numerical results for the static
potential, ratio of the renormalized and bare anisotropies, the string tension,
lowest glueball masses and the mass ratio. Evidence that rotational symmetry is
established more accurately for the Symanzik improved anisotropic action is
presented. The discretization errors in the static potential and the
renormalization of the bare anisotropy are found to be only a few percent
compared to errors of about 20-25% for the unimproved gauge action. Evidence of
scaling in the string tension, antisymmetric mass gap and the mass ratio is
observed in the weak coupling region and the behaviour is tested against
analytic and numerical results obtained in various other Hamiltonian studies of
the theory. We find that more accurate determination of the scaling
coefficients of the string tension and the antisymmetric mass gap has been
achieved, and the agreement with various other Hamiltonian studies of the
theory is excellent. The improved action is found to give faster convergence to
the continuum limit. Very clear evidence is obtained that in the continuum
limit the glueball ratio approaches exactly 2, as expected in a
theory of free, massive bosons.Comment: 13 pages, 15 figures, submitted to Phys. Rev.
How sharp is the chiral crossover phenomenon for realistic meson masses?
The mass dependence of the chiral phase transition is studied in the linear
sigma-model to leading order in a -expansion,
denoting the number of flavours. For realistic meson masses we find a smooth
crossover between to 192.6~[MeV]. The crossover looks more rapid
in the light quark condensate than in thermodynamic quantities like the energy
and entropy densities. The change in the light quark condensate in this
temperature interval is ~50\% of the zero-temperature condensate value,
while the entropy density increases by (~[GeV].
Since the numerical error is particularly large in this region, we cannot rule
out a finite latent heat smaller than 0.2~[GeV/fm]. The chiral transition
is washed out for an average pseudoscalar meson octet mass of 203~[MeV]. This
gives an upper bound on the first-order transition region in the meson mass
parameter space. The corresponding ratio of critical to realistic light current
quark masses is estimated as . This
result is by an order of magnitude larger than the corresponding mean-field
value. Therefore theComment: LaTeX, HD--TVP--94--16, Please contact authors via email for figure
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