6,254 research outputs found
Gerbes and Heisenberg's Uncertainty Principle
We prove that a gerbe with a connection can be defined on classical phase
space, taking the U(1)-valued phase of certain Feynman path integrals as Cech
2-cocycles. A quantisation condition on the corresponding 3-form field strength
is proved to be equivalent to Heisenberg's uncertainty principle.Comment: 12 pages, 1 figure available upon reques
Path-Integral for Quantum Tunneling
Path-integral for theories with degenerate vacua is investigated. The origin
of the non Borel-summability of the perturbation theory is studied. A new
prescription to deal with small coupling is proposed. It leads to a series,
which at low orders and small coupling differs from the ordinary perturbative
series by nonperturbative amount, but is Borel-summable.Comment: 25 pages + 12 figures (not included, but available upon request) [No
changed in content in this version. Problem with line length fixed.
The transition temperature of the dilute interacting Bose gas for internal degrees of freedom
We calculate explicitly the variation of the Bose-Einstein
condensation temperature induced by weak repulsive two-body interactions
to leading order in the interaction strength. As shown earlier by general
arguments, is linear in the dimensionless product
to leading order, where is the density and the scattering length. This
result is non-perturbative, and a direct perturbative calculation of the
amplitude is impossible due to infrared divergences familiar from the study of
the superfluid helium lambda transition. Therefore we introduce here another
standard expansion scheme, generalizing the initial model which depends on one
complex field to one depending on real fields, and calculating the
temperature shift at leading order for large . The result is explicit and
finite. The reliability of the result depends on the relevance of the large
expansion to the situation N=2, which can in principle be checked by systematic
higher order calculations. The large result agrees remarkably well with
recent numerical simulations.Comment: 10 pages, Revtex, submitted to Europhysics Letter
Refined Cauchy/Littlewood identities and six-vertex model partition functions: II. Proofs and new conjectures
We prove two identities of Hall-Littlewood polynomials, which appeared
recently in a paper by two of the authors. We also conjecture, and in some
cases prove, new identities which relate infinite sums of symmetric polynomials
and partition functions associated with symmetry classes of alternating sign
matrices. These identities generalize those already found in our earlier paper,
via the introduction of additional parameters. The left hand side of each of
our identities is a simple refinement of a relevant Cauchy or Littlewood
identity. The right hand side of each identity is (one of the two factors
present in) the partition function of the six-vertex model on a relevant
domain.Comment: 34 pages, 14 figure
A Weyl-covariant tensor calculus
On a (pseudo-) Riemannian manifold of dimension n > 2, the space of tensors
which transform covariantly under Weyl rescalings of the metric is built. This
construction is related to a Weyl-covariant operator D whose commutator [D,D]
gives the conformally invariant Weyl tensor plus the Cotton tensor. So-called
generalized connections and their transformation laws under diffeomorphisms and
Weyl rescalings are also derived. These results are obtained by application of
BRST techniques.Comment: LaTeX, 10 pages. Minor corrections and a reference adde
The prediction of nonlinear longitudinal combustion instability in liquid propellant rockets
An analytical technique was developed to solve nonlinear longitudinal combustion instability problems. The analysis yields the transient and limit cycle behavior of unstable motors and the threshold amplitude required to trigger a linearly stable motor into unstable operation. The limit cycle waveforms were found to exhibit shock wave characteristics for most unstable engine operating conditions. A method of correlating the analytical solutions with experimental data was developed. Calculated results indicate that a second-order solution adequately describes the behavior of combustion instability oscillations over a broad range of engine operating conditions, but that higher order effects must be accounted for in order to investigate engine triggering
Discrete holomorphicity and quantized affine algebras
We consider non-local currents in the context of quantized affine algebras,
following the construction introduced by Bernard and Felder. In the case of
and , these currents can be identified with
configurations in the six-vertex and Izergin--Korepin nineteen-vertex models.
Mapping these to their corresponding Temperley--Lieb loop models, we directly
identify non-local currents with discretely holomorphic loop observables. In
particular, we show that the bulk discrete holomorphicity relation and its
recently derived boundary analogue are equivalent to conservation laws for
non-local currents
The two-point correlation function of three-dimensional O(N) models: critical limit and anisotropy
In three-dimensional O(N) models, we investigate the low-momentum behavior of
the two-point Green's function G(x) in the critical region of the symmetric
phase. We consider physical systems whose criticality is characterized by a
rotational-invariant fixed point. Several approaches are exploited, such as
strong-coupling expansion of lattice non-linear O(N) sigma models,
1/N-expansion, field-theoretical methods within the phi^4 continuum
formulation. In non-rotational invariant physical systems with O(N)-invariant
interactions, the vanishing of space-anisotropy approaching the
rotational-invariant fixed point is described by a critical exponent rho, which
is universal and is related to the leading irrelevant operator breaking
rotational invariance. At N=\infty one finds rho=2. We show that, for all
values of , . Non-Gaussian corrections to the universal
low-momentum behavior of G(x) are evaluated, and found to be very small.Comment: 65 pages, revte
Branching rate expansion around annihilating random walks
We present some exact results for branching and annihilating random walks. We
compute the nonuniversal threshold value of the annihilation rate for having a
phase transition in the simplest reaction-diffusion system belonging to the
directed percolation universality class. Also, we show that the accepted
scenario for the appearance of a phase transition in the parity conserving
universality class must be improved. In order to obtain these results we
perform an expansion in the branching rate around pure annihilation, a theory
without branching. This expansion is possible because we manage to solve pure
annihilation exactly in any dimension.Comment: 5 pages, 5 figure
On the sign of kurtosis near the QCD critical point
We point out that the quartic cumulant (and kurtosis) of the order parameter
fluctuations is universally negative when the critical point is approached on
the crossover side of the phase separation line. As a consequence, the kurtosis
of a fluctuating observable, such as, e.g., proton multiplicity, may become
smaller than the value given by independent Poisson statistics. We discuss
implications for the Beam Energy Scan program at RHIC.Comment: 4 pages, 2 figure
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