933 research outputs found
A String Motivated Approach to the Relativistic Point Particle
Using concepts developed in string theory, Cohen, Moore, Nelson and
Polchinski calculated the propagator for a relativistic point particle.
Following these authors we extend the technique to include the case of closed
world lines. The partition function found corresponds to the Feynmann and
Schwinger proper time formalism. We also explicitly verify that the partition
function is equivalent to the usual path length action partition function. As
an example of a sum over closed world lines, we compute the Euler-Heisenberg
effective Lagrangian in a novel way.Comment: Talk at Balfest, Salerno 200
Zhu reduction for Jacobi -point functions and applications
We establish precise Zhu reduction formulas for Jacobi -point functions which show the absence of any possible poles arising in these formulas. We then exploit this to produce results concerning the structure of strongly regular vertex operator algebras, and also to motivate new differential operators acting on Jacobi forms. Finally, we apply the reduction formulas to the Fermion model in order to create polynomials of quasi-Jacobi forms which are Jacobi forms
Definition and Calculation of the Effective Potential
Two definitions of the effective potential are given, their equivalence is explicitly shown, a sample calculation is then demonstrated for Ί^4 theory. This calculation is based on the method of steepest descent and is given in the "one-loop approximation"
On Exceptional Vertex Operator (Super) Algebras
We consider exceptional vertex operator algebras and vertex operator
superalgebras with the property that particular Casimir vectors constructed
from the primary vectors of lowest conformal weight are Virasoro descendents of
the vacuum. We show that the genus one partition function and characters for
simple ordinary modules must satisfy modular linear differential equations. We
show the rationality of the central charge and module lowest weights,
modularity of solutions, the dimension of each graded space is a rational
function of the central charge and that the lowest weight primaries generate
the algebra. We also discuss conditions on the reducibility of the lowest
weight primary vectors as a module for the automorphism group. Finally we
analyse solutions for exceptional vertex operator algebras with primary vectors
of lowest weight up to 9 and for vertex operator superalgebras with primary
vectors of lowest weight up to 17/2. Most solutions can be identified with
simple ordinary modules for known algebras but there are also four conjectured
algebras generated by weight two primaries and three conjectured extremal
vertex operator algebras generated by primaries of weight 3, 4 and 6
respectively.Comment: 37 page
On the Relationship between the Uniqueness of the Moonshine Module and Monstrous Moonshine
We consider the relationship between the conjectured uniqueness of the
Moonshine Module, , and Monstrous Moonshine, the genus zero
property of the modular invariance group for each Monster group Thompson
series. We first discuss a family of possible meromorphic orbifold
constructions of based on automorphisms of the Leech
lattice compactified bosonic string. We reproduce the Thompson series for all
51 non-Fricke classes of the Monster group together with a new relationship
between the centralisers of these classes and 51 corresponding Conway group
centralisers (generalising a well-known relationship for 5 such classes).
Assuming that is unique, we then consider meromorphic
orbifoldings of and show that Monstrous Moonshine holds if
and only if the only meromorphic orbifoldings of give
itself or the Leech theory. This constraint on the
meromorphic orbifoldings of therefore relates Monstrous
Moonshine to the uniqueness of in a new way.Comment: 53 pages, PlainTex, DIAS-STP-93-0
Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I
We define the partition and -point correlation functions for a vertex
operator superalgebra on a genus two Riemann surface formed by sewing two tori
together. For the free fermion vertex operator superalgebra we obtain a closed
formula for the genus two continuous orbifold partition function in terms of an
infinite dimensional determinant with entries arising from torus Szeg\"o
kernels. We prove that the partition function is holomorphic in the sewing
parameters on a given suitable domain and describe its modular properties.
Using the bosonized formalism, a new genus two Jacobi product identity is
described for the Riemann theta series. We compute and discuss the modular
properties of the generating function for all -point functions in terms of a
genus two Szeg\"o kernel determinant. We also show that the Virasoro vector one
point function satisfies a genus two Ward identity.Comment: A number of typos have been corrected, 39 pages. To appear in Commun.
Math. Phy
Sunshine, Sea, and Season of Birth: MS Incidence in Wales
Maternal sun exposure in gestation and throughout the lifetime is necessary for vitamin D synthesis, and living near the sea is a population level index of seafood consumption. The aim of this study was to estimate the incidence rate of multiple sclerosis (MS) in Wales and examine its association with sun exposure, coastal living, and latitude. The study used a database of MS hospital visits and admissions in Wales between 2002 and 2013. For the 1,909 lower layer super output areas (LSOAs) in Wales, coastal status, population, longitude/latitude, and average sunshine hours per day were obtained. Age-specific and age-standardised MS incidence were calculated and modelled using Poisson regression. The distribution of births by month was compared between MS cases and the combined England and Wales population. There were 3,557 new MS cases between 2002 and 2013, with an average annual incidence of 8.14 (95% CI: 7.69-8.59) among males and 12.97 (95% CI: 12.44-13.50) among females per 100,000 population. The female-to-male ratio was 1.86:1. For both sexes combined, the average annual incidence rate was 9.10 (95% CI: 8.80-9.40). All figures are age-standardized to the 1976 European standard population. Compared to the combined England and Wales population, more people with MS were born in April, observed-to-expected ratio: 1.21 (95% CI: 1.08-1.36). MS incidence varied directly with latitude and inversely with sunshine hours. Proximity to the coast was associated with lower MS incidence only in easterly areas. This study shows that MS incidence rate in Wales is comparable to the rate in Scotland and is associated with environmental factors that probably represent levels of vitamin D
Manipulating Heat Shock Factor-1 in Xenopus Tadpoles: Neuronal Tissues Are Refractory to Exogenous Expression
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