919 research outputs found
The Principles of Social Order. Selected Essays of Lon L. Fuller, edited With an introduction by Kenneth I. Winston
3D N = 1 SYM Chern-Simons theory on the Lattice
We present a method to implement 3-dimensional N = 1 SUSY Yang-Mills theory
(a theory with two real supercharges containing gauge fields and an adjoint
Majorana fermion) on the lattice, including a way to implement the Chern-Simons
term present in this theory. At nonzero Chern-Simons number our implementation
suffers from a sign problem which will make the numerical effort grow
exponentially with volume. We also show that the theory with vanishing
Chern-Simons number is anomalous; its partition function identically vanishes.Comment: v2, minor changes: expanded discussion in section III c, typos
corrected, 17 pages, 9 figure
Consideration in contracts : a fundamental restatement
This lecture is an attempt to restate the law relating to consideration in contracts in the light of the actual decisions of the Courts. Study of a large number of English and Australian legal decisions convinced the author that there was a wide gulf between the conventional accounts of the doctrine of consideration and the law actually enforced in the Courts. The conventional accounts give an impression of rigidity and artificiality in the law which is not always borne out in practice. The general theme of the lecture is that consideration is not an artificial requirement of the law, but merely a search for what appear to the Courts to be good and sufficient reasons for enforcing promises. Although it is directed principally to teachers of law, the lecture also contains a good deal to interest the legal practitioner. Moreover, it will be of particular interest to bodies with responsibility for law reform, as it helps to clarify one area of the law thought by many to be in need of reform
Elliptic operators in even subspaces
In the paper we consider the theory of elliptic operators acting in subspaces
defined by pseudodifferential projections. This theory on closed manifolds is
connected with the theory of boundary value problems for operators violating
Atiyah-Bott condition. We prove an index formula for elliptic operators in
subspaces defined by even projections on odd-dimensional manifolds and for
boundary value problems, generalizing the classical result of Atiyah-Bott.
Besides a topological contribution of Atiyah-Singer type, the index formulas
contain an invariant of subspaces defined by even projections. This homotopy
invariant can be expressed in terms of the eta-invariant. The results also shed
new light on P.Gilkey's work on eta-invariants of even-order operators.Comment: 39 pages, 2 figure
Elliptic operators in odd subspaces
An elliptic theory is constructed for operators acting in subspaces defined
via odd pseudodifferential projections. Subspaces of this type arise as
Calderon subspaces for first order elliptic differential operators on manifolds
with boundary, or as spectral subspaces for self-adjoint elliptic differential
operators of odd order. Index formulas are obtained for operators in odd
subspaces on closed manifolds and for general boundary value problems. We prove
that the eta-invariant of operators of odd order on even-dimesional manifolds
is a dyadic rational number.Comment: 27 page
Asymptotics of the Heat Kernel on Rank 1 Locally Symmetric Spaces
We consider the heat kernel (and the zeta function) associated with Laplace
type operators acting on a general irreducible rank 1 locally symmetric space
X. The set of Minakshisundaram- Pleijel coefficients {A_k(X)}_{k=0}^{\infty} in
the short-time asymptotic expansion of the heat kernel is calculated
explicitly.Comment: 11 pages, LaTeX fil
Spectral curves and the mass of hyperbolic monopoles
The moduli spaces of hyperbolic monopoles are naturally fibred by the
monopole mass, and this leads to a nontrivial mass dependence of the
holomorphic data (spectral curves, rational maps, holomorphic spheres)
associated to hyperbolic multi-monopoles. In this paper, we obtain an explicit
description of this dependence for general hyperbolic monopoles of magnetic
charge two. In addition, we show how to compute the monopole mass of higher
charge spectral curves with tetrahedral and octahedral symmetries. Spectral
curves of euclidean monopoles are recovered from our results via an
infinite-mass limit.Comment: 43 pages, LaTeX, 3 figure
Some Relations between Twisted K-theory and E8 Gauge Theory
Recently, Diaconescu, Moore and Witten provided a nontrivial link between
K-theory and M-theory, by deriving the partition function of the Ramond-Ramond
fields of Type IIA string theory from an E8 gauge theory in eleven dimensions.
We give some relations between twisted K-theory and M-theory by adapting the
method of Diaconescu-Moore-Witten and Moore-Saulina. In particular, we
construct the twisted K-theory torus which defines the partition function, and
also discuss the problem from the E8 loop group picture, in which the
Dixmier-Douady class is the Neveu-Schwarz field. In the process of doing this,
we encounter some mathematics that is new to the physics literature. In
particular, the eta differential form, which is the generalization of the eta
invariant, arises naturally in this context. We conclude with several open
problems in mathematics and string theory.Comment: 23 pages, latex2e, corrected minor errors and typos in published
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