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General Formalism For the BRST Symmetry
In this paper we will discuss Faddeev-Popov method for field theories with a
gauge symmetry in an abstract way. We will then develope a general formalism
for dealing with the BRST symmetry. This formalism will make it possible to
analyse the BRST symmetry for any theory.Comment: Published in Communications in Theoretical Physic
Clustering in complex networks. I. General formalism
We develop a full theoretical approach to clustering in complex networks. A
key concept is introduced, the edge multiplicity, that measures the number of
triangles passing through an edge. This quantity extends the clustering
coefficient in that it involves the properties of two --and not just one--
vertices. The formalism is completed with the definition of a three-vertex
correlation function, which is the fundamental quantity describing the
properties of clustered networks. The formalism suggests new metrics that are
able to thoroughly characterize transitive relations. A rigorous analysis of
several real networks, which makes use of the new formalism and the new
metrics, is also provided. It is also found that clustered networks can be
classified into two main groups: the {\it weak} and the {\it strong
transitivity} classes. In the first class, edge multiplicity is small, with
triangles being disjoint. In the second class, edge multiplicity is high and so
triangles share many edges. As we shall see in the following paper, the class a
network belongs to has strong implications in its percolation properties
Theory of continuum percolation I. General formalism
The theoretical basis of continuum percolation has changed greatly since its
beginning as little more than an analogy with lattice systems. Nevertheless,
there is yet no comprehensive theory of this field. A basis for such a theory
is provided here with the introduction of the Potts fluid, a system of
interacting -state spins which are free to move in the continuum. In the limit, the Potts magnetization, susceptibility and correlation functions
are directly related to the percolation probability, the mean cluster size and
the pair-connectedness, respectively. Through the Hamiltonian formulation of
the Potts fluid, the standard methods of statistical mechanics can therefore be
used in the continuum percolation problem.Comment: 26 pages, Late
Conformal Invariance and Electrodynamics: Applications and General Formalism
The role of the conformal group in electrodynamics in four space-time
dimensions is re-examined. As a pedagogic example we use the application of
conformal transformations to find the electromagnetic field for a charged
particle moving with a constant relativistic acceleration from the Coulomb
electric field for the particle at rest. We also re-consider the reformulation
of Maxwell's equations on the projective cone, which is isomorphic to a
conformal compactification on Minkowski space, so that conformal
transformations, belonging to the group O(4,2), are realised linearly. The
resulting equations are different from those postulated previously and respect
additional gauge invariances which play an essential role in ensuring
consistency with conventional electrodynamics on Minkowski space. The solution
on the projective cone corresponding to a constantly accelerating charged
particle is discussed.Comment: 24 pages, 1 figure, plain tex, uses harvmac, eps
N-fold Supersymmetry in Quantum Mechanics - General Formalism -
We report general properties of N-fold supersymmetry in one-dimensional
quantum mechanics. N-fold supersymmetry is characterized by supercharges which
are N-th polynomials of momentum. Relations between the anti-commutator of the
supercharges and the Hamiltonian, the spectra, the Witten index, the
non-renormalization theorems and the quasi-solvability are examined. We also
present further investigation about a particular class of N-fold supersymmetric
models which we dubbed type A. Algebraic equations which determine a part of
spectra of type A models are presented, and the non-renormalization theorem are
generalized. Finally, we present a possible generalization of N-fold
supersymmetry in multi-dimensional quantum mechanics.Comment: 25 page
New partitioning perturbation theory. 1 - General formalism
General formalism of partitioning perturbation theory - Part
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