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Lattice Coulomb Hamiltonian and Static Color-Coulomb Field
The lattice Coulomb-gauge hamiltonian is derived from the transfer matrix of
Wilson's Euclidean lattice gauge theory, wherein the lattice form of Gauss's
law is satisfied identically. The restriction to a fundamental modular region
(no Gribov copies) is implemented in an effective hamiltonian by the addition
of a "horizon function" to the lattice Coulomb-gauge hamiltonian. Its
coefficient is a thermodynamic parameter that ultimately sets the
scale for hadronic mass, and which is related to the bare coupling constant
by a "horizon condition". This condition determines the low-momentum
behavior of the (ghost) propagator that transmits the instantaneous
longitudinal color-electric field, and thereby provides for a confinement-like
feature in leading order in a new weak-coupling expansion.Comment: 110 pages + 1 fig., uuencoded compressed tar-file (190 kb) revised
and shortened for readability. Technical derivations relegated to appendices.
Concepts clarified in Introduction and Conclusion. One figure adde
Modular and lower-modular elements of lattices of semigroup varieties
The paper contains three main results. First, we show that if a commutative
semigroup variety is a modular element of the lattice Com of all commutative
semigroup varieties then it is either the variety COM of all commutative
semigroups or a nil-variety or the join of a nil-variety with the variety of
semilattices. Second, we prove that if a commutative nil-variety is a modular
element of Com then it may be given within COM by 0-reduced and substitutive
identities only. Third, we completely classify all lower-modular elements of
Com. As a corollary, we prove that an element of Com is modular whenever it is
lower-modular. All these results are precise analogues of results concerning
modular and lower-modular elements of the lattice of all semigroup varieties
obtained earlier by Jezek, McKenzie, Vernikov, and the author. As an
application of a technique developed in this paper, we provide new proofs of
the `prototypes' of the first and the third our results.Comment: 15 page
Orbifolds of Lattice Vertex Operator Algebras at and
Motivated by the notion of extremal vertex operator algebras, we investigate
cyclic orbifolds of vertex operator algebras coming from extremal even
self-dual lattices in and . In this way we construct about one
hundred new examples of holomorphic VOAs with a small number of low weight
states.Comment: 18 pages, LaTe
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