77,914 research outputs found
Creator-annihilator domains and the number operator
We show that for the bosonic Fock representation in infinite dimensions, the
maximal common domain of all creators and annihilators properly contains the
domain of the square-root of the number operator.Comment: 7 pages, no figure
'Twisted duality' for Clifford Algebras
Viewing the complex Clifford algebra of a real inner product space
as a superalgebra, we offer several proofs of the fact that if is a
subspace of the complexification of then the supercommutant of the Clifford
algebra is precisely the Clifford algebra .Comment: 8 page
A tangential approach to trigonometry
We construct the complex tangent as a meromorphic function in the plane,
using an approach developed by Weierstrass in his characterization of analytic
functions that satisfy algebraic addition theorems
Remarks on trigonometric functions after Eisenstein
We modify the Whittaker-Watson account of the Eisenstein approach to the
trigonometric functions, basing these functions independently on the Eisenstein
function
completeness for Fourier series
We note that the Fubini theorem may be used to prove that an function
is determined by its Fourier coefficients
Implicational Completeness
We present a proof of completeness for the implicational propositional
calculus, based on a variant of the Lindenbaum procedure
Conservative inclusion of N\"orlund methods
We offer practical necessary and sufficient conditions in order that every
sequence convergent relative to the N\"orlund summation method be
convergent relative to the N\"orlund summation method without the
requirement that limits be preserved
Automorphisms of Quadratic Liouville Structures
We examine the diffeomorphisms of a symplectic vector space that preserve a
chosen symplectic potential. Our examination yields an explicit description of
these diffeomorphisms when the chosen potential differs from the canonical
potential by the differential of a homogeneous quadratic in one of three broad
classes.Comment: 8 page
Normalization conventions for Newton's constant and the Planck scale in arbitrary spacetime dimension
We calculate, in d spacetime dimensions, the relationship between the
coefficient 1/K^2 of the Einstein-Hilbert term in the action of general
relativity and the coefficient G_N of the force law that results from the
Newtonian limit of general relativity. The result is
K^2=2[(d-2)/(d-3)]Vol(S^[d-2])G_N, where Vol(S^n) is the volume of the unit
n-sphere. While the d=4 case is an elementary calculation in any general
relativity text, the arbitrary case presented here is slightly less well known.
We discuss the relevance of this result for the definition of the so-called
"reduced Planck mass" and comment very briefly on the implications for brane
world models. [abstract abridged]Comment: 4 pages, 2 figures, RevTeX
Neville's primitive elliptic functions: the case
The vanishing of the invariant attached to a lattice singles
out a midpoint lattice and yields a square-root of the associated Weierstrass
function
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