30 research outputs found
Spin, Statistics, and Reflections, I. Rotation Invariance
The universal covering of SO(3) is modelled as a reflection group G_R in a
representation independent fashion. For relativistic quantum fields, the Unruh
effect of vacuum states is known to imply an intrinsic form of reflection
symmetry, which is referred to as "modular P_1CT-symmetry (Bisognano, Wichmann,
1975, 1976, and Guido, Longo, [funct-an/9406005]). This symmetry is used to
construct a representation of G_R by pairs of modular P_1CT-operators. The
representation thus obtained satisfies Pauli's spin-statistics relation.Comment: Accepted for publication in Ann. H. Poincare, (annoying) misprints
correcte
Spin & Statistics in Nonrelativistic Quantum Mechanics, II
Recently a sufficient and necessary condition for Pauli's spin- statistics
connection in nonrelativistic quantum mechanics has been established
[quant-ph/0208151]. The two-dimensional part of this result is extended to
n-particle systems and reformulated and further simplified in a more geometric
language.Comment: 1 figur
Spin, Statistics, and Reflections, II. Lorentz Invariance
The analysis of the relation between modular PCT-symmetry -- a
consequence of the Unruh effect -- and Pauli's spin-statistics relation is
continued. The result in the predecessor to this article is extended to the
Lorentz symmetric situation. A model \G_L of the universal covering
\widetilde{L_+^\uparrow}\cong SL(2,\complex) of the restricted Lorentz group
is modelled as a reflection group at the classical level. Based
on this picture, a representation of \G_L is constructed from pairs of
modular PCT-conjugations, and this representation can easily be verified to
satisfy the spin-statistics relation
Spin & Statistics in Nonrelativistic Quantum Mechanics, I
A necessary and sufficient condition for Pauli's spin-statistics relation is
given for nonrelativistic anyons, bosons, and fermions in two and three spatial
dimensions.
For any point particle species in two spatial dimensions, denote by J the
total (i.e., spin plus orbital) angular momentum of a single particle, and
denote by j the total angular momentum of the corresponding two-particle system
with respect to its center of mass. In three spatial dimensions, write J_z and
j_z for the z-components of these vector operators.
In two spatial dimensions, the spin statistics connection holds if and only
if there exists a unitary operator U such that j=2UJU^*. In three dimensions,
the analogous relation cannot hold as it stands, but restricting it to an
appropriately chosen subspace of the state space yields a sufficient and
necessary condition for the spin-statistics connection.Comment: 15 pages, revised and polished versio
A New Approach to Spin and Statistics
We give an algebraic proof of the spin-statistics connection for the
parabosonic and parafermionic quantum topological charges of a theory of local
observables with a modular PCT-symmetry. The argument avoids the use of the
spinor calculus and also works in 1+2 dimensions. It is expected to be a
progress towards a general spin-statistics theorem including also
(1+2)-dimensional theories with braid group statistics.Comment: LATEX, 15 pages, no figure
-Boundedness, Semipassivity, and the KMS-Condition
The proof of a recent result by Guido and Longo establishing the equivalence
of the KMS-condition with complete -boundedness is shortcut and
generalized in such a way that a covariant version of the theorem is obtained.Comment: 7 pages, 'complete' inserted in statement of main theore