45 research outputs found
Two uniqueness results on the Unruh effect and on PCT-symmetry
The Unruh effect and a closely related form of PCT-symmetry have been proved
in general for finite-component Wightman fields by Bisognano and Wichmann.
While this result incorporates most of the fields occurring in four-dimensional
high-energy physics, there still are field theories of interest that are not
covered (e.g., low-dimensional anyon fields and infinite-component fields).
From the spectrum condition, Borchers has derived a couple of commutation
relations which 'almost, but only almost' imply the Unruh effect and
PCT-symmetry. We show that this result does imply the Unruh effect and
PCT-symmetry provided that the operators involved in Borchers' commutation
relations act geometrically on a local net of observables.Comment: 33 pages, 4 figures, minor stylistic corrections in revised versio
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
Passive States for Essential Observers
The aim of this note is to present a unified approach to the results given in
\cite{bb99} and \cite{bs04} which also covers examples of models not presented
in these two papers (e.g. -dimensional Minkowski space-time for ).
Assuming that a state is passive for an observer travelling along certain
(essential) worldlines, we show that this state is invariant under the isometry
group, is a KMS-state for the observer at a temperature uniquely determined by
the structure constants of the Lie algebra involved and fulfills (a variant of)
the Reeh-Schlieder property. Also the modular objects associated to such a
state and the observable algebra of an observer are computed and a version of
weak locality is examined.Comment: 27 page
Remarks on the Configuration Space Approach to Spin-Statistics
The angular momentum operators for a system of two spin-zero
indistinguishable particles are constructed, using Isham's Canonical Group
Quantization method. This mathematically rigorous method provides a hint at the
correct definition of (total) angular momentum operators, for arbitrary spin,
in a system of indistinguishable particles. The connection with other
configuration space approaches to spin-statistics is discussed, as well as the
relevance of the obtained results in view of a possible alternative proof of
the spin-statistics theorem.Comment: 18 page
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
Could Only Fermions Be Elementary?
In standard Poincare and anti de Sitter SO(2,3) invariant theories,
antiparticles are related to negative energy solutions of covariant equations
while independent positive energy unitary irreducible representations (UIRs) of
the symmetry group are used for describing both a particle and its
antiparticle. Such an approach cannot be applied in de Sitter SO(1,4) invariant
theory. We argue that it would be more natural to require that (*) one UIR
should describe a particle and its antiparticle simultaneously. This would
automatically explain the existence of antiparticles and show that a particle
and its antiparticle are different states of the same object. If (*) is adopted
then among the above groups only the SO(1,4) one can be a candidate for
constructing elementary particle theory. It is shown that UIRs of the SO(1,4)
group can be interpreted in the framework of (*) and cannot be interpreted in
the standard way. By quantizing such UIRs and requiring that the energy should
be positive in the Poincare approximation, we conclude that i) elementary
particles can be only fermions. It is also shown that ii) C invariance is not
exact even in the free massive theory and iii) elementary particles cannot be
neutral. This gives a natural explanation of the fact that all observed neutral
states are bosons.Comment: The paper is considerably revised and the following results are
added: in the SO(1,4) invariant theory i) the C invariance is not exact even
for free massive particles; ii) neutral particles cannot be elementar
Commissioning of the vacuum system of the KATRIN Main Spectrometer
The KATRIN experiment will probe the neutrino mass by measuring the
beta-electron energy spectrum near the endpoint of tritium beta-decay. An
integral energy analysis will be performed by an electro-static spectrometer
(Main Spectrometer), an ultra-high vacuum vessel with a length of 23.2 m, a
volume of 1240 m^3, and a complex inner electrode system with about 120000
individual parts. The strong magnetic field that guides the beta-electrons is
provided by super-conducting solenoids at both ends of the spectrometer. Its
influence on turbo-molecular pumps and vacuum gauges had to be considered. A
system consisting of 6 turbo-molecular pumps and 3 km of non-evaporable getter
strips has been deployed and was tested during the commissioning of the
spectrometer. In this paper the configuration, the commissioning with bake-out
at 300{\deg}C, and the performance of this system are presented in detail. The
vacuum system has to maintain a pressure in the 10^{-11} mbar range. It is
demonstrated that the performance of the system is already close to these
stringent functional requirements for the KATRIN experiment, which will start
at the end of 2016.Comment: submitted for publication in JINST, 39 pages, 15 figure