28 research outputs found
Universal Central Extensions of Gauge Algebras and Groups
We show that the canonical central extension of the group of sections of a
Lie group bundle over a compact manifold, constructed in [NW09], is universal.
In doing so, we prove universality of the corresponding central extension of
Lie algebras in a slightly more general setting.Comment: 9 pages, LaTeX. Changes w.r.t. version 2: minor changes (final
version). To appear in J. Reine Angew. Mat
Possible alternative mechanism to SUSY: conservative extensions of the Poincar\'e group
A group theoretical mechanism is outlined, which can indecomposably extend
the Poincar\'e group by the compact internal (gauge) symmetries at the price of
allowing some nilpotent (or, more precisely: solvable) internal symmetries in
addition. Due to the presence of this nilpotent part, the prohibitive argument
of the well known Coleman-Mandula and McGlinn no-go theorems do not go through.
In contrast to SUSY or extended SUSY, in our construction the symmetries
extending the Poincar\'e group will be all internal, i.e. they do not act on
the spacetime, merely on some internal degrees of freedom -- hence the name:
conservative extensions of the Poincar\'e group. Using the Levi decomposition
and O'Raifeartaigh theorem, the general structure of all possible conservative
extensions of the Poincar\'e group is outlined, and a concrete example group is
presented with U(1) being the compact gauge group component. It is argued that
such nilpotent internal symmetries may be inapparent symmetries of some more
fundamental field variables, and therefore do not carry an ab initio
contradiction with the present experimental understanding in particle physics.
The construction is compared to (extended) SUSY, since SUSY is somewhat
analogous to the proposed mechanism. It is pointed out, however, that the
proposed mechanism is less irregular in comparison to SUSY, in certain aspects.
The only exoticity needed in comparison to a traditional gauge theory setting
is that the full group of internal symmetries is not purely compact, but is a
semi-direct product of a nilpotent and of a compact part.Comment: 10 pages, contribution to Proceedings of X. International Symposium
on Quantum Theory and Symmetries, Springer (2018
Information-theoretic postulates for quantum theory
Why are the laws of physics formulated in terms of complex Hilbert spaces?
Are there natural and consistent modifications of quantum theory that could be
tested experimentally? This book chapter gives a self-contained and accessible
summary of our paper [New J. Phys. 13, 063001, 2011] addressing these
questions, presenting the main ideas, but dropping many technical details. We
show that the formalism of quantum theory can be reconstructed from four
natural postulates, which do not refer to the mathematical formalism, but only
to the information-theoretic content of the physical theory. Our starting point
is to assume that there exist physical events (such as measurement outcomes)
that happen probabilistically, yielding the mathematical framework of "convex
state spaces". Then, quantum theory can be reconstructed by assuming that (i)
global states are determined by correlations between local measurements, (ii)
systems that carry the same amount of information have equivalent state spaces,
(iii) reversible time evolution can map every pure state to every other, and
(iv) positivity of probabilities is the only restriction on the possible
measurements.Comment: 17 pages, 3 figures. v3: some typos corrected and references updated.
Summarizes the argumentation and results of arXiv:1004.1483. Contribution to
the book "Quantum Theory: Informational Foundations and Foils", Springer
Verlag (http://www.springer.com/us/book/9789401773027), 201
On the existence of topological hairy black holes in SU(N) EYM theory with a negative cosmological constant
We investigate the existence of black hole solutions of four dimensional su(N) EYM theory with a negative cosmological constant. Our analysis differs from previous works in that we generalise the field equations to certain non-spherically symmetric spacetimes. We prove the existence of non-trivial solutions for any integer N, with N−1 gauge degrees of freedom. Specifically, we prove two results: existence of solutions for fixed values of the initial parameters and as |Λ|→∞, and existence of solutions for any Λ<0 in some neighbourhood of existing trivial solutions. In both cases we can prove the existence of `nodeless' solutions, i.e. such that all gauge field functions have no zeroes; this fact is of interest as we anticipate that some of them may be stable