2,798 research outputs found
U-duality in three and four dimensions
Using generalised geometry we study the action of U-duality acting in three
and four dimensions on the bosonic fields of eleven dimensional supergravity.
We compare the U-duality symmetry with the T-duality symmetry of double field
theory and see how the and SL(5) U-duality groups reduce
to the SO(2,2) and SO(3,3) T-duality symmetry groups of the type IIA theory. As
examples we dualise M2-branes, both black and extreme. We find that uncharged
black M2-branes become charged under U-duality, generalising the Harrison
transformation, while extreme M2-branes will become new extreme M2-branes. The
resulting tension and charges are quantised appropriately if we use the
discrete U-duality group .Comment: v1: 35 pages; v2: minor corrections in section 4.1.2, many references
added; v3: further discussion added on the conformal factor of the
generalised metric in section 2 and on the Wick-rotation used to construct
examples in section
Quantization on a torus without position operators
We formulate quantum mechanics in the two-dimensional torus without using
position operators. We define an algebra with only momentum operators and shift
operators and construct irreducible representation of the algebra. We show that
it realizes quantum mechanics of a charged particle in a uniform magnetic
field. We prove that any irreducible representation of the algebra is unitary
equivalent to each other. This work provides a firm foundation for the
noncommutative torus theory.Comment: 12 pages, LaTeX2e, the title is changed, minor corrections are made,
references are added. To be published in Modern Physics Letters
Three results on representations of Mackey Lie algebras
I. Penkov and V. Serganova have recently introduced, for any non-degenerate
pairing of vector spaces, the Lie algebra
consisting of endomorphisms of whose
duals preserve . In their work, the category
of -modules which are finite
length subquotients of the tensor algebra is singled out and
studied. In this note we solve three problems posed by these authors concerning
the categories . Denoting by
the category with the same objects as
but regarded as -modules, we first
show that when and are paired by dual bases, the functor
taking a module to
its largest weight submodule with respect to a sufficiently nice Cartan
subalgebra of is a tensor equivalence. Secondly, we prove that
when and are countable-dimensional, the objects of
have finite length as -modules.
Finally, under the same hypotheses, we compute the socle filtration of a simple
object in as a -module.Comment: 9 page
Reciprocal relativity of noninertial frames: quantum mechanics
Noninertial transformations on time-position-momentum-energy space {t,q,p,e}
with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and
the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of
transformations contains the Lorentz group as the inertial special case. In the
limit of small forces and velocities, it reduces to the expected Hamilton
transformations leaving invariant the symplectic metric and the nonrelativistic
line element ds^2=dt^2. The U(1,3) transformations bound relative velocities by
c and relative forces by b. Spacetime is no longer an invariant subspace but is
relative to noninertial observer frames. Born was lead to the metric by a
concept of reciprocity between position and momentum degrees of freedom and for
this reason we call this reciprocal relativity.
For large b, such effects will almost certainly only manifest in a quantum
regime. Wigner showed that special relativistic quantum mechanics follows from
the projective representations of the inhomogeneous Lorentz group. Projective
representations of a Lie group are equivalent to the unitary reprentations of
its central extension. The same method of projective representations of the
inhomogeneous U(1,3) group is used to define the quantum theory in the
noninertial case. The central extension of the inhomogeneous U(1,3) group is
the cover of the quaplectic group Q(1,3)=U(1,3)*s H(4). H(4) is the
Weyl-Heisenberg group. A set of second order wave equations results from the
representations of the Casimir operators
Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes
This article aims at advancing the recently introduced exponential method for
renormalisation in perturbative quantum field theory. It is shown that this new
procedure provides a meaningful recursive scheme in the context of the
algebraic and group theoretical approach to renormalisation. In particular, we
describe in detail a Hopf algebraic formulation of Bogoliubov's classical
R-operation and counterterm recursion in the context of momentum subtraction
schemes. This approach allows us to propose an algebraic classification of
different subtraction schemes. Our results shed light on the peculiar algebraic
role played by the degrees of Taylor jet expansions, especially the notion of
minimal subtraction and oversubtractions.Comment: revised versio
Weak commutation relations of unbounded operators: nonlinear extensions
We continue our analysis of the consequences of the commutation relation
[S,T]=\Id, where and are two closable unbounded operators. The {\em
weak} sense of this commutator is given in terms of the inner product of the
Hilbert space \H where the operators act. {We also consider what we call,
adopting a physical terminology}, a {\em nonlinear} extension of the above
commutation relations
A generalized no-broadcasting theorem
We prove a generalized version of the no-broadcasting theorem, applicable to
essentially \emph{any} nonclassical finite-dimensional probabilistic model
satisfying a no-signaling criterion, including ones with ``super-quantum''
correlations. A strengthened version of the quantum no-broadcasting theorem
follows, and its proof is significantly simpler than existing proofs of the
no-broadcasting theorem.Comment: 4 page
Fourier Duality as a Quantization Principle
The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes
essential use of Fourier duality. The extension of this property to more
general phase spaces requires the use of Kac algebras, which provide the
necessary background for the implementation of Fourier duality on general
locally compact groups. Kac algebras -- and the duality they incorporate -- are
consequently examined as candidates for a general quantization framework
extending the usual formalism. Using as a test case the simplest non-trivial
phase space, the half-plane, it is shown how the structures present in the
complete-plane case must be modified. Traces, for example, must be replaced by
their noncommutative generalizations - weights - and the correspondence
embodied in the Weyl-Wigner formalism is no more complete. Provided the
underlying algebraic structure is suitably adapted to each case, Fourier
duality is shown to be indeed a very powerful guide to the quantization of
general physical systems.Comment: LaTeX 2.09 with NFSS or AMSLaTeX 1.1. 97Kb, 43 pages, no figures.
requires subeqnarray.sty, amssymb.sty, amsfonts.sty. Final version with (few)
text and (crucial) typos correction
Determination of the relative effects of temperature, pH and water activity in food systems: a meta-analysis study
The aim of this study is to use ComBase to determine the relative effects of temperature, pH, and water activity in the
inactivation rates of Salmonella enterica in a range of foods. This is performed to determine whether any of the above factors
have a dominant effect on survival. The inactivation rates of Salmonella were obtained from original raw data in the ComBase
browser and from complete ComBase data for Salmonella. A total of 972 data of different types of food systems and data of
individual types of food from ComBase were analysed. Over the range of 0–90°C, the z values calculated for the food data is
14°C. At 0–46°C relevant to intermediate moisture foods (IMF), the z values for the food data was 22°C, indicating a
moderate effect of temperature. The z value for inactivation at 47–90°C was 11°C, indicating that temperature has an important
effect on survival. This study shows that the effect of temperature is clearer at high temperatures than in the low temperature
region. It suggests that the inactivation of Salmonella in food systems is slightly dominated by temperature and that the pH
and aw levels appear to be less influential
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