347 research outputs found
The Renormalization Group flow of unimodular f(R) gravity
Unimodular gravity is classically equivalent to General Relativity. This
equivalence extends to actions which are functions of the curvature scalar. At
the quantum level, the dynamics could differ. Most importantly, the
cosmological constant is not a coupling in the unimodular action, providing a
new vantage point from which to address the cosmological constant fine-tuning
problem. Here, a quantum theory based on the asymptotic safety scenario is
studied, and evidence for an interacting fixed point in unimodular f(R) gravity
is found. We study the fixed point and its properties, and also discuss the
compatibility of unimodular asymptotic safety with dynamical matter, finding
evidence for its compatibility with the matter degrees of freedom of the
Standard Model.Comment: 17 pages, 2 figures; new version with some clarifications, identical
to version to appear in JHE
Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gr{\"o}bner bases
This paper is a sequel to "Computing diagonal form and Jacobson normal form
of a matrix using Groebner bases", J. of Symb. Computation, 46 (5), 2011. We
present a new fraction-free algorithm for the computation of a diagonal form of
a matrix over a certain non-commutative Euclidean domain over a computable
field with the help of Gr\"obner bases. This algorithm is formulated in a
general constructive framework of non-commutative Ore localizations of
-algebras (OLGAs). We split the computation of a normal form of a matrix
into the diagonalization and the normalization processes. Both of them can be
made fraction-free. For a matrix over an OLGA we provide a diagonalization
algorithm to compute and with fraction-free entries such that
holds and is diagonal. The fraction-free approach gives us more information
on the system of linear functional equations and its solutions, than the
classical setup of an operator algebra with rational functions coefficients. In
particular, one can handle distributional solutions together with, say,
meromorphic ones. We investigate Ore localizations of common operator algebras
over and use them in the unimodularity analysis of transformation
matrices . In turn, this allows to lift the isomorphism of modules over an
OLGA Euclidean domain to a polynomial subring of it. We discuss the relation of
this lifting with the solutions of the original system of equations. Moreover,
we prove some new results concerning normal forms of matrices over non-simple
domains. Our implementation in the computer algebra system {\sc
Singular:Plural} follows the fraction-free strategy and shows impressive
performance, compared with methods which directly use fractions. Since we
experience moderate swell of coefficients and obtain simple transformation
matrices, the method we propose is well suited for solving nontrivial practical
problems.Comment: 25 pages, to appear in Journal of Symbolic Computatio
QCDF90: Lattice QCD with Fortran 90
We have used Fortran 90 to implement lattice QCD. We have designed a set of
machine independent modules that define fields (gauge, fermions, scalars,
etc...) and overloaded operators for all possible operations between fields,
matrices and numbers. With these modules it is very simple to write high-level
efficient programs for QCD simulations. To increase performances our modules
also implements assignments that do not require temporaries, and a machine
independent precision definition. We have also created a useful compression
procedure for storing the lattice configurations, and a parallel implementation
of the random generators. We have widely tested our program and modules on
several parallel and single processor supercomputers obtaining excellent
performances.Comment: LaTeX file, 8 pages, no figures. More information available at:
http://hep.bu.edu/~leviar/qcdf90.htm
A Uniqueness Theorem for Constraint Quantization
This work addresses certain ambiguities in the Dirac approach to constrained
systems. Specifically, we investigate the space of so-called ``rigging maps''
associated with Refined Algebraic Quantization, a particular realization of the
Dirac scheme. Our main result is to provide a condition under which the rigging
map is unique, in which case we also show that it is given by group averaging
techniques. Our results comprise all cases where the gauge group is a
finite-dimensional Lie group.Comment: 23 pages, RevTeX, further comments and references added (May 26. '99
Can quantum fluctuations differentiate between standard and unimodular gravity?
We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is achieved by means of a partial gauge fixing of diffeomorphisms together with a careful definition of the unimodular measure. The statement holds also in the presence of matter. As an explicit example, we consider scalar-tensor theories and compute the corresponding logarithmic divergences in both settings. In spite of significant differences in the coupling of the scalar field to gravity, the results are equivalent for all couplings, including non-minimal ones
Logic Integer Programming Models for Signaling Networks
We propose a static and a dynamic approach to model biological signaling
networks, and show how each can be used to answer relevant biological
questions. For this we use the two different mathematical tools of
Propositional Logic and Integer Programming. The power of discrete mathematics
for handling qualitative as well as quantitative data has so far not been
exploited in Molecular Biology, which is mostly driven by experimental
research, relying on first-order or statistical models. The arising logic
statements and integer programs are analyzed and can be solved with standard
software. For a restricted class of problems the logic models reduce to a
polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic
model enables enumeration of possible time resolutions in poly-logarithmic
time. Computational experiments are included
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