742 research outputs found
Prolegomena to an operator theory of computation
Defining computation as information processing (information dynamics) with information as a relational property of data structures (the difference in one system that makes a difference in another system) makes it very suitable to use operator formulation, with similarities to category theory. The concept of the operator is exceedingly important in many knowledge areas as a tool of theoretical studies and practical applications. Here we introduce the operator theory of computing, opening new opportunities for the exploration of computing devices, processes, and their networks
On higher-derivative gauge theories
In this work we study the main properties and the one-loop renormalization of
a Yang-Mills theory in which the kinetic term contains also a fourth-order
differential operator; in particular, we add to the Yang-Mills Lagrangian the
most general contribution of mass dimension six, weighted with a dimensionful
parameter. This model is renormalizable; in the literature two values for the
beta function for the gauge coupling have been reported, one obtained using the
heat kernel approach and one with Feynman diagrams. In this work we repeat the
computation using heat kernel techniques confirming the latter result. We also
considered coupling with matter.
We then study the supersymmetric extension of the model; this is a nontrivial
task because of the complicate structure of the higher-derivative term. Some
partial results were known, but a computation of the beta functions for the
full supersymmetric non-Abelian higher-derivative gauge theory was missing. We
make use of the (unextended) supersymmetric higher-derivative Lagrangian
density for the Yang-Mills field in six spacetime dimensions derived in
arXiv:hep-th/0505082; by dimensional reduction we obtain the N=1 and N=2
supersymmetric higher-derivative super-Yang-Mills Lagrangian in four spacetime
dimensions, whose beta function we evaluate using heat kernels. We also deduce
the beta function for N=4 supersymmetry.Comment: Based on the thesis prepared as final dissertation for the MSc degree
in Physics at the University of Padova. 68 pages; added reference in 1.
Bases for qudits from a nonstandard approach to SU(2)
Bases of finite-dimensional Hilbert spaces (in dimension d) of relevance for
quantum information and quantum computation are constructed from angular
momentum theory and su(2) Lie algebraic methods. We report on a formula for
deriving in one step the (1+p)p qupits (i.e., qudits with d = p a prime
integer) of a complete set of 1+p mutually unbiased bases in C^p. Repeated
application of the formula can be used for generating mutually unbiased bases
in C^d with d = p^e (e > or = 2) a power of a prime integer. A connection
between mutually unbiased bases and the unitary group SU(d) is briefly
discussed in the case d = p^e.Comment: From a talk presented at the 13th International Conference on
Symmetry Methods in Physics (Dubna, Russia, 6-9 July 2009) organized in
memory of Prof. Yurii Fedorovich Smirnov by the Bogoliubov Laboratory of
Theoretical Physics of the JINR and the ICAS at Yerevan State University
Clifford quantum computer and the Mathieu groups
One learned from Gottesman-Knill theorem that the Clifford model of quantum
computing \cite{Clark07} may be generated from a few quantum gates, the
Hadamard, Phase and Controlled-Z gates, and efficiently simulated on a
classical computer. We employ the group theoretical package GAP\cite{GAP} for
simulating the two qubit Clifford group . We already found that
the symmetric group S(6), aka the automorphism group of the generalized
quadrangle W(2), controls the geometry of the two-qubit Pauli graph
\cite{Pauligraphs}. Now we find that the {\it inner} group
exactly contains
two normal subgroups, one isomorphic to (of order
16), and the second isomorphic to the parent (of order 5760) of the
alternating group A(6). The group stabilizes an {\it hexad} in the
Steiner system attached to the Mathieu group M(22). Both groups
A(6) and have an {\it outer} automorphism group , a feature we associate to two-qubit quantum entanglement.Comment: version for the journal Entrop
A new integrable system on the sphere and conformally equivariant quantization
Taking full advantage of two independent projectively equivalent metrics on
the ellipsoid leading to Liouville integrability of the geodesic flow via the
well-known Jacobi-Moser system, we disclose a novel integrable system on the
sphere , namely the "dual Moser" system. The latter falls, along with the
Jacobi-Moser and Neumann-Uhlenbeck systems, into the category of (locally)
St\"ackel systems. Moreover, it is proved that quantum integrability of both
Neumann-Uhlenbeck and dual Moser systems is insured by means of the conformally
equivariant quantization procedure.Comment: LaTeX, 33 pages. Minor corrections. Published versio
Renormalized Kaluza-Klein theories
Using six-dimensional quantum electrodynamics () as an example we
study the one-loop renormalization of the theory both from the six and
four-dimensional points of view. Our main conclusion is that the properly
renormalized four dimensional theory never forgets its higher dimensional
origin. In particular, the coefficients of the neccessary extra counterterms in
the four dimensional theory are determined in a precise way. We check our
results by studying the reduction of on a two-torus.Comment: LaTeX, 36 pages. A new section added; references improved, typos
fixe
Open Boundary Condition, Wilson Flow and the Scalar Glueball Mass
A major problem with periodic boundary condition on the gauge fields used in
current lattice gauge theory simulations is the trapping of topological charge
in a particular sector as the continuum limit is approached. To overcome this
problem open boundary condition in the temporal direction has been proposed
recently. One may ask whether open boundary condition can reproduce the
observables calculated with periodic boundary condition. In this work we find
that the extracted lowest glueball mass using open and periodic boundary
conditions at the same lattice volume and lattice spacing agree for the range
of lattice scales explored in the range 3 GeV 1/a 5 GeV. The
problem of trapping is overcome to a large extent with open boundary and we are
able to extract the glueball mass at even larger lattice scale 5.7
GeV. To smoothen the gauge fields and to reduce the cut off artifacts recently
proposed Wilson flow is used. The extracted glueball mass shows remarkable
insensitivity to the lattice spacings in the range explored in this work, 3 GeV
1/a 5.7 GeV.Comment: Replacement agrees with published versio
First-Quantized Theory of Expanding Universe from Field Quantization in Mini-Superspace
We propose an improved variant of the third-quantization scheme, for the
spatially homogeneous and isotropic cosmological models in Einstein gravity
coupled with a neutral massless scalar field. Our strategy is to specify a
semi-Riemannian structure on the mini-superspace and to consider the quantum
Klein-Gordon field on the mini-superspace. Then, the Hilbert space of this
quantum system becomes inseparable, which causes the creation of infinite
number of universes. To overcome this issue, we introduce a vector bundle
structure on the Hilbert space and the connection of the vector bundle. Then,
we can define a consistent unitary time evolution of the quantum universe in
terms of the connection field on the vector bundle. By doing this, we are able
to treat the quantum dynamics of a single-universe state. We also find an
appropriate observable set constituting the CCR-algebra, and obtain the
Schr\"odinger equation for the wave function of the single-universe state. We
show that the present quantum theory correctly reproduces the classical
solution to the Einstein equation.Comment: 21 pages, 1 figure, published versio
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