854 research outputs found
Dirac Quantization of Parametrized Field Theory
Parametrized field theory (PFT) is free field theory on flat spacetime in a
diffeomorphism invariant disguise. It describes field evolution on arbitrary
foliations of the flat spacetime instead of only the usual flat ones, by
treating the `embedding variables' which describe the foliation as dynamical
variables to be varied in the action in addition to the scalar field. A formal
Dirac quantization turns the constraints of PFT into functional Schrodinger
equations which describe evolution of quantum states from an arbitrary Cauchy
slice to an infinitesimally nearby one.This formal Schrodinger picture- based
quantization is unitarily equivalent to the standard Heisenberg picture based
Fock quantization of the free scalar field if scalar field evolution along
arbitrary foliations is unitarily implemented on the Fock space. Torre and
Varadarajan (TV) showed that for generic foliations emanating from a flat
initial slice in spacetimes of dimension greater than 2, evolution is not
unitarily implemented, thus implying an obstruction to Dirac quantization.
We construct a Dirac quantization of PFT,unitarily equivalent to the standard
Fock quantization, using techniques from Loop Quantum Gravity (LQG) which are
powerful enough to super-cede the no- go implications of the TV results. The
key features of our quantization include an LQG type representation for the
embedding variables, embedding dependent Fock spaces for the scalar field, an
anomaly free representation of (a generalization of) the finite transformations
generated by the constraints and group averaging techniques. The difference
between 2 and higher dimensions is that in the latter, only finite gauge
transformations are defined in the quantum theory, not the infinitesimal ones.Comment: 33 page
A quantum logical and geometrical approach to the study of improper mixtures
We study improper mixtures from a quantum logical and geometrical point of
view. Taking into account the fact that improper mixtures do not admit an
ignorance interpretation and must be considered as states in their own right,
we do not follow the standard approach which considers improper mixtures as
measures over the algebra of projections. Instead of it, we use the convex set
of states in order to construct a new lattice whose atoms are all physical
states: pure states and improper mixtures. This is done in order to overcome
one of the problems which appear in the standard quantum logical formalism,
namely, that for a subsystem of a larger system in an entangled state, the
conjunction of all actual properties of the subsystem does not yield its actual
state. In fact, its state is an improper mixture and cannot be represented in
the von Neumann lattice as a minimal property which determines all other
properties as is the case for pure states or classical systems. The new lattice
also contains all propositions of the von Neumann lattice. We argue that this
extension expresses in an algebraic form the fact that -alike the classical
case- quantum interactions produce non trivial correlations between the
systems. Finally, we study the maps which can be defined between the extended
lattice of a compound system and the lattices of its subsystems.Comment: submitted to the Journal of Mathematical Physic
Монетизация научных исследований
Academic research plays a pivotal role in advancing knowledge and driving innovation. However, the dissemination and utilization of this research often face challenges, particularly in terms
of financial sustainability. This paper explores the various strategies and considerations for monetizing
academic research papers, aiming to foster a more effective and sustainable knowledge ecosystem.
It also focuses on increasing the economy of publishing academic research papers for author and free
to read for audience.Академические исследования играют ключевую роль в развитии знаний и стимулировании
инноваций. Однако распространение и использование этих исследований часто сталкиваются
с проблемами, особенно с точки зрения финансовой устойчивости. В этой работе рассматриваются различные стратегии монетизации научных исследований с целью создания более эффективной и устойчивой экосистемы знаний
Faster Algorithms for the Geometric Transportation Problem
Let R, B be a set of n points in R^d, for constant d, where the points of R have integer supplies, points of B have integer demands, and the sum of supply is equal to the sum of demand. Let d(.,.) be a suitable distance function such as the L_p distance. The transportation problem asks to find a map tau : R x B --> N such that sum_{b in B}tau(r,b) = supply(r), sum_{r in R}tau(r,b) = demand(b), and sum_{r in R, b in B} tau(r,b) d(r,b) is minimized. We present three new results for the transportation problem when d(.,.) is any L_p metric:
* For any constant epsilon > 0, an O(n^{1+epsilon}) expected time randomized algorithm that returns a transportation map with expected cost O(log^2(1/epsilon)) times the optimal cost.
* For any epsilon > 0, a (1+epsilon)-approximation in O(n^{3/2}epsilon^{-d}polylog(U)polylog(n)) time, where U is the maximum supply or demand of any point.
* An exact strongly polynomial O(n^2 polylog n) time algorithm, for d = 2
Parametrizations of density matrices
This article gives a brief overview of some recent progress in the
characterization and parametrization of density matrices of finite dimensional
systems. We discuss in some detail the Bloch-vector and Jarlskog
parametrizations and mention briefly the coset parametrization. As applications
of the Bloch parametrization we discuss the trace invariants for the case of
time dependent Hamiltonians and in some detail the dynamics of three-level
systems. Furthermore, the Bloch vector of two-qubit systems as well as the use
of the polarization operator basis is indicated. As the main application of the
Jarlskog parametrization we construct density matrices for composite systems.
In addition, some recent related articles are mentioned without further
discussion.Comment: 31 pages. v2: 32 pages, Abstract and Introduction rewritten and
Conclusion section added, references adde
Large quantum gravity effects: Unexpected limitations of the classical theory
3-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly
soluble under the assumption of axi-symmetry. The solution is used to probe
several quantum gravity issues. In particular, it is shown that the quantum
fluctuations in the geometry are large unless the number and frequency of
photons satisfy the inequality . Thus, even when
there is a single photon of Planckian frequency, the quantum uncertainties in
the metric are significant. Results hold also for a sector of the 4-dimensional
theory (consisting of Einstein Rosen gravitational waves).Comment: 8 pages, No figures, ReVTe
The parameterized complexity of some geometric problems in unbounded dimension
We study the parameterized complexity of the following fundamental geometric
problems with respect to the dimension : i) Given points in \Rd,
compute their minimum enclosing cylinder. ii) Given two -point sets in
\Rd, decide whether they can be separated by two hyperplanes. iii) Given a
system of linear inequalities with variables, find a maximum-size
feasible subsystem. We show that (the decision versions of) all these problems
are W[1]-hard when parameterized by the dimension . %and hence not solvable
in time, for any computable function and constant
%(unless FPT=W[1]). Our reductions also give a -time lower bound
(under the Exponential Time Hypothesis)
The Spin-Statistics Theorem for Anyons and Plektons in d=2+1
We prove the spin-statistics theorem for massive particles obeying braid
group statistics in three-dimensional Minkowski space. We start from first
principles of local relativistic quantum theory. The only assumption is a gap
in the mass spectrum of the corresponding charged sector, and a restriction on
the degeneracy of the corresponding mass.Comment: 21 pages, 2 figures. Citation added; Minor modifications of Appendix
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