141 research outputs found
Probabilities in the general boundary formulation
We give an introductory account of the general boundary formulation of
quantum theory. We refine its probability interpretation and emphasize a
conceptual and historical perspective. We give motivations from quantum gravity
and illustrate them with a scenario for describing gravitons in quantum
gravity.Comment: 7 pages, LaTeX + jpconf, contribution to proceedings of DICE2006,
Piombino, Italy, September 2006; v2: typos corrected (including title) and
references update
Discrete Dynamics: Gauge Invariance and Quantization
Gauge invariance in discrete dynamical systems and its connection with
quantization are considered. For a complete description of gauge symmetries of
a system we construct explicitly a class of groups unifying in a natural way
the space and internal symmetries. We describe the main features of the gauge
principle relevant to the discrete and finite background. Assuming that
continuous phenomena are approximations of more fundamental discrete processes,
we discuss -- with the help of a simple illustration -- relations between such
processes and their continuous approximations. We propose an approach to
introduce quantum structures in discrete systems, based on finite gauge groups.
In this approach quantization can be interpreted as introduction of gauge
connection of a special kind. We illustrate our approach to quantization by a
simple model and suggest generalization of this model. One of the main tools
for our study is a program written in C.Comment: 15 pages; CASC 2009, Kobe, Japan, September 13-17, 200
q-deformation of
We construct the action of the quantum double of \uq on the standard
Podle\'s sphere and interpret it as the quantum projective formula generalizing
to the q-deformed setting the action of the Lorentz group of global conformal
transformations on the ordinary Riemann sphere.Comment: LaTeX, 16 pages, we add a reference where an alternative construction
of the q-Lorentz group action on the Podles sphere is give
Lorentz invariant and supersymmetric interpretation of noncommutative quantum field theory
In this paper, using a Hopf-algebraic method, we construct deformed
Poincar\'e SUSY algebra in terms of twisted (Hopf) algebra. By adapting this
twist deformed super-Poincar\'e algrebra as our fundamental symmetry, we can
see the consistency between the algebra and non(anti)commutative relation among
(super)coordinates and interpret that symmetry of non(anti)commutative QFT is
in fact twisted one. The key point is validity of our new twist element that
guarantees non(anti)commutativity of space. It is checked in this paper for N=1
case. We also comment on the possibility of noncommutative central charge
coordinate. Finally, because our twist operation does not break the original
algebra, we can claim that (twisted) SUSY is not broken in contrast to the
string inspired SUSY in N=1 non(anti)commutative superspace.Comment: 15 pages, LaTeX. v3:One section added, typos corrected, to appear in
Int. J. Mod. Phys.
Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covariance
We argue that the holographic principle may be hinted at already from
low-energy considerations, assuming diffeomorphism invariance, quantum
mechanics and Minkowski-like causality. We consider the states of finite
spacelike hypersurfaces in a diffeomorphism-invariant QFT. A low-energy
regularization is assumed. We note a natural dependence of the Hilbert space on
a codimension-2 boundary surface. The Hilbert product is defined dynamically,
in terms of transition amplitudes which are described by a path integral. We
show that a canonical basis is incompatible with these assumptions, which opens
the possibility for a smaller Hilbert-space dimension than canonically
expected. We argue further that this dimension may decrease with surface area
at constant volume, hinting at holographic area-proportionality. We draw
comparisons with other approaches and setups, and propose an interpretation for
the non-holographic space of graviton states at asymptotically-Minkowski null
infinity.Comment: 13 pages, 9 eps figures. Added Section VI, improved presentation.
Expanded and split the Introduction into two sections. Added Section VII.
Added reference
Dual Computations of Non-abelian Yang-Mills on the Lattice
In the past several decades there have been a number of proposals for
computing with dual forms of non-abelian Yang-Mills theories on the lattice.
Motivated by the gauge-invariant, geometric picture offered by dual models and
successful applications of duality in the U(1) case, we revisit the question of
whether it is practical to perform numerical computation using non-abelian dual
models. Specifically, we consider three-dimensional SU(2) pure Yang-Mills as an
accessible yet non-trivial case in which the gauge group is non-abelian. Using
methods developed recently in the context of spin foam quantum gravity, we
derive an algorithm for efficiently computing the dual amplitude and describe
Metropolis moves for sampling the dual ensemble. We relate our algorithms to
prior work in non-abelian dual computations of Hari Dass and his collaborators,
addressing several problems that have been left open. We report results of spin
expectation value computations over a range of lattice sizes and couplings that
are in agreement with our conventional lattice computations. We conclude with
an outlook on further development of dual methods and their application to
problems of current interest.Comment: v1: 18 pages, 7 figures, v2: Many changes to appendix, minor changes
throughout, references and figures added, v3: minor corrections, 22 page
Causality and statistics on the Groenewold-Moyal plane
Quantum theories constructed on the noncommutative spacetime called the
Groenewold-Moyal plane exhibit many interesting properties such as Lorentz and
CPT noninvariance, causality violation and twisted statistics. We show that
such violations lead to many striking features that may be tested
experimentally. These theories predict Pauli forbidden transitions due to
twisted statistics, anisotropies in the cosmic microwave background radiation
due to correlations of observables in spacelike regions and Lorentz and CPT
violations in scattering amplitudes.Comment: 12 pages, 1 figure. Based on the talk given by APB at the Workshop
"Theoretical and Experimental Aspects of the Spin Statisics Connection and
Related Symmetries", Stazione Marittima Conference Center, Trieste, Italy
from the 21st to the 25th of October 200
Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
In this article we study the quantization of a free real scalar field on a
class of noncommutative manifolds, obtained via formal deformation quantization
using triangular Drinfel'd twists. We construct deformed quadratic action
functionals and compute the corresponding equation of motion operators. The
Green's operators and the fundamental solution of the deformed equation of
motion are obtained in terms of formal power series. It is shown that, using
the deformed fundamental solution, we can define deformed *-algebras of field
observables, which in general depend on the spacetime deformation parameter.
This dependence is absent in the special case of Killing deformations, which
include in particular the Moyal-Weyl deformation of the Minkowski spacetime.Comment: LaTeX 14 pages, no figures, svjour3.cls style; v2: clarifications and
references added, compatible with published versio
Dual variables and a connection picture for the Euclidean Barrett-Crane model
The partition function of the SO(4)- or Spin(4)-symmetric Euclidean
Barrett-Crane model can be understood as a sum over all quantized geometries of
a given triangulation of a four-manifold. In the original formulation, the
variables of the model are balanced representations of SO(4) which describe the
quantized areas of the triangles. We present an exact duality transformation
for the full quantum theory and reformulate the model in terms of new variables
which can be understood as variables conjugate to the quantized areas. The new
variables are pairs of S^3-values associated to the tetrahedra. These
S^3-variables parameterize the hyperplanes spanned by the tetrahedra (locally
embedded in R^4), and the fact that there is a pair of variables for each
tetrahedron can be viewed as a consequence of an SO(4)-valued parallel
transport along the edges dual to the tetrahedra. We reconstruct the parallel
transport of which only the action of SO(4) on S^3 is physically relevant and
rewrite the Barrett-Crane model as an SO(4) lattice BF-theory living on the
2-complex dual to the triangulation subject to suitable constraints whose form
we derive at the quantum level. Our reformulation of the Barrett-Crane model in
terms of continuous variables is suitable for the application of various
analytical and numerical techniques familiar from Statistical Mechanics.Comment: 33 pages, LaTeX, combined PiCTeX/postscript figures, v2: note added,
TeX error correcte
Jordanian Twist Quantization of D=4 Lorentz and Poincare Algebras and D=3 Contraction Limit
We describe in detail two-parameter nonstandard quantum deformation of D=4
Lorentz algebra , linked with Jordanian deformation of
. Using twist quantization technique we obtain
the explicit formulae for the deformed coproducts and antipodes. Further
extending the considered deformation to the D=4 Poincar\'{e} algebra we obtain
a new Hopf-algebraic deformation of four-dimensional relativistic symmetries
with dimensionless deformation parameter. Finally, we interpret
as the D=3 de-Sitter algebra and calculate the contraction
limit ( -- de-Sitter radius) providing explicit Hopf algebra
structure for the quantum deformation of the D=3 Poincar\'{e} algebra (with
masslike deformation parameters), which is the two-parameter light-cone
-deformation of the D=3 Poincar\'{e} symmetry.Comment: 13 pages, no figure
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