88 research outputs found

### A first-principles approach to physics based on locality and operationalism

Starting from the guiding principles of spacetime locality and
operationalism, a general framework for a probabilistic description of nature
is proposed. Crucially, no notion of time or metric is assumed, neither any
specific physical model. Remarkably, the emerging framework converges with a
recently proposed formulation of quantum theory, obtained constructively from
known quantum physics. At the same time the framework also admits statistical
theories of classical physics.Comment: 8 pages, LaTeX + PoS, contribution to the proceedings of the
conference "Frontiers of Fundamental Physics 14" (Marseille, 2014

### S-matrix at spatial infinity

We provide a new method to construct the S-matrix in quantum field theory.
This method implements crossing symmetry manifestly by erasing the a priori
distinction between in- and out-states. It allows the description of processes
where the interaction weakens with distance in space, but remains strong in the
center at all times. It should also be applicable to certain spacetimes where
the conventional method fails due to lack of temporal asymptotic states.Comment: 4 pages, LaTeX + revtex4; v2: normalization factors corrected; v3:
two paragraphs added, minor corrections and enhancements, reference list
updated; v4: references corrected/update

### Affine holomorphic quantization

We present a rigorous and functorial quantization scheme for affine field
theories, i.e., field theories where local spaces of solutions are affine
spaces. The target framework for the quantization is the general boundary
formulation, allowing to implement manifest locality without the necessity for
metric or causal background structures. The quantization combines the
holomorphic version of geometric quantization for state spaces with the Feynman
path integral quantization for amplitudes. We also develop an adapted notion of
coherent states, discuss vacuum states, and consider observables and their
Berezin-Toeplitz quantization. Moreover, we derive a factorization identity for
the amplitude in the special case of a linear field theory modified by a
source-like term and comment on its use as a generating functional for a
generalized S-matrix.Comment: 42 pages, LaTeX + AMS; v2: expanded to improve readability, new
sections 3.1 (geometric data) and 3.3 (core axioms), minor corrections,
update of references; v3: further update of reference

### Coherent states in fermionic Fock-Krein spaces and their amplitudes

We generalize the fermionic coherent states to the case of Fock-Krein spaces,
i.e., Fock spaces with an idefinite inner product of Krein type. This allows
for their application in topological or functorial quantum field theory and
more specifically in general boundary quantum field theory. In this context we
derive a universal formula for the amplitude of a coherent state in linear
field theory on an arbitrary manifold with boundary.Comment: 20 pages, LaTeX + AMS + svmult (included), contribution to the
proceedings of the conference "Coherent States and their Applications: A
Contemporary Panorama" (Marseille, 2016); v2: minor corrections and added
axioms from arXiv:1208.503

### Renormalization of Discrete Models without Background

Conventional renormalization methods in statistical physics and lattice
quantum field theory assume a flat metric background. We outline here a
generalization of such methods to models on discretized spaces without metric
background. Cellular decompositions play the role of discretizations. The group
of scale transformations is replaced by the groupoid of changes of cellular
decompositions. We introduce cellular moves which generate this groupoid and
allow to define a renormalization groupoid flow.
We proceed to test our approach on several models. Quantum BF theory is the
simplest example as it is almost topological and the renormalization almost
trivial. More interesting is generalized lattice gauge theory for which a
qualitative picture of the renormalization groupoid flow can be given. This is
confirmed by the exact renormalization in dimension two.
A main motivation for our approach are discrete models of quantum gravity. We
investigate both the Reisenberger and the Barrett-Crane spin foam model in view
of their amenability to a renormalization treatment. In the second case a lack
of tunable local parameters prompts us to introduce a new model. For the
Reisenberger and the new model we discuss qualitative aspects of the
renormalization groupoid flow. In both cases quantum BF theory is the UV fixed
point.Comment: 40 pages, 17 figures, LaTeX + AMS + XY-pic + eps; added subsection
4.3 on relation to spin network diagrams, reference added, minor adjustment

### Classification of Differential Calculi on U_q(b+), Classical Limits, and Duality

We give a complete classification of bicovariant first order differential
calculi on the quantum enveloping algebra U_q(b+) which we view as the quantum
function algebra C_q(B+). Here, b+ is the Borel subalgebra of sl_2. We do the
same in the classical limit q->1 and obtain a one-to-one correspondence in the
finite dimensional case. It turns out that the classification is essentially
given by finite subsets of the positive integers. We proceed to investigate the
classical limit from the dual point of view, i.e. with ``function algebra''
U(b+) and ``enveloping algebra'' C(B+). In this case there are many more
differential calculi than coming from the q-deformed setting. As an
application, we give the natural intrinsic 4-dimensional calculus of
kappa-Minkowski space and the associated formal integral.Comment: 22 pages, LaTeX2e, uses AMS macro

### Structure Theorem for Covariant Bundles on Quantum Homogeneous Spaces

The natural generalization of the notion of bundle in quantum geometry is
that of bimodule. If the base space has quantum group symmetries one is
particularly interested in bimodules covariant (equivariant) under these
symmetries. Most attention has so far been focused on the case with maximal
symmetry -- where the base space is a quantum group and the bimodules are
bicovariant. The structure of bicovariant bimodules is well understood through
their correspondence with crossed modules.
We investigate the ``next best'' case -- where the base space is a quantum
homogeneous space and the bimodules are covariant. We present a structure
theorem that resembles the one for bicovariant bimodules. Thus, there is a
correspondence between covariant bimodules and a new kind of ``crossed''
modules which we define. The latter are attached to the pair of quantum groups
which defines the quantum homogeneous space.
We apply our structure theorem to differential calculi on quantum homogeneous
spaces and discuss a related notion of induced differential calculus.Comment: 7 pages; talk given at QGIS X, Prague, June 2001; typos correcte

### General boundary quantum field theory: Foundations and probability interpretation

We elaborate on the proposed general boundary formulation as an extension of
standard quantum mechanics to arbitrary (or no) backgrounds. Temporal
transition amplitudes are generalized to amplitudes for arbitrary spacetime
regions. State spaces are associated to general (not necessarily spacelike)
hypersurfaces. We give a detailed foundational exposition of this approach,
including its probability interpretation and a list of core axioms. We explain
how standard quantum mechanics arises as a special case. We include a
discussion of probability conservation and unitarity, showing how these
concepts are generalized in the present framework. We formulate vacuum axioms
and incorporate spacetime symmetries into the framework. We show how the
Schroedinger-Feynman approach is a suitable starting point for casting quantum
field theories into the general boundary form. We discuss the role of
operators.Comment: 30 pages, 5 figures, LaTeX; v2: typos corrected, footnote and remark
added, references added/updated; v3: more typos corrected; v4: with
corrections of the published versio

### Reverse Engineering Quantum Field Theory

An approach to the foundations of quantum theory is advertised that proceeds
by "reverse engineering" quantum field theory. As a concrete instance of this
approach, the general boundary formulation of quantum theory is outlined.Comment: 5 pages, LaTeX + aipproc (included), contribution to the proceedings
of the conference "Quantum Theory: Reconsideration of Foundations - 6"
(V\"axj\"o, 2012

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