172 research outputs found
S-Matrix for AdS from General Boundary QFT
The General Boundary Formulation (GBF) is a new framework for studying
quantum theories. After concise overviews of the GBF and Schr\"odinger-Feynman
quantization we apply the GBF to resolve a well known problem on Anti-deSitter
spacetime where due to the lack of temporally asymptotic free states the usual
S-matrix cannot be defined. We construct a different type of S-matrix plus
propagators for free and interacting real Klein-Gordon theory.Comment: 4 pages, 5 figures, Proceedings of LOOPS'11 Madrid, to appear in IOP
Journal of Physics: Conference Series (JPCS
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
Two-dimensional quantum Yang-Mills theory with corners
The solution of quantum Yang-Mills theory on arbitrary compact two-manifolds
is well known. We bring this solution into a TQFT-like form and extend it to
include corners. Our formulation is based on an axiomatic system that we hope
is flexible enough to capture actual quantum field theories also in higher
dimensions. We motivate this axiomatic system from a formal
Schroedinger-Feynman quantization procedure. We also discuss the physical
meaning of unitarity, the concept of vacuum, (partial) Wilson loops and
non-orientable surfaces.Comment: 31 pages, 6 figures, LaTeX + AMS; minor corrections, reference
update
The Unruh-deWitt Detector and the Vacuum in the General Boundary formalism
We discuss how to formulate a condition for choosing the vacuum state of a
quantum scalar field on a timelike hyperplane in the general boundary
formulation (GBF) using the coupling to an Unruh-DeWitt detector. We explicitly
study the response of an Unruh-DeWitt detector for evanescent modes which occur
naturally in quantum field theory in the presence of the equivalent of a
dielectric boundary. We find that the physically correct vacuum state has to
depend on the physical situation outside of the boundaries of the spacetime
region considered. Thus it cannot be determined by general principles
pertaining only to a subset of spacetime.Comment: Version as published in CQ
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
General boundary quantum field theory: Timelike hypersurfaces in Klein-Gordon theory
We show that the real massive Klein-Gordon theory admits a description in
terms of states on various timelike hypersurfaces and amplitudes associated to
regions bounded by them. This realizes crucial elements of the general boundary
framework for quantum field theory. The hypersurfaces considered are
hyperplanes on the one hand and timelike hypercylinders on the other hand. The
latter lead to the first explicit examples of amplitudes associated with finite
regions of space, and admit no standard description in terms of ``initial'' and
``final'' states. We demonstrate a generalized probability interpretation in
this example, going beyond the applicability of standard quantum mechanics.Comment: 25 pages, LaTeX; typos correcte
Spatially asymptotic S-matrix from general boundary formulation
We construct a new type of S-matrix in quantum field theory using the general
boundary formulation. In contrast to the usual S-matrix the space of free
asymptotic states is located at spatial rather than at temporal infinity.
Hence, the new S-matrix applies to situations where interactions may remain
important at all times, but become negligible with distance. We show that the
new S-matrix is equivalent to the usual one in situations where both apply.
This equivalence is mediated by an isomorphism between the respective
asymptotic state spaces that we construct. We introduce coherent states that
allow us to obtain explicit expressions for the new S-matrix. In our formalism
crossing symmetry becomes a manifest rather than a derived feature of the
S-matrix.Comment: 27 pages, LaTeX + revtex4; v2: various corrections, 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
Spin Foam Diagrammatics and Topological Invariance
We provide a simple proof of the topological invariance of the Turaev-Viro
model (corresponding to simplicial 3d pure Euclidean gravity with cosmological
constant) by means of a novel diagrammatic formulation of the state sum models
for quantum BF-theories. Moreover, we prove the invariance under more general
conditions allowing the state sum to be defined on arbitrary cellular
decompositions of the underlying manifold. Invariance is governed by a set of
identities corresponding to local gluing and rearrangement of cells in the
complex. Due to the fully algebraic nature of these identities our results
extend to a vast class of quantum groups. The techniques introduced here could
be relevant for investigating the scaling properties of non-topological state
sums, being proposed as models of quantum gravity in 4d, under refinement of
the cellular decomposition.Comment: 20 pages, latex with AMS macros and eps figure
Deformed Schrodinger symmetry on noncommutative space
We construct the deformed generators of Schroedinger symmetry consistent with
noncommutative space. The examples of the free particle and the harmonic
oscillator, both of which admit Schroedinger symmetry, are discussed in detail.
We construct a generalised Galilean algebra where the second central extension
exists in all dimensions. This algebra also follows from the Inonu--Wigner
contraction of a generalised Poincare algebra in noncommuting space.Comment: 9 pages, LaTeX, abstract modified, new section include
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