382 research outputs found
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
The Unruh Effect in General Boundary Quantum Field Theory
In the framework of the general boundary formulation (GBF) of scalar quantum
field theory we obtain a coincidence of expectation values of local observables
in the Minkowski vacuum and in a particular state in Rindler space. This
coincidence could be seen as a consequence of the identification of the
Minkowski vacuum as a thermal state in Rindler space usually associated with
the Unruh effect. However, we underline the difficulty in making this
identification in the GBF. Beside the Feynman quantization prescription for
observables that we use to derive the coincidence of expectation values, we
investigate an alternative quantization prescription called Berezin-Toeplitz
quantization prescription, and we find that the coincidence of expectation
values does not exist for the latter
Boundary Quantum Field Theory on the Interior of the Lorentz Hyperboloid
We construct local, boost covariant boundary QFT nets of von Neumann algebras
on the interior of the Lorentz hyperboloid LH = {x^2 - t^2 > R^2, x>0}, in the
two-dimensional Minkowski spacetime. Our first construction is canonical,
starting with a local conformal net on the real line, and is analogous to our
previous construction of local boundary CFT nets on the Minkowski half-space.
This net is in a thermal state at Hawking temperature. Then, inspired by a
recent construction by E. Witten and one of us, we consider a unitary semigroup
that we use to build up infinitely many nets. Surprisingly, the one-particle
semigroup is again isomorphic to the semigroup of symmetric inner functions of
the disk. In particular, by considering the U(1)-current net, we can associate
with any given symmetric inner function a local, boundary QFT net on LH. By
considering different states, we shall also have nets in a ground state, rather
than in a KMS state.Comment: 18 page
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
Reflection Scattering Matrix of the Ising Model in a Random Boundary Magnetic Field
The physical properties induced by a quenched surface magnetic field in the
Ising model are investigated by means of boundary quantum field theory in
replica space. Exact boundary scattering amplitudes are proposed and used to
study the averaged quenched correlation functions.Comment: 37 pages (Latex), including 16 figures, one reference adde
Schr\"odinger-Feynman quantization and composition of observables in general boundary quantum field theory
We show that the Feynman path integral together with the Schr\"odinger
representation gives rise to a rigorous and functorial quantization scheme for
linear and affine field theories. Since our target framework is the general
boundary formulation, the class of field theories that can be quantized in this
way includes theories without a metric spacetime background. We also show that
this quantization scheme is equivalent to a holomorphic quantization scheme
proposed earlier and based on geometric quantization. We proceed to include
observables into the scheme, quantized also through the path integral. We show
that the quantized observables satisfy the canonical commutation relations, a
feature shared with other quantization schemes also discussed. However, in
contrast to other schemes the presented quantization also satisfies a
correspondence between the composition of classical observables through their
product and the composition of their quantized counterparts through spacetime
gluing. In the special case of quantum field theory in Minkowski space this
reproduces the operationally correct composition of observables encoded in the
time-ordered product. We show that the quantization scheme also generalizes
other features of quantum field theory such as the generating function of the
S-matrix.Comment: 47 pages, LaTeX + AMS; v2: minor corrections, references update
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
- …