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Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
Quantum gauge theories with finite-dimensional representation spaces are constructed that can have canonical gauge field theories as singular limits. They describe nature as a recursive quantum assembly by iterating Fermi-Dirac…
A modular quantum architecture is given for the space-time, particles, and fields of the Standard Model and General Relativity. It assumes a right-handed neutrino, so that based on their multiplet structure all fundamental fermions have…
Set theory reduces all processes to assembly and disassembly. A similar architecture is proposed for nature as quantum computer. It resolves the classical space-time underlying Feynman diagrams into a quantum network of creation and…
Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum…
Present-day quantum field theory can be regularized by a decomposition into quantum simplices. This replaces the infinite-dimensional Hilbert space by a high-dimensional spinor space and singular canonical Lie groups by regular spin groups.…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire…
In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We…
Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold'' . Such discretization by…
We explain that a bulk with arbitrary dimensions can be added to the space over which a quantum field theory is defined. This gives a TQFT such that its correlation functions in a slice are the same as those of the original quantum field…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can physics be simulated by a quantum computer? Do we believe that a quantum field is ultimately made of a numerable set of quantum systems that are unitarily interacting? A…
It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…
We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ``infinite'', Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot…
An algebraic system is introduced, which is very useful for doing scattering calculations in quantum field theory. It is the set of all real numbers greater than or equal to -m^2 with parity designation and a special rule for addition and…