Related papers: Neutrix Calculus and Finite Quantum Field Theory
We introduce regular charts as physical reference frames in spacetime, and we show that general spacetimes can always be fully captured by regular charts. Effective quantum field theories (QFTs) can be conveniently defined in regular…
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in…
Quantum Electrodynamics (QED) has been so successful a theory that it is taken as a model for the production of further quantum theories. However, when the prescription for quantising electromagnetic interactions that so successfully…
Lattice regularization is a standard technique for the nonperturbative definition of a quantum theory of fields. Several approaches to the construction of a quantum theory of gravity adopt this technique either explicitly or implicitly. A…
We explore the implications of restricting the framework of quantum theory and quantum computation to finite fields. The simplest proposed theory is defined over arbitrary finite fields and loses the notion of unitaries. This makes such…
We demonstrate our simple strategy for renormalization with QED at one-loop level, basing on an elaboration of the effective field theory philosophy. No artificial regularization or deformation of the original theory is introduced here and…
In this contribution, we discuss the asymptotic safety scenario for quantum gravity with a functional renormalisation group approach that disentangles dynamical metric fluctuations from the background metric. We review the state of the art…
The mutual conceptual incompatibility between GR and QM/QFT is generally seen as the most essential motivation for the development of a theory of Quantum Gravity (QG). It leads to the insight that, if gravity is a fundamental interaction…
It has been suggested that higher-derivative gravity theories coupled to a scalar field with shift symmetry may be an important candidate for a quantum gravity. We show that this class of gravity theories are renormalizable in D = 3 and 4…
The process algebra has been used successfully to provide a novel formulation of quantum mechanics in which non-relativistic quantum mechanics (NRQM) emerges as an effective theory asymptotically. The process algebra is applied here to the…
QJT (Quantum Jet Theory) is the quantum theory of jets, which can be canonically identified with truncated Taylor series. Ultralocality requires a novel quantization scheme, where dynamics is treated as a constraint in the history phase…
Quantum fields are shown to provide an example of infinite-dimensional quantum groups. A dictionary is established between quantum field and quantum group concepts: the expectation value over the vacuum is the counit, Wick's theorem is the…
We define an entropy for a quantum field theory by combining quantum fluctuations, scaling and the maximum entropy concept. This entropy has different behavior in asymptotically free and non--asymptotically free theories. We find that the…
The quantum gravity is formulated based on gauge principle. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge potential. A preliminary study on gravitational gauge group…
Real-Space renormalization group techniques are developed for tackling large curvature fluctuations in quantum gravity. Within cells of invariant volume $a^4$, only certain types of fluctuations are allowed. Normal coordinates are used to…
A fundamental length is introduced into physics in a way which respects the principles of relativity and quantum field theory. This improves the properties of quantum field theory: divergences are removed. How to quantize gravity is also…
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…
It is generally believed that quantum gravity is necessary to resolve the known tensions between general relativity and the quantum field theories of the standard model. Since perturbatively quantized gravity is non-renormalizable, the…
Physics in the vicinity of an ultraviolet stable fixed point of a quantum field theory is parametrized by a renormalization group invariant macroscopic length scale, the correlation length $\xi,$ with the quantum effective action a function…
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for…