相关论文: General quantization
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…
I discuss the ontological assumptions and implications of General Relativity. I maintain that General Relativity is a theory about gravitational fields, not about space-time. The latter is a more basic ontological category, that emerges…
The field theory quantized on the {\it light-front} is compared with the conventional equal-time quantized theory. The arguments based on the {\it microcausality} principle imply that the light-front field theory may become nonlocal with…
A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some…
A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous, algebraic generalization. This presentation serves to make a comprehensive discussion in which other…
The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…
The relation between symmetry reduction before and after quantization of a field theory is discussed using a toy model: the axisymmetric Klein-Gordon field. We consider three possible notions of symmetry at the quantum level: invariance…
Quantum field theory can be physically regularized by modularizing it on several levels of aggregation. Since computation is already thoroughly modularized, physical experiments are treated here as quantum relativistic cellular computations…
This letter serves as the generalization of the work 2505.16436, where we investigated the quantum field theory in Klein space which has two time directions. We extend studies to the general spacetime $\mathbb{R}^{n,d-n}\,(n,d-n\geq2)$ in a…
A local conception is proposed to reconcile quantum theory with general relativity, which allows one to avoid some difficulties --- as e.g. vacuum catastrophe --- of the global approach.
It is well-known that there exist infinitely-many inequivalent representations of the canonical (anti)-commutation relations of Quantum Field Theory (QFT). A way out, suggested by Algebraic QFT, is to instead define the quantum theory as…
Usually quantum theory is formulated in terms of the evolution of states through spacelike surfaces. However, a generalization of this formulation is needed for field theory in spacetimes not foliable by spacelike surfaces, or in quantum…
The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an…
Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link…
We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the K\"ahler case, state spaces arise as spaces of…
The quantization rules recently proposed by M. Navarro (and independently I.V. Kanatchikov) for a finite-dimensional formulation of quantum field theory are applied to the Klein-Gordon and the Dirac fields to obtain the quantum equations of…
Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global…
Although general relativity is a predictively successful theory, it treats matter as classical rather than as quantum. For this reason, it will have to be replaced by a more fundamental quantum theory of gravity. Attempts to formulate a…