Related papers: Quantum and Classical Fields in the Finite-Dimensi…
An alternative quantization of the gravitational Hamiltonian constraint of the $k=-1$ Friedmann-Robertson-Walker model is proposed by treating the Euclidean term and the Lorentzian term independently, mimicking the treatment of full loop…
Segal's hypothesis that physical theories drift toward simple groups follows from a general quantum principle and suggests a general quantization process. I general-quantize the scalar meson field in Minkowski space-time to illustrate the…
In quantum field theories, field redefinitions are often employed to remove redundant operators in the Lagrangian, making calculations simpler and physics more evident. This technique requires some care regarding, among other things, the…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…
It is argued that the massive non-Abelian gauge field theory without involving Higgs bosons may be well established on the basis of gauge-invariance principle because the dynamics of the field is gauge-invariant in the physical space…
We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the Poisson…
A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta…
For more than half a century, covariant and differential geometric methods have been playing a central role in the development of Quantum Field Theory (QFT). After a brief historic overview of the major scientific achievements using these…
Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, $A_{\mu}(x)\rightarrow A_{\mu}(x)+\partial_{\mu}\varphi(x)$, into a group law. In…
Krein space quantization and the ambient space formalism have been successfully applied to address challenges in quantum geometry (e.g., quantum gravity) and the axiomatic formulation of quantum Yang-Mills theory, including phenomena such…
After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a…
The classical theory of gravity predicts its own demise -- singularities. We therefore attempt to quantize gravitation, and present here a new approach to the quantization of gravity wherein the concept of time is derived by imposing the…
We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum…
Quantum Information and the new informational paradigm are entering the domain of quantum field theory and gravity, suggesting the quantum automata framework. The quantum automaton is the minimal-assumption extension to the Planck and…
The long-standing challenge to describing charged particle dynamics in strong classical electromagnetic fields is how to incorporate classical radiation, classical radiation reaction and quantized photon emission into a consistent unified…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…