Related papers: Toward a finite-dimensional formulation of Quantum…
The existing field theories are based on the properties of closed exterior forms, which are invariant ones and correspond to conservation laws for physical fields. Hence, to understand the foundations of field theories and their unity, one…
Realistic dynamical theories of measurement based on the diffusion of quantum states are nonunitary, whereas quantum field theory and its generalizations are unitary. This problem in the quantum field theory of quantum state diffusion (QSD)…
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
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…
Mean field theory for the time evolution of quantum meson fields is studied in terms of the functional Schroedinger picture with a time-dependent Gaussian variational wave functional. We first show that the equations of motion for the…
The basic principles of the quantum mechanics in the K-field formalism are stated in the paper. The basic distinction of this theory arises from that the quantum theory equations (including well-known Schrodinger, Klein-Gordon and quadratic…
We propose a way to encode acceleration directly into quantum fields, establishing a new class of fields. Accelerated quantum fields, as we have named them, have some very interesting properties. The most important is that they provide a…
A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.
The observation that spacetime and quantum fields on it have to be dynamically produced in any theory of quantum gravity implies that quantum gravity should be defined on the configuration space of fields rather than spacetime. Such a…
Even the uninitiated will know that Quantum Field Theory cannot be introduced systematically in just four lectures. I try to give a reasonably connected outline of part of it, from second quantization to the path-integral technique in…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
Brane model of universe is considered for a particle. Conservation laws inside the brane are obtained. Equation of motion is derived for a particle using variation principle from these conservation laws. This equation includes terms…
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…
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…
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates.…
This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The…
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the…
Polymomentum canonical theories, which are manifestly covariant multi-parameter generalizations of the Hamiltonian formalism to field theory, are considered as a possible basis of quantization. We arrive at a multi-parameter hypercomplex…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological…