Related papers: The CP(N-1) Affine Gauge Theory in the Dynamical S…
Quantum theory of field (extended) objects without a priori space-time geometry has been represented. Intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space $CP(N-1)$ are used instead of space-time…
In the present article I propose a non-linear relativistic 4-d field model originated by the internal dynamics in CP(N-1). There is no initially distinction between `particle' and `field', and the space-time manifold is derivable. The main…
A non-linear relativistic 4D field model of a quantum particle which emerges from the internal dynamics in the quantum phase space $CP(N-1)$ is proposed. In this model there is no distinction between `particle' and its `surrounding field',…
Gauge fields frequently used as an independent construction additional to so-called wave fields of matter. This artificial separation is of course useful in some applications (like Berry's interactions between the "heavy" and "light"…
State-dependent gauge principle invoked to realize the relativity to a measuring device, has been proposed. Self-consistent global (cosmic) potential forms the state space of the fundamental field and its connection, agreed with…
In order to prevent ``unavoidable'' break-down of the ``peaceful coexistence'' between foundations of quantum theory and relativity I propose a new type of a quantum gauge theory (superrelativity). This differs from ordinary gauge theories…
The reconstruction of the unitary symmetry \cite{TFD} under non-linear dynamical mapping Hilbert space of action amplitudes $C^N$ onto projective Hilbert space $CP(N-1)$ \cite{Le1} has been applied here to the quantum dynamics of elementary…
The ordinary linear quantum theory predicts the quantum correlations at any distance (the universal superposition principle). It creates the decoherence problem since quantum interactions entangle states into non-separable combination. On…
Noncommutative geometry is a mathematical framework that expresses the structure of space-time in terms of operator algebras. By using the tools of quantum mechanics to describe the geometry, noncommutative space-times are expected to give…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
Affine quantum gravity involves (i) affine commutation relations to ensure metric positivity, (ii) a regularized projection operator procedure to accomodate first- and second-class quantum constraints, and (iii) a hard-core interpretation…
In this work it is shown that there is an inherent nonlinear evolution in the dynamics of the so-called generalized coherent states. To show this, the immersion of a classical manifold into the Hilbert space of quantum mechanics is…
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is…
We show that a simple OSp(1/2) worldline gauge theory in 0-brane phase space (X,P), with spin degrees of freedom, formulated for a d+2 dimensional spacetime with two times X^0,, X^0', unifies many physical systems which ordinarily are…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Affine variables, which have the virtue of preserving the positive-definite character of matrix-like objects, have been suggested as replacements for the canonical variables of standard quantization schemes, especially in the context of…
By exploring a possible physical realisation of the geometric concept of noncommutative tangent bundle, we outline an axiomatic quantum picture of space as topological manifold and time as a count of its reconfiguration events.
It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle.…
We introduce a non-perturbative continuum framework to study the dynamics of quantum field theory (QFT), applied here to the CP(N-1) model, using Ecalle's theory of resurgent trans-series, combined with the physical principle of continuity,…