Quantum dynamics and state-dependent affine gauge fields on CP(N-1)

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" sub-systems) but it is restrictive on the fundamental level of "elementary" particles and entangled states. It is shown that the linear superposition of action states and non-linear dynamics of the local dynamical variables form an oscillons of energy representing non-local particles - "lumps" arising together with their "affine gauge potential" agrees with Fubini-Study metric. I use the conservation laws of local dynamical variables (LDV's) during affine parallel transport in complex projective Hilbert space $CP(N-1)$ for twofold aim. Firstly, I formulate the variation problem for the ``affine gauge potential" as system of partial differential equations \cite{Le1}. Their solutions provide embedding quantum dynamics into dynamical space-time whose state-dependent coordinates related to the qubit spinor subjected to Lorentz transformations of "quantum boosts" and "quantum rotations". Thereby, the problem of quantum measurement being reformulated as the comparison of LDV's during their affine parallel transport in $CP(N-1)$, is inherently connected with space-time emergences. Secondly, the important application of these fields is the completeness of quantum theory. The EPR and Schr\"odinger's Cat paradoxes are discussed from the point of view of the restored Lorentz invariance due to the affine parallel transport of local Hamiltonian of the soliton-like field.Comment: 15 pages, no figure

Quantum Geometry of the Dynamical Space-time

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 coordinates. The fate of quantum system modeled by the generalized coherent states is rooted in this manifold. Dynamical (state-dependent) space-time arises only at the stage of the quantum "yes/no" measurement. The quantum measurement of the gauge ``field shell'' of the generalized coherent state is described in terms of the affine parallel transport of the local dynamical variables in $CP(N-1)$.Comment: 23 pages, LaTeX, minor textual imrovement

Self-interacting Electron as the Gauge Field Under the Ultimate Separation of the Absolute Quantum Motions

The problem of the reason of physical motion needs a review in the framework of quantum theory. The Aristotle's mistake, Galileo-Newton progress, Einstein physical geometry established the fundamental role of the spacetime geometry in the motion of fields and bodies. Quantum theory poses a new question about the motion of the quantum states and its reason in the quantum state space. The standard approach of quantum theory uses so-called method of the classical analogy where the action functional contains in the additive manner three terms: matter (free particles) + free fields + interaction term. Such approach leads to the quantum state space as some space of functions defined on the spacetime. I think if one try to understand the peculiarity of the self-interacting quantum particles together with its "field shell" then the classical scheme should be replaced. Then the role of the spacetime should be revised: the space of the unlocated pure quantum degrees of freedom and its geometry will play the fundamental role and the local dynamical spacetime arises as representation of the internal quantum motions (inverse representation). I will discuss in this work a small but important change in the formulation of the field equations for the energy-momentum, orbital momentum and kinetic momentum of the self-interacting electron.Comment: 13 page

Super-Relativity and State-Dependent Gauge Fields

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 Fubini-Study metric of $CP(N-1)$, serves as state-dependent gauge potential. In this framework the linearity of the ordinary quantum mechanics appears as a `tangent approximation' to the totally nonlinear underlying pre-dynamical `functional' field theory on $CP(N-1)$.Comment: 20 pages, LaTeX, submitted to the Foundations of Physics Letters, some formulas improved, minor grammatical change

Underlying Field Structure of Matter

Intrinsic unfication of quantum theory and general relativity based on the underlying quantum dynamics of fundamental field has been proposed.Comment: 16 pages, LaTe

The quantum state-dependent gauge fields of Jacobi

It is commonly understood that the Yang-Mills non-Abelian gauge fields is the natural generalization of the well known Abelian gauge group symmetry $U(1)$ in the electrodynamics. Taking into account that the problems of the localization and divergences in QFT are not solved in the framework of the Standard Model (SM), I proposed a different approach to the quantum theory of the single self-interacting electron. In connection with this theory, I would like attract the attention to the state-dependent gauge transformations $U(1) \times U(N-1)$ associated with the Jacobi vector fields of the geodesic variations in the complex projective Hilbert space $CP(N-1)$ of the unlocated quantum states (UQS's).Comment: 28 pages, 1 figur

The Quantum Relativity and Dynamical Spacetime

Quantum field theory (QFT) based on the principles of special relativity (SR) and it is in fact the \emph{kinematic theory of fields}. The root assumption is that there is "relativistic description" of \emph{any} isolated quantum system in the so-called class of inertial systems even if the internal interactions or self-interactions lie outside of the formal QFT itself. In such a situation we cannot be sure that the principle of relativity in the present form is universally applicable since this principle arose from the Maxwell electrodynamics. As we know Einstein was insisted to generalize this principle in the attempt to find the relativistic description of gravity. Together with this the Galileo-Newton principle of inertia was modified with essential reservations \cite{Einstein_1921,Le13,Le15,Le16,Le18}. New kind of sub-atomic interactions have definitely more complicated nature and mostly unknown laws. It is clear that the present QFT (kinematic theory of fields) may serve merely as a limit of some \emph{dynamical theory of quantum fields}.Comment: 1

The CP(N-1) Affine Gauge Theory in the Dynamical Space-time

An attempt to build quantum theory of field (extended) objects without a priori space-time geometry has been represented. Space-time coordinates are replaced by the intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space $CP(N-1)$. The fate of a quantum system modeled by the generalized coherent states is rooted in this manifold. Dynamical (state-dependent) space-time arises only at the stage of the quantum "yes/no" measurement. The quantum measurement of the gauge ``field shell'' of the generalized coherent state is described in terms of the affine parallel transport of the local dynamical variables in $CP(N-1)$.Comment: 22 pages, LaTe

The quantum origin of inertia and the radiation reaction of self-interacting electron

The internal structure of self-interacting quantum particle like electron is independent on space-time position. Then at least infinitesimal kinematic space-time shift, rotation or boost lead to the equivalent internal quantum state. This assumption may be treated as internal (quantum) formulation of the inertia principle. Dynamical transformation of quantum setup generally leads to deformation of internal quantum state and measure of this deformation may be used as quantum counterpart of force instead of a macroscopic acceleration. The reason of inertia arises, thereby, as a consequence an internal motion of quantum state and its reaction on dynamical quantum setup deformation. The quantum origin of the inertia has been discussed in this article in the framework of "eigen-dynamics" of self-interacting relativistic extended quantum electron. Namely, a back reaction of spin and charge "fast" degrees of freedom on "slow" driving environment during "virtual measurement" leads to the appearance of state dependent non-Abelian gauge fields in dynamical 4D space-time. Analysis of simplified dynamics has been applied to the energy-momentum behavior in the relation with runaway solutions of previous models of an electron.Comment: 23 pages, 8 figures, essential reformulation with application to the radiation reaction of self-interacting electro

Super-relativity in the quantum theory

The relativity to the measuring device in quantum theory, i.e. the covariance of local dynamical variables relative transformations to moving quantum reference frame in Hilbert space, may be achieved only by the rejection of super-selection rule. In order to avoid the subjective nuance, I emphasis that the notion of "measurement" here, is nothing but the covariant differentiation procedure in the functional quantum phase space $CP(N-1)$, having pure objective sense of evolution. Transition to the local moving quantum reference frame leads to some particle-like solutions of quasi-linear field PDE in the dynamical space-time. Thereby, the functionally covariant quantum dynamics gives the perspective to unify the Einstein relativity and quantum principles which are obviously contradictable under the standard approaches.Comment: 16 pages, 1 figure, LaTeX, corrected typo