Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0812.0065

Morphogenesis and dynamics of quantum state

Peter Leifer

Published Nov 29, 2008• 1 citation
arXivHTMLPDF

Abstract

New construction of 4D dynamical space-time (DST) has been proposed in the framework of unification of relativity and quantum theory. Such unification is based solely on the fundamental notion of generalized coherent state (GCS) of N-level system and the geometry of unitary group SU(N) acting in state space $C^N$. Neither contradictable notion of quantum particle, nor space-time coordinates (that cannot be a priori attached to nothing) are used in this construction. Morphogenesis of the "field shell"-lump of GCS and its dynamics have been studied for N=2 in DST. The main technical problem is to find non-Abelian gauge field arising from conservation law of the local Hailtonian vector field. The last one may be expressed as parallel transport of local Hamiltonian in projective Hilbert space $CP(N-1)$. Co-movable local "Lorentz frame" being attached to GCS is used for qubit encoding result of comparison of the parallel transported local Hamiltonian in infinitesimally close points. This leads to quasi-linear relativistic field equations with soliton-like solutions for "field shell" in emerged DST. The terms "comparison" and "encoding" resemble human's procedure, but here they have objective content realized in invariant quantum dynamics. The dynamical motion of the lump in DST may be associated with "kinesis" time whereas the evolution parameter describing morphogenesis of GCS evolving in $CP(N-1)$, may be naturally identified with "metabole" time.

DOI
10.48550/arxiv.0812.0065

Related papers

Particle-unparticle duality in super-relativity

Peter Leifer

New method of shaping quantum "particle - unparticle" vacuum excitations has been proposed in the framework of unification of relativity and quantum theory. Such unification is based solely on the notion of generalized coherent state (GCS) of N-level system and the geometry of unitary group SU(N) acting in state space $C^N$. Initially, neither contradictable notion of quantum particle, nor space-time coordinates (that cannot be a priori attached to nothing) are used in this construction. Quantum measurement of local dynamical variables (LDV) leads to the emergence of 4D dynamical space-time (DST). Morphogenesis of the "field shell" of GCS and its dynamics have been studied for N=2 in DST.

arXiv:0901.2694•Jan 18, 2009•1 citation

Quantum Geometry of the Dynamical Space-time

Peter Leifer

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 $CP(N-1)$.

arXiv:physics/0611179•Nov 20, 2006•0 citations

Reconstruction of the unitary symmetry in super-relativity

Peter Leifer

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 vacuum excitations. The "vacuum manifold of virtual action states" is represented here by $CP(N-1)$ whereas its tangent vectors define local dynamical variables (LDV's) describing "matter". The conservation laws of LDV's express self-conservation of the "material particles" during continuous evolution being expressed as the affine parallel transport agrees with Fubuni-Study metric, create the "affine gauge potential" as the solution of the partial differential equations. Such procedure embeds the quantum dynamics into dynamical space-time whose state-dependent coordinates arose due to encoding results of quantum measurement by the qubit spinor whose components subjected to Lorentz transformations of "quantum boosts" and "quantum rotations". Thereby, in the framework of super-relativity, the objective character of the quantum measurement is inherently related to the dynamical space-time structure that replaces the notion of "observer".

arXiv:0808.3172•Aug 23, 2008•3 citations

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

Peter Leifer

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 $CP(N-1)$.

arXiv:physics/0605218•May 25, 2006•0 citations

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

Peter Leifer

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 Schrödinger'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.

arXiv:0804.1931•Apr 11, 2008•2 citations

The affine gauge theory in the quantum phase space CP(N-1)

Peter Leifer

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 idea is to base the theory on the relative amplitudes solely. Quantum measurements will be described in terms of the parallel transport of the local dynamical variables and a specific gauge reduction of the full state vector to the Qubit coherent state. I will discuss here field equations of quantum particle arising in the dynamical space-time.

arXiv:gr-qc/0503083•Mar 19, 2005•4 citations
New construction of 4D dynamical space-time (DST) has been proposed in the framework of unification of relativity and quantum theory. Such unification is based solely on the fundamental notion of generalized coherent state (GCS) of N-level system and the geometry of unitary group SU(N) acting in state space CNC^NCN. Neither contradictable notion of quantum particle, nor space-time coordinates (that cannot be a priori attached to nothing) are used in this construction. Morphogenesis of the "field shell"-lump of GCS and its dynamics have been studied for N=2 in DST. The main technical problem is to find non-Abelian gauge field arising from conservation law of the local Hailtonian vector field. The last one may be expressed as parallel transport of local Hamiltonian in projective Hilbert space CP(N−1)CP(N-1)CP(N−1). Co-movable local "Lorentz frame" being attached to GCS is used for qubit encoding result of comparison of the parallel transported local Hamiltonian in infinitesimally close points. This leads to quasi-linear relativistic field equations with soliton-like solutions for "field shell" in emerged DST. The terms "comparison" and "encoding" resemble human's procedure, but here they have objective content realized in invariant quantum dynamics. The dynamical motion of the lump in DST may be associated with "kinesis" time whereas the evolution parameter describing morphogenesis of GCS evolving in CP(N−1)CP(N-1)CP(N−1), may be naturally identified with "metabole" time.
New method of shaping quantum "particle - unparticle" vacuum excitations has been proposed in the framework of unification of relativity and quantum theory. Such unification is based solely on the notion of generalized coherent state (GCS) of N-level system and the geometry of unitary group SU(N) acting in state space CNC^NCN. Initially, neither contradictable notion of quantum particle, nor space-time coordinates (that cannot be a priori attached to nothing) are used in this construction. Quantum measurement of local dynamical variables (LDV) leads to the emergence of 4D dynamical space-time (DST). Morphogenesis of the "field shell" of GCS and its dynamics have been studied for N=2 in DST.
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)CP(N-1)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)CP(N-1)CP(N−1).
The reconstruction of the unitary symmetry \cite{TFD} under non-linear dynamical mapping Hilbert space of action amplitudes CNC^NCN onto projective Hilbert space CP(N−1)CP(N-1)CP(N−1) \cite{Le1} has been applied here to the quantum dynamics of elementary vacuum excitations. The "vacuum manifold of virtual action states" is represented here by CP(N−1)CP(N-1)CP(N−1) whereas its tangent vectors define local dynamical variables (LDV's) describing "matter". The conservation laws of LDV's express self-conservation of the "material particles" during continuous evolution being expressed as the affine parallel transport agrees with Fubuni-Study metric, create the "affine gauge potential" as the solution of the partial differential equations. Such procedure embeds the quantum dynamics into dynamical space-time whose state-dependent coordinates arose due to encoding results of quantum measurement by the qubit spinor whose components subjected to Lorentz transformations of "quantum boosts" and "quantum rotations". Thereby, in the framework of super-relativity, the objective character of the quantum measurement is inherently related to the dynamical space-time structure that replaces the notion of "observer".
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)CP(N-1)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)CP(N-1)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)CP(N-1)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)CP(N-1)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 Schrödinger'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.
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 idea is to base the theory on the relative amplitudes solely. Quantum measurements will be described in terms of the parallel transport of the local dynamical variables and a specific gauge reduction of the full state vector to the Qubit coherent state. I will discuss here field equations of quantum particle arising in the dynamical space-time.