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:0901.2694

Particle-unparticle duality in super-relativity

Peter Leifer

Published Jan 18, 2009• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.0901.2694

Related papers

Morphogenesis and dynamics of quantum state

Peter Leifer

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.

arXiv:0812.0065•Nov 29, 2008•1 citation

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

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

Super-relativity in the quantum theory

Peter Leifer

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.

arXiv:physics/0702135•Feb 16, 2007•0 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

Superluminal, contradiction and unification between quantum theory and special relativity

Yi‐Fang Chang

First, some superluminal phenomena are introduced. Next, based on the complete special relativity which includes the generalized Lorentz transformation (GLT) and superluminal in the spacelike interval, we search contradiction between the uncertainty principle in quantum mechanics and strict classification of the timelike-spacelike intervals in special relativity. Third, we propose new interpretation of the duality in the double-slit experiment that is the particle-wave duality corresponds to the timelike and spacelike intervals, respectively. Such the duality is mutually exclusive and complementary. Fourth, we derive the new LT and GLT for very small space and time, and research possible unification of quantum theory and complete special relativity.

International Journal of Physics and Applications•Jan 1, 2022•0 citations
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.
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.
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".
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 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)CP(N-1)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.
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).
First, some superluminal phenomena are introduced. Next, based on the complete special relativity which includes the generalized Lorentz transformation (GLT) and superluminal in the spacelike interval, we search contradiction between the uncertainty principle in quantum mechanics and strict classification of the timelike-spacelike intervals in special relativity. Third, we propose new interpretation of the duality in the double-slit experiment that is the particle-wave duality corresponds to the timelike and spacelike intervals, respectively. Such the duality is mutually exclusive and complementary. Fourth, we derive the new LT and GLT for very small space and time, and research possible unification of quantum theory and complete special relativity.