arXiv subjects

Peter Leifer

Publications and source records attributed to Peter Leifer.

At least 19 recordsLinked to original sources

arXiv2019

The non-Abelian field current of the self-interacting quantum electron

Internal degrees of freedoms of the quantum electron (spin and charge) introduced by Dirac lead to the non-Abelian field configuration of the electron in the complex projective Hilbert space $CP(3)$ of the unlocated quantum states (UQS). Such fields represented by the coefficient functions of the local dynamical variables (LDV's) corresponding $SU(4)$ generators of the Poincaré group. These generators describe the deformation of the UQS by the dynamical shifts, boosts and rotations. Interaction of this non-Abelian field with the electrodynamics-like gauge field (internal+external) will suppress the divergency of the Jacobi vector field in the vicinity of the "north pole" in $CP(3)$. Thereby, the stable "bundle" of the nearby geodesics comprises the lump-like quantum self-interacting electron.

physics.gen-ph↗

arXiv2018

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.

physics.gen-ph↗

arXiv2018

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}.

physics.gen-ph↗

arXiv2016

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).

physics.gen-ph↗

arXiv2013

The role of the $CP(N-1)$ geometry in the intrinsic unification of the general relativity and QFT

Einstein's program of the unified field theory transformed nowadays to the TOE requiring new primordial elements and relations between them. Definitely, they must be elements of the quantum nature. One of most fundamental quantum elements are pure quantum states. Their basic relations are defined by the geometry of the complex projective Hilbert space. In the framework of such geometry all physical concepts should be formulated and derived in the natural way. Analysis following this logic shows that inertia and inertial forces are originated not in space-time but it the space of quantum states since they are generated by the deformation of quantum states as a reaction on an external interaction or self-interaction. In particular, inertia law generalized by Einstein during development of general relativity (GR) will be expressed in intrinsic quantum terms. It is assumed that quantum formulation of the inertia law should clarify the old problem of inertial mass (dynamical mass generation). The conservation of energy-momentum following form this law has been applied to self-interacting quantum Dirac's electron.

physics.gen-ph↗

arXiv2011

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.

physics.gen-ph↗

arXiv2011

Self-interacting quantum electron

A model of self-interacting quantum non-local Dirac's electron has been proposed. Its dynamics was revealed by the projective representation of operators corresponding to spin/charge degrees of freedom. Energy-momentum field is described by the system of quasi-linear "field-shell" PDE's following from the conservation law expressed by the affine parallel transport of the energy momentum vector field in CP(3). I discuss here travel-wave solutions of these equations and the "off-shell" dispersion law asymptotically coinciding with the "on-shell" de Broglie dispersion law.

physics.gen-ph↗

arXiv2010

"Field-shell" of the self-interacting quantum electron

Self-interacting dynamics of non-local Dirac's electron has been proposed. This dynamics was revealed by the projective representation of operators corresponding to spin/charge degrees of freedom. Energy-momentum field is described by the system of quasi-linear ``field-shell" PDE's following from the conservation law expressed by the affine parallel transport in $CP(3)$ \cite{Le1}. We discuss here solutions of these equations in the connection with the following problems: curvature of $CP(3)$ as a potential source of electromagnetic fields and the self-consistent problem of the electron mass.

physics.gen-ph↗

arXiv2009

Towards the demystificatiom of quantum interference

It has been shown that velocity of propagation of wave front cannot coincide with observable velocity of quantum particles. It is additional argument leads to conclusion that phase wave of de Broglie cannot be associated with single "elementary" particle like electron. Therefore quantum interference under linear superposition cannot describe energy distribution in extended quantum particles. Essentially new approach is required in order to establish non-linear relativistic wave equations with soliton-like solutions.

physics.gen-ph↗

arXiv2009

Particle-unparticle duality in super-relativity

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.

physics.gen-ph↗

arXiv2008

Morphogenesis and dynamics of quantum state

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.

physics.gen-ph↗

arXiv2008

Quantum geometry of the Cartan control problem

The Cartan control problem of the quantum circuits discussed from the differential geometry point of view. Abstract unitary transformations of $SU(2^n)$ are realized physically in the projective Hilbert state space $CP(2^n-1)$ of the n-qubit system. Therefore the Cartan decomposition of the algebra $AlgSU(2^n-1)$ into orthogonal subspaces $h$ and $b$ such that $[h,h] \subseteq h, [b,b] \subseteq h, [b,h] \subseteq b$ is state-dependent and thus requires the representation in the local coordinates.

physics.gen-ph↗

arXiv2008

Reconstruction of the unitary symmetry in super-relativity

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".

physics.gen-ph↗

arXiv2008

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 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.

physics.gen-ph↗

arXiv2007

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.

physics.gen-ph↗

arXiv2006

Objective quantum theory based on the CP(N-1) affine gauge fields

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 the other hand the linear quantum theory prevents the existence of the localizable solutions, and after all, leads to the divergences problem in the quantum field theory. In order to overcome these difficulties the non-perturbative nonlinearity originated by the curvature of the compact quantum phase space has been used.

physics.gen-ph↗

arXiv2006

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 $CP(N-1)$.

physics.gen-ph↗

arXiv2006

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 $CP(N-1)$.

physics.gen-ph↗