3,459 research outputs found
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 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 , 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 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 .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 , 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 .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 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
associated with the Jacobi vector fields of the geodesic variations in the
complex projective Hilbert space 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 . 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 .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 , 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
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