On the Evaluation of Scalarproducts of Nonlinear Spinorfield State Functionals

1981 ◽  
Vol 36 (10) ◽  
pp. 1024-1031
Author(s):  
H. Stumpf
Keyword(s):  
Quantum Theory ◽  
State Space ◽  
Quark Model ◽  
A Priori ◽  
Preceding Paper ◽  
Functional Space ◽  
Nonlinear Field ◽  
Metrical Structure ◽  
Metric Tensor ◽  
Linear State

The metrical structure of the linear state space of a quantized nonlinear field cannot be given a priori. Rather it is determined by the dynamics of the field itself. For the evaluation of state norms and scalarproducts this metric must be known. In functional quantum theory the metrical structure is expressed by the metric tensor G (j) in functional space. Equivalent to the knowledge of G (j) is the knowledge of the set of dual state functionals {|S(j, a)〉} together with the corre-sponding original state functionals {|F(j, a)〉} . In preceding papers attempts were made to calculate G (j). In this paper an approach is made to determine the dual state functionals directly. Equations are derived which have to be satisfied by the dual functionals. The method works in those state sectors which are characterized by real (monopole) particles or monopole ghosts, while it does not work for multipole ghost states. Norm calculations are performed for local monopole fermion states and local monopole boson states of the lepton-quark model derived in a preceding paper.

scholarly journals ON PATH-DEPENDENT STATE SPACE FOR THE PROCA FIELD

1999 ◽  
Vol 14 (21) ◽  
pp. 1383-1390 ◽  
Author(s):  
ROLANDO GAITAN
Keyword(s):  
Quantum Theory ◽  
State Space ◽  
Functional Integration ◽  
Functional Space ◽  
Vacuum State ◽  
Space Representation ◽  
Integration Measure ◽  
Path Dependent ◽  
Dependent State ◽  
Gauge Formulation

A gauge formulation for the Proca model quantum theory in an open path functional space representation is revisited. The path-dependent vacuum state and the functional integration measure needed to define an internal product in the state space are obtained. Finally, a possible scheme for the construction of creation–annihilation path-dependent operators is presented.

Symmetry Conditions on Nonlinear Spinor Field Functionals/The symmetry conditions of nonlinear spinor theory of elementary particles, i.e. the definitions of quantum numbers, are given for the nonlinear spinor field functionals.

1970 ◽  
Vol 25 (11) ◽  
pp. 1556-1561 ◽  
Author(s):  
H. Stumpf ◽  
K. Scheerer ◽  
H.G. Märtl
Keyword(s):  
Quantum Theory ◽  
Spinor Field ◽  
Preceding Paper ◽  
Functional Space ◽  
Invariance Group ◽  
Mathematical Meaning ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
Quantum Numbers ◽  
Symmetry Properties

The operator equations of quantum theory can be replaced formally by functional equations of corresponding Schwinger functionals 1-3. To give this formalism a physical and mathematical meaning one has to develop a complete functional quantum theory as has been proposed in a preceding paper4. Then the complete physical information has to be given by functional operations only. Especially the quantum numbers of ordinary quantum theory have to be reproduced functionally. As the quantum numbers are defined by the eigenvalues of the generators of the corresponding invariance groups, one has to investigate these quantities in functional space. This is done in this paper. To have a definite model we consider the nonlinear spinor field with noncanonical relativistic Heisenberg quantization 5 the form invariance group of which is the Poincare group. Although this model has still other symmetry properties we restrict ourselves to the discussion of the quantum number conditions resulting from this group, as the considerations for other groups and models are quite analogous.

scholarly journals The Invariant Set Postulate: a new geometric framework for the foundations of quantum theory and the role played by gravity

2009 ◽  
Vol 465 (2110) ◽  
pp. 3165-3185 ◽  
Author(s):  
T. N. Palmer
Keyword(s):  
Quantum Theory ◽  
Science Fiction ◽  
State Space ◽  
Fractal Geometry ◽  
Quantum Physics ◽  
Nonlinear Dynamical Systems ◽  
Physical Reality ◽  
Invariant Set ◽  
Geometric Framework

A new law of physics is proposed, defined on the cosmological scale but with significant implications for the microscale. Motivated by nonlinear dynamical systems theory and black-hole thermodynamics, the Invariant Set Postulate proposes that cosmological states of physical reality belong to a non-computable fractal state-space geometry I , invariant under the action of some subordinate deterministic causal dynamics D I . An exploratory analysis is made of a possible causal realistic framework for quantum physics based on key properties of I . For example, sparseness is used to relate generic counterfactual states to points p ∉ I of unreality, thus providing a geometric basis for the essential contextuality of quantum physics and the role of the abstract Hilbert Space in quantum theory. Also, self-similarity, described in a symbolic setting, provides a possible realistic perspective on the essential role of complex numbers and quaternions in quantum theory. A new interpretation is given to the standard ‘mysteries’ of quantum theory: superposition, measurement, non-locality, emergence of classicality and so on. It is proposed that heterogeneities in the fractal geometry of I are manifestations of the phenomenon of gravity. Since quantum theory is inherently blind to the existence of such state-space geometries, the analysis here suggests that attempts to formulate unified theories of physics within a conventional quantum-theoretic framework are misguided, and that a successful quantum theory of gravity should unify the causal non-Euclidean geometry of space–time with the atemporal fractal geometry of state space. The task is not to make sense of the quantum axioms by heaping more structure, more definitions, more science fiction imagery on top of them, but to throw them away wholesale and start afresh. We should be relentless in asking ourselves: From what deep physical principles might we derive this exquisite structure? These principles should be crisp, they should be compelling. They should stir the soul. Chris Fuchs ( Gilder 2008 , p. 335)

Observability Analysis for a Single-Phase Inverter Using Linear State-Space Equations

2021 ◽  
Author(s):  
Jeanpierre D. Valentin Acevedo ◽  
Eduardo I. Ortiz-Rivera ◽  
Rachid Darbali-Zamora
Keyword(s):  
State Space ◽  
Single Phase ◽  
Phase Inverter ◽  
Observability Analysis ◽  
Single Phase Inverter ◽  
Linear State

Stewart Platform Model with Uncertain Parameters

2010 ◽  
Vol 164 ◽  
pp. 177-182 ◽  
Author(s):  
Lukas Březina ◽  
Tomáš Březina
Keyword(s):  
State Space ◽  
Controller Design ◽  
State Space Model ◽  
Stewart Platform ◽  
Dynamics Model ◽  
H Infinity ◽  
Uncertain Dynamics ◽  
Six Dof ◽  
Linear State ◽  
Nominal Position

The paper deals with development of uncertain dynamics model of a six DOF parallel mechanism (Stewart platform) suitable for H-infinity controller design. The model is based on linear state space models of the machine obtained by linearization of the SimMechanics model. The linearization is performed for two positions of the machine in its workspace. It is the nominal position and the position where each link of the machine reaches its maximal length. The uncertainties are then represented as differences between parameters of corresponding state-space matrices. The uncertain state space model is then obtained using upper linear fractional transformation. There are also mentioned several notes regarding H-infinity controller designed according to the obtained model.

Optimal State-Space Control of a Gas Turbine Engine

1992 ◽  
Vol 114 (4) ◽  
pp. 763-767 ◽  
Author(s):  
J. W. Watts ◽  
T. E. Dwan ◽  
C. G. Brockus
Keyword(s):  
State Space ◽  
Gas Turbine ◽  
State Space Model ◽  
Gas Turbine Engine ◽  
The State ◽  
Operating Conditions ◽  
Turbine Engine ◽  
Analog Control ◽  
Linear State ◽  
High Level

An analog fuel control for a gas turbine engine was compared with several state-space derived fuel controls. A single-spool, simple cycle gas turbine engine was modeled using ACSL (high level simulation language based on FORTRAN). The model included an analog fuel control representative of existing commercial fuel controls. The ACSL model was stripped of nonessential states to produce an eight-state linear state-space model of the engine. The A, B, and C matrices, derived from rated operating conditions, were used to obtain feedback control gains by the following methods: (1) state feedback; (2) LQR theory; (3) Bellman method; and (4) polygonal search. An off-load transient followed by an on-load transient was run for each of these fuel controls. The transient curves obtained were used to compare the state-space fuel controls with the analog fuel control. The state-space fuel controls did better than the analog control.

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