Interaction picture

About: Interaction picture is a research topic. Over the lifetime, 452 publications have been published within this topic receiving 7562 citations. The topic is also known as: Dirac picture.

Anomalous Ward identities in spinor field theories

Abstract: We consider the model of a spinor field with arbitrary internal degrees of freedom having arbitrary nonderivative coupling to external scalar, pseudoscalar, vector, and axial-vector fields. By carefully defining the $S$ matrix in the interaction picture, the vector and axial-vector currents associated with the external vector and axial-vector fields are found to satisfy anomalous Ward identities. If we require that the vector currents satisfy the usual Ward identities, the divergence of the axial-vector current contains well-defined anomalous terms. These terms are explicitly calculated.

Quantum Theory of the Electromagnetic Field in a Variable-Length One-Dimensional Cavity

Abstract: The quantum theory of linearly polarized light propagating in a 1‐dimensional cavity bounded by moving mirrors is formulated by utilizing the symplectic structure of the space of solutions of the wave equation satisfied by the Coulomb‐gauge vector potential. The theory possesses no Hamiltonian and no Schrodinger picture. Photons can be created by the exciting effect of the moving mirrors on the zero‐point field energy. A calculation indicates that the number of photons created is immeasurably small for nonrelativistic mirror trajectories and continuous mirror velocities. Automorphic transformations of the wave equation are used to calculate mode functions for the cavity, and adiabatic expansions for these transformations are derived. The electromagnetic field may be coupled to matter by means of a transformation from the interaction picture to the Heisenberg picture; this transformation is generated by an interaction Hamiltonian.

A Fourth-Order Runge–Kutta in the Interaction Picture Method for Simulating Supercontinuum Generation in Optical Fibers

Abstract: An efficient algorithm, which exhibits a fourth-order global accuracy, for the numerical solution of the normal and generalized nonlinear Schrodinger equations is presented. It has applications for studies of nonlinear pulse propagation and spectral broadening in optical fibers. Simulation of supercontinuum generation processes, in particular, places high demands on numerical accuracy, which makes efficient high-order schemes attractive. The algorithm that is presented here is an adaptation for use in the nonlinear optics field of the fourth-order Runge-Kutta in the Interaction Picture (RK4IP) method, which was originally developed for studies on Bose-Einstein condensates. The performance of the RK4IP method is validated and compared to a number of conventional methods by modeling both the propagation of a second-order soliton and the generation of supercontinuum radiation. It exhibits the expected global fourth-order accuracy for both problems studied and is the most accurate and efficient of the methods tested.

Wave-function quantum stochastic differential equations and quantum-jump simulation methods

Abstract: The quantum-stochastic-differential-equation formulation of driven quantum-optical systems is carried out in the interaction picture, and quantum stochastic differential equations for wave functions are derived on the basis of physical principles. The Ito form is shown to be the most practical, since it already contains all the radiation reaction terms. The connection between this formulation and the master equation is shown to be very straightforward. In particular, a direct connection is made to the theory of continuous measurements, which leads directly to the method of quantum-jump simulations of solutions of the master equation. It is also shown that all conceivable spectral and correlation-function information in output fields is accessible by means of an augmentation of the simulation process. Finally, the question of the reality of the jumps used in the simulations is posed.

Foundations of quantum mechanics

Abstract: (Volume II).- IX Representation of Hilbert Spaces by Function Spaces.- 1 Maximal Decision Observables.- 2 Representation of ? as ?2(Sp(A), ?) where Sp(A) is the Spectrum of a Scale Observable A.- 3 Improper Scalar and Vector Functions Defined on Sp(A).- 4 Transformation of One Representation into Another.- 5 Position and Momentum Representation.- 6 Degenerate Spectra.- X Equations of Motion.- 1 The Heisenberg Picture.- 2 The Schrodinger Picture.- 3 The Interaction Picture.- 4 Time Reversal Transformations.- XI The Spectrum of One-Electron Systems.- 1 The Effect of the Emission of a Photon.- 2 Ensembles Consisting of Bound States.- 3 The Spectrum of Hydrogen-like Atoms.- 4 The Eigenfunctions for the Discrete Spectrum.- 5 The Continuous Spectrum.- 6 Perturbation Theory.- 7 Perturbation Computations and Symmetry.- 8 The Spectrum of Alkali Atoms.- 9 Electron Spin.- 10 Addition of Angular Momentum.- 11 Fine Structure of Hydrogen and Alkali Metals.- XII Spectrum of Two-Electron Systems.- 1 The Hilbert Space and the Hamiltonian Operator for the Internal Motion of Atoms with n Electrons.- 2 The Spectrum of Two-Electron Atoms.- 3 Ritz Variational Principle.- 4 The Fine Structure of the Helium Spectrum.- XIII Selection Rules and the Intensity of Spectral Lines.- 1 Intensity of Spectral Lines.- 2 Representation Theory and Matrix Elements.- 3 Selection Rules for One-Electron Spectra.- 4 Selection Rules for the Helium Spectrum.- XIV Spectra of Many-Electron Systems.- 1 Energy Terms in the Absence of Spin.- 2 Fine Structure Splitting of Spectral Lines.- 3 Structure Principles.- 4 The Periodic System of the Elements.- 5 Selection and Intensity Rules.- 6 Zeeman Effect.- 7 f Electron Problems and the Symmetric Group.- 8 The Characters for the Representations of Sf and Un.- 9 Perturbation Computations.- XV Molecular Spectra and the Chemical Bond.- 1 The Hamiltonian Operator for a Molecule.- 2 The Form of the Eigenfunctions.- 3 The Ionized Hydrogen Molecule.- 4 Structure Principles for Molecular Energy Levels.- 5 Formation of a Molecule from Two Atoms.- 6 The Hydrogen Molecule.- 7 The Chemical Bond.- 8 Spectra of Diatomic Molecules.- 9 The Effect of Electron Spin on Molecular Energy Levels.- XVI Scattering Theory.- 1 General Properties of Ensembles Used in Scattering Experiments.- 2 General Properties of Effects Used in Scattering Experiments.- 3 Separation of Center of Mass Motion.- 4 Wave Operators and the Scattering Operator.- 4.1 Definition of the Wave Operators.- 4.2 Some General Properties of Wave Operators.- 4.3 Wave Operators and the Spectral Representation of the Hamiltonian Operators.- 4.4 The S Operator.- 4.5 A Sufficient Condition for the Existence of Normal Wave Operators.- 4.6 The Existence of Complete Wave Operators.- 4.7 Stationary Scattering Theory.- 4.8 Scattering of a Pair of Identical Elementary Systems.- 4.9 Multiple-Channel Scattering Theory.- 5 Examples of Wave Operators and Scattering Operators.- 5.1 Scattering of an Elementary System of Spin $$ \frac{1}{2} $$ by an Elementary System of Spin 0.- 5.2 The Born Approximation.- 5.3 Scattering of an Electron by a Hydrogen Atom.- 6 Examples of Registrations in Scattering Experiments.- 6.1 The Effect of the "Impact"(Volume II).- IX Representation of Hilbert Spaces by Function Spaces.- 1 Maximal Decision Observables.- 2 Representation of ? as ?2(Sp(A), ?) where Sp(A) is the Spectrum of a Scale Observable A.- 3 Improper Scalar and Vector Functions Defined on Sp(A).- 4 Transformation of One Representation into Another.- 5 Position and Momentum Representation.- 6 Degenerate Spectra.- X Equations of Motion.- 1 The Heisenberg Picture.- 2 The Schrodinger Picture.- 3 The Interaction Picture.- 4 Time Reversal Transformations.- XI The Spectrum of One-Electron Systems.- 1 The Effect of the Emission of a Photon.- 2 Ensembles Consisting of Bound States.- 3 The Spectrum of Hydrogen-like Atoms.- 4 The Eigenfunctions for the Discrete Spectrum.- 5 The Continuous Spectrum.- 6 Perturbation Theory.- 7 Perturbation Computations and Symmetry.- 8 The Spectrum of Alkali Atoms.- 9 Electron Spin.- 10 Addition of Angular Momentum.- 11 Fine Structure of Hydrogen and Alkali Metals.- XII Spectrum of Two-Electron Systems.- 1 The Hilbert Space and the Hamiltonian Operator for the Internal Motion of Atoms with n Electrons.- 2 The Spectrum of Two-Electron Atoms.- 3 Ritz Variational Principle.- 4 The Fine Structure of the Helium Spectrum.- XIII Selection Rules and the Intensity of Spectral Lines.- 1 Intensity of Spectral Lines.- 2 Representation Theory and Matrix Elements.- 3 Selection Rules for One-Electron Spectra.- 4 Selection Rules for the Helium Spectrum.- XIV Spectra of Many-Electron Systems.- 1 Energy Terms in the Absence of Spin.- 2 Fine Structure Splitting of Spectral Lines.- 3 Structure Principles.- 4 The Periodic System of the Elements.- 5 Selection and Intensity Rules.- 6 Zeeman Effect.- 7 f Electron Problems and the Symmetric Group.- 8 The Characters for the Representations of Sf and Un.- 9 Perturbation Computations.- XV Molecular Spectra and the Chemical Bond.- 1 The Hamiltonian Operator for a Molecule.- 2 The Form of the Eigenfunctions.- 3 The Ionized Hydrogen Molecule.- 4 Structure Principles for Molecular Energy Levels.- 5 Formation of a Molecule from Two Atoms.- 6 The Hydrogen Molecule.- 7 The Chemical Bond.- 8 Spectra of Diatomic Molecules.- 9 The Effect of Electron Spin on Molecular Energy Levels.- XVI Scattering Theory.- 1 General Properties of Ensembles Used in Scattering Experiments.- 2 General Properties of Effects Used in Scattering Experiments.- 3 Separation of Center of Mass Motion.- 4 Wave Operators and the Scattering Operator.- 4.1 Definition of the Wave Operators.- 4.2 Some General Properties of Wave Operators.- 4.3 Wave Operators and the Spectral Representation of the Hamiltonian Operators.- 4.4 The S Operator.- 4.5 A Sufficient Condition for the Existence of Normal Wave Operators.- 4.6 The Existence of Complete Wave Operators.- 4.7 Stationary Scattering Theory.- 4.8 Scattering of a Pair of Identical Elementary Systems.- 4.9 Multiple-Channel Scattering Theory.- 5 Examples of Wave Operators and Scattering Operators.- 5.1 Scattering of an Elementary System of Spin $$ \frac{1}{2} $$ by an Elementary System of Spin 0.- 5.2 The Born Approximation.- 5.3 Scattering of an Electron by a Hydrogen Atom.- 6 Examples of Registrations in Scattering Experiments.- 6.1 The Effect of the "Impact" of a Microsystem on a Surface.- 6.2 Counting Microsystems Scattered into a Solid Angle.- 6.3 The Scattering Cross Section.- 7 Survey of Other Problems in Scattering Theory.- XVII The Measurement Process and the Preparation Process.- 1 The Problem of Consistency.- 2 Measurement Scattering Processes.- 2.1 Measurement with a Microscope.- 2.2 Measurement Scattering Morphisms.- 2.3 Properties of Measurement Scattering Morphisms.- 3 Measurement Transformations.- 3.1 Measurement Transformation Morphisms.- 3.2 Properties of Measurement Transformation Morphisms.- 4 Transpreparations.- 4.1 Reduction of a Preparation Procedure by Means of a Registration Procedure.- 4.2 Transpreparation by Means of Scattering.- 4.3 Collapse of Wave Packets?.- 4.4 The Einstein-Podolski-Rosen Paradox.- 5 Measurements of the First Kind.- 6 The Physical Importance of Scattering Processes Used for Registration and Preparation.- 6.1 Sequences of Measurement Scatterings and Measurement Transformations.- 6.2 Physical Importance of Measurement Scattering and Measurement Transformations.- 6.3 Chains of Transpreparations.- 6.4 The Importance of Transpreparators for the Preparation Process.- 6.5 Unstable States.- 7 Complex Preparation and Registration Processes.- XVIII Quantum Mechanics, Macrophysics and Physical World Views.- 1 Universality of Quantum Mechanics?.- 2 Macroscopic Systems.- 3 Compatibility of the Measurement Process with Preparation and Registration Procedures.- 4 "Point in Time" of Measurement in Quantum Mechanics?.- 5 Relationships Between Different Theories and Quantum Mechanics.- 6 Quantum Mechanics and Cosmology.- 7 Quantum Mechanics and Physical World Views.- Appendix V Groups and Their Representations.- 1 Groups.- 2 Cosets and Invariant Subgroups.- 3 Isomorphisms and Homomorphisms.- 4 Isomorphism Theorem.- 5 Direct Products.- 6 Representations of Groups.- 7 The Irreducible Representations of a Finite Group.- 8 Orthogonality Relations for the Elements of Irreducible Representation Matrices.- 9 Representations of the Symmetric Group.- 10 Topological Groups.- 10.1 The Species of Structure: Topological Group.- 10.2 Uniform Structures of Groups.- 10.3 Lie Groups.- 10.4 Representations of Topological Groups.- 10.5 Group Rings of Compact Lie Groups.- 10.6 Representations in Hilbert Space.- 10.7 Representations up to a Factor.- References.