NDLI: Hyperbolic Quantization

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Advances in Applied Clifford Algebras : Volume 26

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Geometric Algebra and Particle Dynamics

Pseudo-Unitary Conformal Spin Structures

Wave-Functions for Spin-3/2 and Integer Spin Fields

Twistors in Geometric Algebra

A Relativistic Algebraic Approach to the Q/C Interface: Implications for “Quantum Reality”

Clifford Algebras and Matrix Factorizations

Geometrical Interpretation of the U(1), SU(2), SU(3) Gauges and of the Energy-Momentum Tensors in the Electron, Electroweak and Quark Chromodynamics Theories

The Hermitian Clifford Analysis Toolbox

Pure Spinor Geometry: Its Possible Role in Quantum Physics

Parabolic Geometries Related with Several Fueter Operators

Oriented Conformal Geometric Algebra

Non-Localisation des Électrons en Mouvement

A Spin Gauge Model of a Family of Particles

On a Class of Inner Spherical Monogenics and their Primitives

Spinors and Pre-Metric Electromagnetism

The Barut Second-Order Equation: Lagrangian, Dynamical Invariants and Interactions

On Hyperbolic Function Theory

The Application of a Discrete Function Theory to the Solution of the Navier-Stokes Equations

Spherical Wavelet Transform

Geometric Tri-Product of the Spin Domain and Clifford Algebras

Parameter Estimation from Uncertain Data in Geometric Algebra

Quadratic Forms over $${\mathbb{Z}}$$ from Diophantus to the 290 Theorem

Some Ways to Secure Elliptic Curve Cryptosystems

Exponentials of Bivectors and their Symplectic Counterparts

Inverse Kinematics Computation in Computer Graphics and Robotics Using Conformal Geometric Algebra

Clifford Fourier Transform on Multivector Fields and Uncertainty Principles for Dimensions n = 2 (mod 4) and n = 3 (mod 4)

Quantum Fractals. Geometric Modeling of Quantum Jumps with Conformal Maps

Premetric Electrodynamics

Clifford Modules and Twisted K-Theory

START : Inventio Principia Geometrica Physicae

Geometric Formulation of the Many-Electron Theory

Hyperbolic Quantization

Symplectic Dirac Operator and its Generalization

A Generalization of Monogenic Functions to Fine Domains

On Meson Algebras

On the Boundedness of Calderón-Zygmund Operators with Monogenic Kernels

Banach Envelopes of Monogenic Hardy Spaces

Origin of Complex and Quaternionic Wavefunctions in Quantum Mechanics: the Scale-Relativistic View

Diffeomorphism Invariance and Local Lorentz Invariance

Quaternionic Operator Methods in Fluid Dynamics

A New Adjacency Matrix for Finite Graphs

New Perspectives on the Kähler Calculus and Wave Functions

The Kähler-Dirac Equation with Non-Scalar-Valued Differential Form

Powers of the Parabolic Dirac Operator

Advances in Applied Clifford Algebras : Volume 18, Issue 2, May 2008

Advances in Applied Clifford Algebras : Volume 18, Issue 1, February 2008

Advances in Applied Clifford Algebras : Volume 17

Advances in Applied Clifford Algebras : Volume 16

Advances in Applied Clifford Algebras : Volume 15

Advances in Applied Clifford Algebras : Volume 14

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Advances in Applied Clifford Algebras : Volume 12

Advances in Applied Clifford Algebras : Volume 11

Advances in Applied Clifford Algebras : Volume 10

Advances in Applied Clifford Algebras : Volume 9

Advances in Applied Clifford Algebras : Volume 8

Advances in Applied Clifford Algebras : Volume 7

Hyperbolic Quantization

Content Provider	Springer Nature Link
Author	Khrennikov, Andrei
Copyright Year	2008
Abstract	We demonstrated that classical mechanics have, besides the well known quantum deformation, another deformation – so called hyperbolic quantum mechanics. The classical Poisson bracket can be obtained as the limit h → 0 not only of the ordinary Moyal bracket, but also hyperbolic analogue of the Moyal bracket. Thus there are two different deformations of classical phase-space: complex Hilbert space and hyperbolic Hilbert space (module over a so called hyperbolic algebra – the two-dimensional Clifford algebra). Ordinary (complex) and hyperbolic quantum mechanics are characterized by two types of interference perturbation of the classical formula of total probability: ordinary cos-interference and hyperbolic cosh-interference.
Ending Page	852
Page Count	10
Starting Page	843
File Format	PDF
ISSN	01887009
e-ISSN	16614909
Journal	Advances in Applied Clifford Algebras
Issue Number	3
Volume Number	18
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2008-06-16
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical Methods in Physics pseudo-differential operators Clifford algebras, spinors Mathematical and Computational Physics Applications in quantum physics Applications of Mathematics hyperbolic quantum mechanics Physics Two-dimensional Clifford algebras
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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