Relativistic wave equations with fractional derivatives and pseudodifferential operators

Keywords

Covariant transformation, Mathematics, Relativistic wave equations, Mathematical physics, Dirac (video compression format)

References

• Lorentz-Invariant Pseudo-Differential Wave EquationsDaniel G. Barci, C. G. Bollini, L. E. Oxman — 1998
• L-matrix theory : or, The grammar of Dirac matricesAlladi Ramakrishnan — 1972
• Symmetries of Equations of Quantum MechanicsA. G. Nikitin, W. I. Fushchich, В. И. Фущич — 1994
• Introduction to Pseudodifferential and Fourier Integral OperatorsFrançois Trèves — 1980
• Cubic root of Klein-Gordon equationMikhail S. Plyushchay, Michel Rausch de Traubenberg — 2000
• Integrals and seriesA. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev — 1992
• Linearization of polynomialsN. Fleury, Michel Rausch de Traubenberg — 1992
• The Pauli matrices in n dimensions and finest gradings of simple Lie algebrasJ. Patera, Hans Zassenhaus — 1988
• Synthesis of Covariant Particle EquationsL. L. Foldy — 1956
• The “square root” of the Dirac equation within supersymmetryJ. Szwed — 1986
• Z3-grading and the cubic root of the Dirac equationRichard Kerner — 1992
• DIRAC EQUATION WITH FRACTIONAL DERIVATIVES OF ORDER 2/3Andrea Raspini — 2000
• Relativistic Invariance and the Square‐Root Klein‐Gordon EquationJ. Sucher — 1963
• The Pseudodifferential operator square root of the Klein-Gordon equationCláus Lämmerzahl — 1993
• Operator of Fractional Derivative in the Complex PlaneP. Závada — 1998
• Second Quantization of the Square-Root Klein-Gordon Operator.John R. Lindsay Smith — 2017
• Second Quantization of the Square-Root Klein-Gordon Operator, Microscopic Causality, Propagators, and InteractionsJohn R. Lindsay Smith — 2017

Cited by

• The Convergence of Economic DevelopmentsMichèle Caputo — 2012
• Stationarity–conservation laws for fractional differential equations with variable coefficientsMa$lslash$gorzata Klimek — 2002
• Gauge invariant fractional electromagnetic fieldsMatheus J. Lazo — 2011
• Aspects of the Coarse-Grained-Based Approach to a Low-Relativistic Fractional Schr\"odinger EquationJosé Weberszpil, Cresus F. L. Godinho, Aleksey Cherman — 2012
• Repulsive Casimir force from fractional Neumann boundary conditionsSungbin Lim, Lee-Peng Teo — 2009
• Fractional Dynamics from Einstein Gravity, General Solutions, and Black HolesSergiu I. Vacaru — 2010
• Stochastic quantization of nonlocal fieldsSungbin Lim, S. V. Muniandy — 2004
• FRACTIONAL DIRAC OPERATORS AND LEFT-RIGHT FRACTIONAL CHAMSEDDINE–CONNES SPECTRAL BOSONIC ACTION PRINCIPLE IN NONCOMMUTATIVE GEOMETRYRami Ahmad El‐Nabulsi — 2010
• Stationarity-conservation laws for certain linear fractional differential equationsMalgorzata Klimek — 2001
• Geometry and field theory in multi-fractional spacetimeGianluca Calcagni — 2011
• Cosmology of the Lifshitz universeGianluca Calcagni — 2009
• Complexified quantum field theory and “mass without mass” from multidimensional fractional actionlike variational approach with dynamical fractional exponentsAhmad Rami El-Nabulsi — 2009
• Fractional derivative quantum fields at positive temperatureSungbin Lim — 2006
• Fractional Dirac operators and deformed field theory on Clifford algebraRami Ahmad El‐Nabulsi — 2009
• Finite temperature Casimir effect for a massless fractional Klein-Gordon field with fractional Neumann conditionsChai Hok Eab, Sungbin Lim, Lee-Peng Teo — 2007
• Anomalous g-Factors for Charged Leptons in a Fractional Coarse-Grained ApproachJ. Weberszpil, J. A. Helayël-Neto — 2013
• A memory model of sedimentation in water reservoirsMichèle Caputo, José M. Carcione — 2013
• Simulating Fractional Derivatives Using MatlabChunmei Chi, Feng Gao — 2013
• FRACTIONAL FIELD THEORIES FROM MULTI-DIMENSIONAL FRACTIONAL VARIATIONAL PROBLEMSRami Ahmad El‐Nabulsi — 2008
• Topological symmetry breaking of self-interacting fractional Klein–Gordon field theories on toroidal spacetimeSungbin Lim, Lee-Peng Teo — 2008

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