General Fractional Noether Theorem and Non-Holonomic Action Principle

Author:

Tarasov Vasily E.12ORCID

Affiliation:

1. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia

2. Department of Physics, 915, Moscow Aviation Institute (National Research University), Moscow 125993, Russia

Abstract

Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non-Lagrangian field theory. The use of the GFC allows us to take into account a wide class of nonlocalities in space and time compared to the usual fractional calculus. The use of non-holonomic variation equations allows us to consider field equations and equations of motion for a wide class of irreversible processes, dissipative and open systems, non-Lagrangian and non-Hamiltonian field theories and systems. In addition, the proposed GF action principle and the GF Noether theorem are generalized to equations containing general fractional integrals (GFI) in addition to general fractional derivatives (GFD). Examples of field equations with GFDs and GFIs are suggested. The energy–momentum tensor, orbital angular-momentum tensor and spin angular-momentum tensor are given for general fractional non-Lagrangian field theories. Examples of application of generalized first Noether’s theorem are suggested for scalar end vector fields of non-Lagrangian field theory.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference174 articles.

1. Bogoliubov, N.N., and Shirkov, D.V. (1980). Introduction to the Theory of Quantized Fields, John Wiley and Sons Inc.. [3rd ed.].

2. Roman, P. (1969). Introduction to Quantum Field Theory, John Wiley and Sons Inc.

3. Itzykson, C., and Zuber, J.-B. (2006). Quantum Field Theory, Dover Publications.

4. Barut, A.O. (1980). Electrodynamics and Classical Theory of Fields and Particles, Dover Publications Inc.

5. Bogush, A.A., and Moroz, L.G. (2004). Introduction to Theory of Classical Fields, Editorial URSS. [2nd ed.].

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