A multivector derivative approach to Lagrangian field theory

Journal Article · Fri Oct 01 04:00:00 EDT 1993 · Foundations of Physics; (United States)

DOI:https://doi.org/10.1007/BF01883781· OSTI ID:7271465

Lasenby, A; Gull, S ^[1]; Doran, C ^[2]

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1. MRAO, Cavendish Lab., Cambridge (United Kingdom)
2. DAMTP, Cambridge (United Kingdom)

A new calculus, based upon the multivector derivative, is developed for Lagrangian mechanics and field theory, providing streamlined and rigorous derivations of the Euler-Lagrange equations. A more general form of Noether's theorem is found which is appropriate to both discrete and continuous symmetries. This is used to find the conjugate currents of the Dirac theory, where it improves on techniques previously used for analyses of local observables. General formulas for the canonical stress-energy and angular-momentum tensors are derived, with spinors and vectors treated in a unified way. It is demonstrated that the antisymmetric terms in the stress-energy tensor are crucial to the correct treatment of angular momentum. The multivector derivative is extended to provide a functional calculus for linear functions which is more compact and more powerful than previous formalisms. This is demonstrated in a reformulation of the functional derivative with respect to the metric, which is then used to recover the full canonical stress-energy tensor. Unlike conventional formalisms, which result in a symmetric stress-energy tensor, this reformulation retains the potentially important antisymmetric contribution. 23 refs.

• OSTI ID: 7271465
• Journal Information: Foundations of Physics; (United States), Journal Name: Foundations of Physics; (United States) Vol. 23:10; ISSN 0015-9018; ISSN FNDPA4
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL CALCULUS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
FIELD THEORIES
LAGRANGIAN FIELD THEORY
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
TENSORS
VECTORS
WAVE EQUATIONS