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Changing Observers – A Glance at Invariant Theory Based on the Principle of the Correct Index Picture

In: Quantum Field Theory III: Gauge Theory

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  • Eberhard Zeidler

    (Max Planck Institute for Mathematics in the Sciences)

Abstract

Invariant theory plays a crucial role in all branches of mathematics and in modern physics. Invariant theory has its roots in celestial mechanics (Lagrange’s contributions to the three-body problem), the motion of rigid bodies (Euler’s spinning top), Cauchy’s theory of elasticity, number theory, projective geometry, and differential geometry. In his fundamental work Disquisitiones arithmeticae on number theory from 1801, Gauss (1777–1855) studied invariants of quadratic forms under unimodular linear substitutions with integral coefficients. Later on, more general results on quadratic forms were obtained by Jacobi (1804–1851), Sylvester (1814–1897), and Hermite (1822–1901).

Suggested Citation

  • Eberhard Zeidler, 2011. "Changing Observers – A Glance at Invariant Theory Based on the Principle of the Correct Index Picture," Springer Books, in: Quantum Field Theory III: Gauge Theory, chapter 8, pages 439-556, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-22421-8_9
    DOI: 10.1007/978-3-642-22421-8_9
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