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The Cauchy-Riemann equations have a simple expression in terms of the vector derivative, and the geometric algebra form generalises to higher dimensions, recovering the Maxwell and Dirac equations in spacetime.

The Cauchy-Riemann equations have a simple expression in terms of the vector derivative, and the geometric algebra form generalises to higher dimensions, recovering the Maxwell and Dirac equations in spacetime.

22 Feb 2015: MIT2 2003 25. Maxwell Equations• Assume no magnetisation and polarisation. effects and revert to natural units• Maxwell equations become, in GA form. • ... Analytic Functions. Spacetime Vector Derivative. Maxwell Equations. STA Form. Application.

17 Dec 2020: expression in terms of the vector derivative, and the geometric algebra form generalises to higher dimensions, recovering the Maxwell and Dirac equations in spacetime.

Lectures take place in the new Maxwell Centre in West Cambridge.

1 Nov 2016: Three dimensions. L6 S7. Maxwell equations in vacuum around sources and currents, in natural units. ... Remove the curl term via. Find. All 4 of Maxwell’s equations in 1!

1 Nov 2016: Remove the curl term via. Find. All 4 of Maxwell’s equations in 1! ... Or. So. Recall Faraday bivector. So finally. Unification. The most compact formulation of the Maxwell equations.

22 Feb 2015: vector derivative• Same as the Maxwell equation, so similar. propagator structure• Electromagnetic coupling from gauge.

14 Oct 2015: Analytic functions. • Unifying Maxwell’s equations. • Projective and conformal.

14 Oct 2015: Rotations in arbitrary dimensions. Lorentz transformations. Lie groups. Analytic functions. Unifying Maxwell’s equations.

17 Dec 2020: Geometric Algebra http://geometry.mrao.cam.ac.uk Cambridge University Geometric Algebra Research Thu, 17 Dec 2020 17:19:51 0000 en-GB hourly 1 https://wordpress.org/?v=5.1.19 Complex Eigenvalues in Geometric Algebra

7 Nov 2015: Three dimensions. L6 S7. Maxwell equations in vacuum around sources and currents, in natural units. ... Remove the curl term via. Find. All 4 of Maxwell’s equations in 1!

7 Nov 2015: Remove the curl term via. Find. All 4 of Maxwell’s equations in 1! ... Or. So. Recall Faraday bivector. So finally. Unification. The most compact formulation of the Maxwell equations.

17 Dec 2020: Chris Doran – Geometric Algebra http://geometry.mrao.cam.ac.uk Cambridge University Geometric Algebra Research Thu, 17 Dec 2020 17:19:51 0000 en-GB hourly 1 https://wordpress.org/?v=5.1.19 Complex Eigenvalues in Geometric Algebra

22 Feb 2015: We need a notion of a vector field to discretise Maxwell equations (or anything else useful).

19 Feb 2015: The firstapplication of this is to electromagnetic scattering problems. We describea general method for solving the full Maxwell equations in the presence ofan arbitrarily-shaped conductor. ... 2 Electromagnetism. The Maxwell equations can be written. E =

14 Feb 2015: The vector derivative plays a central role in thespacetime algebra form of both the Maxwell and Dirac theories. ... In Section 2.2 we saw how tocombine Maxwell’s equations into the single equation F = J.

5 Feb 2015: Conformal transformations arealso considered, and we show how non-conservation of their conjugate tensors isrelated to the mass term in coupled Maxwell-Dirac theory. ... ÃL(A)̃ L〉1 = 0F = J. (4.59). With the identity F = (A) = 0, this yields the

2 Feb 2015: Relativity is introduced in Section 5,where we show how Maxwell’s equations can be combined into a single relationin geometric algebra, and give a simple general formula for the electromagneticfield ... F = E iB, (9). whereE = 12 (F γ0Fγ0) , iB =. 12

19 Feb 2015: The Maxwell equations canthen be written as. F = J, (37)where J is the current. ... This is not merely a cosmetic exercise. The vectorderivative is directly invertible, which provides a number of new tech-niques for solving the Maxwell equations.