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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.

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.

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.

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.

14 Feb 2015: The effect of thegravitational fields on the Maxwell equations can be interpreted as defining thedielectric properties of the vacuum ([7]).

25 Mar 2015: graphics). Applications of GA. Works extremely well withelectromagnetismAll four Maxwell equations combineto one: F = J, in which the isinvertibleLeads to novel methods for treatingEM scatteringGA also leads to a different approachto

14 Feb 2015: Lagrangian field theory is considered in Chapter 6. A unifying framework forvectors, tensors and spinors is developed and applied to problems in Maxwell andDirac theory.

18 Feb 2015: In tensor notation,Maxwell’s equations are. µFµν = Jν, [αFµν] = 0. ... h̄(a) 7 Rh̄(a)R̃. (3.18)Now consider an equation such as Maxwell’s equation, which we saw in.

15 Feb 2015: In tensor notation, the Maxwell equations take theform. µFµν = Jν, [αFµν] = 0, (2.42). ... We see from (2.46) that the vectorderivative plays a central role in Maxwell theory, as well as Dirac theory.

16 Feb 2015: For example, Maxwell’s equations can be combined into a singlemultivector equation with an invertible differential operator [13].