Hilbert-Einstein versus Einstein-Cartan theories of gravity, tiny difference due to fermions.ġ1. Mesons made out of quarks and metric as a gravimeson.ġ0. Spin of fermions, Dirac actions in different dimensions, coupling to gravity and to Higgs fields.ĩ. Quarks, leptons, Higgs fields, gauge fields and graviquarks (Einstein-Cartan theory of gravity)Ĩ. Why electromagnetism for d=3 is equivalent to ether theory.ħ.Unified description of gravity and Standard model as SU(3)xSU(2)xU(1)x Spin(3,1) gauge theory. Electromagnetism as a theory of 1-form, Maxwell’s equations and generalization of electromagnetic duality to the theory of p-forms in d-dimensional spaces. Berezin integral and Hodge *-operation as an odd Fourier transform, Laplacians and quadratic actions for p-forms, abelian gauge symmetry and propagation of waves.Ħ. Supermanifolds and homological vector fields, de Rham differential graded algebra of differential forms and cohomology.ĥ. Why it is impossible to move faster than light.Ĥ. Motion of particles in a curved space-time, conserved quantity and Einstein’s formula. Differential geometry arising from motion of machines and least action principle.ģ. Modern view on Newton’s mechanics, missed zeroth law and renormalization.Ģ. In the main line physics for mathematicians we will cover (in a relatively nonstandard way) the following topics.ġ. In this semester we will discuss classical theory, and we will come to quantum theory in the next semester. Dear all, we are starting the zoom course, the aim of this course is to explain modern physics for mathematicians and provide physicists with adequate mathematical tools for description of the Standard model and gravity in a unified way.
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