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Lecture 5 Motion of a charged particle in a magnetic field
Lecture 5 Motion of a charged particle in a magnetic field

... qi ≡ xi = (x1 , x2 , x3 ) and q̇i ≡ vi = (ẋ1 , ẋ2 , ẋ3 ) N.B. form of Lagrangian more natural in relativistic formulation: −qv µ Aµ = −qϕ + qv · A where v µ = (c, v) and Aµ = (ϕ/c, A) Canonical momentum: pi = ∂ẋi L = mvi + qAi no longer given by mass × velocity – there is an extra term! ...
Department of Physics Indian Institute of Technology Kanpur
Department of Physics Indian Institute of Technology Kanpur

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... (a) Find the electrostatic field everywhere in space. (b) The shell is now rotating around its axis (ẑ-axis) with the frequency ω0 = const. The rotating insulator produces a surface current density. Find the magnetic field generated everywhere in space. (c) After a while the cylinder starts to slow ...
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... systematic and powerful tool to study the low energy or large distance behavior of a many-body system, in particular the critical behavior near a second order (or continuous) phase transition point. A prototype of such phase transition occurs in the Landau-Ginzburg model, namely a real φ4 theory wit ...
Progress In N=2 Field Theory
Progress In N=2 Field Theory

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... 12.6 Mass terms in : an attempted generalisation Experimental tests of the Weinberg–Salam theory 13.1 The search for the gauge bosons 13.2 The W± bosons 13.3 The Z boson 13.4 The number of lepton families 13.5 The measurement of partial widths 13.6 Left–right production cross-section asymmetry and l ...
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Progress In N=2 Field Theory - Rutgers Physics

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Workshop on Geometry and Physics 2017 Feb 25

B.3 Time dependent quantum mechanics
B.3 Time dependent quantum mechanics

... to be compared with eq. 2. Such pairs of coupled differential equations for two functions, one having a (-) sign, the other a (+) sign, are called symplectic, or ‘area preserving.’ Classically this means an area xp is mapped into an equal area in phase space at a later time. Quantum mechanically i ...
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Scalar field theory

In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation.The only fundamental scalar quantum field that has been observed in nature is the Higgs field. However, scalar quantum fields feature in the effective field theory descriptions of many physical phenomena. An example is the pion, which is actually a pseudoscalar.Since they do not involve polarization complications, scalar fields are often the easiest to appreciate second quantization through. For this reason, scalar field theories are often used for purposes of introduction of novel concepts and techniques.The signature of the metric employed below is (+, −, −, −).
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