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Atomic Nuclear Physics

# Introduction to string theory by Van Proeyen A.

By Van Proeyen A.

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Quantum optics: quantum theories of spontaneous emission

The aim of this text is to check spontaneous emission from a number of assorted viewpoints, even supposing a wide a part of it will likely be dedicated to the quantum statistical theories of spontaneous emission that have been constructed lately, and to discussing the interrelations between diverse ways.

Additional resources for Introduction to string theory

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7: (important repetition of particle mechanics). Repeat first how charged objects are described in electromagnetism. 23) where the last integral is over the world-line L describing the history of the particle. Check that the Euler-Lagrange equations for Aµ give rise to Maxwell equations with a source. g. that the particle is stationary at X = 0, and X 0 = t. Check that the canonical momentum conjugate to X µ (τ ) is Πµ = δS = mX˙ µ + qAµ . 24) We have seen that open strings generate a background determined by a gauge vector Aµ .

The string frame action is adapted to string perturbation theory and has a universal dependence on the dilaton and on the string coupling. 2) and counts the loops: StrFr Sg−loop ∼ gS−2+2g . 54) In the Einstein frame, gravity and the scalar are decoupled in the kinetic energy. Therefore in this frame, the metric describes the physical gravitational field. Hence, this action is needed when analyzing gravitational physics, in particular for solutions of the effective action that describe black holes and other spacetime geometries.

2) and show how this gives rise to the Gr and G may be needed: if the Lagrangian is invariant under a symmetry up to a total derivative, δ( )L = ∂α K α ( ), then the Noether current is J α ( ) = δ∂δLα φ δ( )φ − K α ( ), where the first term involves a sum over all fields φ. Further it is useful to have the relations ρ+ = 0 0 2 0 ρ− = , 0 −2 0 0 . With similar methods as in the bosonic case, we can calculate the algebra of the currents. g. G1/2 , Gr and L−r−1/2 and a similar one for the R case. 4: Advanced: the generators L±1 , L0 and G±1/2 form a closed subalgebra.