perturbation theory


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perturbation theory

n.
A set of mathematical methods often used to obtain approximate solutions to equations for which no exact solution is possible, feasible, or known.
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It explains space-time; the theory of special relativity and its application to the classical description of the motion of a free particle and a field; the quantum formulation of field theory; quantum electrodynamics and the Fermi theory of neutron beta decay; problems associated with the quantization of the electromagnetic field; the Dirac equation and spinor fields; the structure of the interaction term between charged particles and the electromagnetic field; the derivation of relativistic perturbation theory and its application to the calculation of observable quantities; and neutrino oscillations.
In conventional chiral perturbation theory the [eta]' is not included explicitly, although it does show up in the form of a contribution to a coupling coefficient of the Lagrangian, a so-called low-energy constant (LEC).
The four lectures explain composition operators on the space of real analytic functions and Hardy-Orlicz spaces, shine a Hilbertian lamp on the bidisk, and consider several problems in perturbation theory. No index is provided.
and the Russian Academy of Sciences, Russia) present the elder's T-products approach in the theory of a particle interacting with bosonic fields, describe one version of finite-temperature perturbation theory for the polaron partition function and the ground-state energy developed on the basis of the T-product formalism, discuss the equilibrium-state investigation for the Frohlich polaron model while deriving Bogolubov's inequality for the reduced free energy of the polaron, and review some problems related to nonequilibrium polaron theory including polaron kinetics.
The author has organized the main body of his text in ten chapters devoted to a case study of the ground state energy of a hybrid harmonic-quartic oscillator, Bohr-Sommerfeld quantization, semi-classical matrix elements of observables and perturbation theory, and a wide variety of other related subjects.
Among the topics are types of nanostructures, model quantum mechanics problems, time-dependent perturbation theory, and characterization.
Lectures include Heisenberg equations, eigenfunctions, scattering, one-dimensional particles and perturbation theory among others.
The second section focuses on integrable systems and their Whitham perturbation theory, including direct and inverse scattering problems for the heat operator, classical and modern examples of famous integrable systems, the construction of integrable hierarchies associated with the theory of Gromov-Witten invariants of smooth projective varieties, the Hamiltonian formulation of the Whitham method in the presence of pseudo-phases, classical mechanical systems that are Liouville integrable, self-adjoint rank two commuting ordinary differential operators, and commuting scalar ordinary differential operators.
Linear Hamiltonian systems, perturbation theory, and simplectic mechanics.
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