Titlebook: Quantum Theory, Groups and Representations; An Introduction Peter Woit Textbook 2017 Peter Woit 2017 Lie algebras.Lie groups.quantization.q

Custodian

The Poisson Bracket and Symplectic Geometry,We have seen that the quantum theory of a free particle corresponds to the construction of a representation of the Heisenberg Lie algebra in terms of operators . and ., together with a choice of Hamiltonian ..

SSRIS

Quadratic Polynomials and the Symplectic Group,In Chapters . and ., we studied in detail the Heisenberg Lie algebra as the Lie algebra of linear functions on phase space.

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Semi-direct Products,The theory of a free particle is largely determined by its group of symmetries, the group of symmetries of three-dimensional space, a group which includes a subgroup . of spatial translations, and a subgroup .(3) of rotations.

引起

Peter WoitSystematically emphasizes the role of Lie groups, Lie algebras, and their unitary representation theory in the foundations of quantum mechanics.Introduces fundamental structures and concepts of repres

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Isthmus

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Momentum and the Free Particle, moving in physical space .. This is something quite different from the classical mechanical description of a free particle, which will be reviewed in chapter .. A common way of motivating this is to begin with the 1924 suggestion by de Broglie that just as photons may behave like either particles o

Debrief

Hamiltonian Vector Fields and the Moment Map,n’s equations .and the tangent vectors of these parametrized curves provide a vector field on phase space. Such vector fields are called Hamiltonian vector fields. There is a distinguished choice of ., the Hamiltonian function ., which gives the velocity vector fields for time evolution trajectories

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The Quantum Free Particle as a Representation of the Euclidean Group,known for relativistic theories, where it is the representation theory of the Poincaré group that is relevant, a topic that will be discussed in chapter .. It is less well known that even in the non-relativistic case, the Euclidean group .(3) of symmetries of space plays a similar role, with irreduc