Geometric Quantization

غزاله اصغری  (دانشکده فیزیک دانشگاه صنعتی شریف)

Abstract:   The word “quantization” is used both in physics and mathematics in many different senses. The common basis of all these theories is that the classical and quantum mechanics are just different realizations of the same abstract scheme. Geometric quantization goal is the construction of quantum objects using the geometry of the corresponding classical objects as a point of departure. The geometric quantization procedure falls into the following three steps: prequantization, polarization and metaplectic correction. Prequantization produces a natural Hilbert space together with a quantization procedure for observables that exactly transforms Poisson brackets on the classical side into commutators on the quantum side. Nevertheless, the prequantum Hilbert space is generally understood to be “too big”. The idea is that one should then select a Poisson commuting set of n-variables on the 2n-dimensional phase space and consider functions that depend only on these n variables. The n variables can be either real-valued, resulting in a position-style Hilbert space, or complex valued. A polarization is a coordinate independent description on such a choice of n Poisson-commuting functions. The metaplectic correction is a technical modification of the above procedure that is necessary in the case of real polarization and often convenient for complex polarization.

یکشنبه 10 بهمن ماه 1395، ساعت 15:00

    دانشکده فیزیک، تالار پرتوی