Topology and Inequivalent Quantizations of Abelian Sigma Model
نویسنده
چکیده
The abelian sigma model in (1+1) dimensions is a field theoretical model which has a field φ : S1 → S1. An algebra of the quantum field is defined respecting the topological aspect of the model. It is shown that the zero-mode has an infinite number of inequivalent quantizations. It is also shown that when a central extension is introduced into the algebra, the winding operator and the momenta operators satisfy anomalous commutators.
منابع مشابه
Topology and quantization of abelian sigma model in ( 1 + 1 ) dimensions ∗
It is known that there exist an infinite number of inequivalent quantizations on a topologically nontrivial manifold even if it is a finitedimensional manifold. In this paper we consider the abelian sigma model in (1+ 1) dimensions to explore a system having infinite degrees of freedom. The model has a field variable φ : S → S. An algebra of the quantum field is defined respecting the topologic...
متن کاملGeometric quantization on a coset space G/H
Geometric quantization on a coset space G/H is considered, intending to recover Mackey’s inequivalent quantizations. It is found that the inequivalent quantizations can be obtained by adopting the symplectic 2-form which leads to Wong’s equation. The irreducible representations of H which label the inequivalent quantizations arise from Weil’s theorem, which ensures a Hermitian bundle over G/H t...
متن کاملZero-mode, winding number and quantization of abelian sigma model in (1+1) dimensions
We consider the U(1) sigma model in the two dimensional spacetime S × R, which is a field-theoretical model possessing a nontrivial topology. It is pointed out that its topological structure is characterized by the zero-mode and the winding number. A new type of commutation relations is proposed to quantize the model respecting the topological nature. Hilbert spaces are constructed to be repres...
متن کاملGeometric quantization on homogeneous spaces and the meaning of ‘inequivalent’ quantizations
Consideration of the geometric quantization of the phase space of a particle in an external Yang-Mills field allows the results of the Mackey-Isham quantization procedure for homogeneous configuration spaces to be reinterpreted. In particular, a clear physical interpretation of the ‘inequivalent’ quantizations occurring in that procedure is given.
متن کاملQuantum Mechanically Induced Wess-Zumino Term in the Principal Chiral Model
It is argued that, in the two dimensional principal chiral model, the Wess-Zumino term can be induced quantum mechanically, allowing the model with the critical value of the coupling constant λ = 8π/|k| to turn into the WessZumino-Novikov-Witten model at the quantum level. The Wess-Zumino term emerges from the inequivalent quantizations possible on a sphere hidden in the configuration space of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1995