Dihedral symmetry of periodic chain: quantization and coherent states
نویسندگان
چکیده
Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group Zn of arbitrary order n = 2, 3, . . ., but as its symmetry group a larger group — the non-Abelian dihedral group Dn — is taken. The corresponding group related coherent states are constructed and their overcompleteness proved. Our approach based on geometric symmetry can be used as a kinematic framework for matrix methods in quantum chemistry of ring molecules. PACS numbers: 03.65.Ta, 03.65.-w, 42.50.-p Submitted to: J. Phys. A: Math. Theor.
منابع مشابه
Calculations of Dihedral Groups Using Circular Indexation
In this work, a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$. Each element of the sequence represents a vertex of the polygon. Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis. Here each symmetry is considered as a system that takes an input circular sequence and g...
متن کاملReduced Gutzwiller Formula with Symmetry: Case of a Finite Group
We consider a classical Hamiltonian H on R2d, invariant by a finite group of symmetry G, whose Weyl quantization Ĥ is a selfadjoint operator on L2(Rd). If χ is an irreducible character of G, we investigate the spectrum of its restriction Ĥχ to the symmetry subspace Lχ(R d) of L2(Rd) coming from the decomposition of Peter-Weyl. We give reduced semi-classical asymptotics of a regularised spectral...
متن کاملCoherent states and the quantization of 1+1-dimensional Yang-Mills theory
This paper discusses the canonical quantization of 1+1-dimensional Yang-Mills theory on a spacetime cylinder, from the point of view of coherent states, or equivalently, the Segal-Bargmann transform. Before gauge symmetry is imposed, the coherent states are simply ordinary coherent states labeled by points in an infinite-dimensional linear phase space. Gauge symmetry is imposed by projecting th...
متن کاملSymmetry classes of polynomials associated with the dihedral group
In this paper, we obtain the dimensions of symmetry classes of polynomials associated with the irreducible characters of the dihedral group as a subgroup of the full symmetric group. Then we discuss the existence of o-basis of these classes.
متن کاملفرمولبندی هندسی کوانتش تغییرشکل برزین
In this paper we try to formulate the Berezin quantization on projective Hilbert space P(H) and use its geometric structure to construct a correspondence between a given classical theory and a given quantum theory. It wil be shown that the star product in berezin quantization is equivalent to the Posson bracket on coherent states manifold M, embodded in P(H), and the Berezin method is used to...
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 2007