Bicovariant Calculus in Quantum Theory and a Generalization of the Gauss Law
نویسندگان
چکیده
We construct a deformation of the quantum algebra Fun(T G) associated with Lie group G to the case where G is replaced by a quantum group Gq which has a bicovariant calculus. The deformation easily allows for the inclusion of the current algebra of left and right invariant one forms. We use it to examine a possible generalization of the Gauss law commutation relations for gauge theories based on Gq. PACS:
منابع مشابه
The Problem of Differential Calculus on Quantum Groups
The bicovariant differential calculi on quantum groups of Woronowicz have the drawback that their dimensions do not agree with that of the corresponding classical calculus. In this paper we discuss the first-order differential calculus which arises from a simple quantum Lie algebra lh(g). This calculus has the correct dimension and is shown to be bicovariant and complete. But it does not satisf...
متن کاملDifferential calculus on Hopf Group Coalgebra
Quantum groups, from a mathematical point of view, may be introduced by making emphasis on their q−deformed enveloping algebra aspects [1,2], which leads to the quantized enveloping algebras, or by making emphasis in the R−matrix formalism that describes the deformed group algebra. Also, they are mathematically well defined in the framework of Hopf algebra [3]. Quantum groups provide an interes...
متن کاملCLASSIFICATION OF BICOVARIANT DIFFERENTIAL CALCULI ON THE JORDANIAN QUANTUM GROUPS GLh,g(2) AND SLh(2) AND QUANTUM LIE ALGEBRAS
We classify all 4-dimensional first order bicovariant calculi on the Jordanian quantum group GLh,g(2) and all 3-dimensional first order bicovariant calculi on the Jordanian quantum group SLh(2). In both cases we assume that the bicovariant bimodules are generated as left modules by the differentials of the quantum group generators. It is found that there are 3 1-parameter families of 4-dimensio...
متن کاملMatrix product representation of gauge invariant states in a Z2 lattice gauge theory
The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. In this work, we propose an efficient variational method based on the matrix product ansatz for a Z2 lattice gauge theory on a spatial ladder chain. Gauge invariant low-lying states are identified by evaluating expectation values of the Gauss law operator aft...
متن کاملGauge invariance in a Z2 hamiltonian lattice gauge theory
We propose an efficient variational method for Z2 lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. On the ladder lattice, we identify gauge invariant low-lying states by evaluating expectation value...
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 2008