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1.
We construct a family of spin chain Hamiltonians, which have the affine quantum group symmetry
. Their eigenvalues coincide with the eigenvalues of the usual spin chain Hamiltonians, but have the degeneracy of levels, corresponding to the affine
. The space of states of these spin chains is formed by the tensor product of the fully reducible representations of the quantum group.
The fermionic representations of the constructed spin chain Hamiltonians show that we have obtained new extensions of the Hubbard Hamiltonians. All of them are integrable and have the affine quantum group symmetry. The exact ground state of such type of model is presented, exhibiting superconducting behavior via the η-pairing mechanism. 相似文献
2.
Projective Systems of Imprimitivity and Applications for the Galilei Group in 1+2 and 1+3 Dimensions
D. R. Grigore 《Fortschritte der Physik》1996,44(1):63-84
The study of the projective unitary irreducible representations of the Galilei group (in 1+3 and 1+2 dimensions) is usually done using firstly some group extensions techniques (in this way one is reduced to the study of true unitary representations) and then Mackey induction procedure. In this paper we reobtain these results using a different approach based on the notion of projective systems of imprimitivity due also to Mackey. This extension of the usual Mackey procedure is presented rather extensively and illustrated by detailed computations concerning the classification of the projective unitary irreducible representations. 相似文献
3.
We show how to construct irreducible projective representations of the infinite dimensional Lie group Map (S
1,
), by embedding it into the group of Bogoliubov automorphisms of the CAR. Using techniques of G. Segal for extending certain representations of Map (S
1, SU(2)) we show that our representations extend to give representations of a certain infinite dimensional superalgebra. We relate our work to the well known boson-fermion correspondence which exists in 1+1 dimensions. 相似文献
4.
In recent times a new kind of representations has been used to describe superselection sectors of the observable net over a curved spacetime, taking into account the effects of the fundamental group of the spacetime. Using this notion of representation, we prove that any net of C*-algebras over S 1 admits faithful representations, and when the net is covariant under Diff(S 1), it admits representations covariant under any amenable subgroup of Diff(S 1). 相似文献
5.
Franklin E. Schroeck 《International Journal of Theoretical Physics》2009,48(12):3586-3595
The quarks and particles’ mass and mass/spin relations are provided with coordinates in configuration space and/or momentum
space by means of the marriage of ordinary Poincaré group representations with a non-associative algebra made through a demisemidirect
product, in the notation of Leibniz algebras. Thus, we circumvent the restriction that the Poincaré group cannot be extended
to a larger group by any means (including the (semi)direct product) to get even the mass relations. Finally, we will discuss a connection between
the phase space representations of the Poincaré group and the phase space representations of the associated Leibniz algebra. 相似文献
6.
In this paper we present systematic differential representations
for the dynamical group SO(4). These representations include the
left and the right differential representations and the left and
the right adjoint differential representations in both the group
parameter space and its coset spaces. They are the generalization
of the differential representations of the SO(3) rotation group in
the Euler angles. These representations may find their applications in
the study of the physical systems with SO(4) dynamical symmetry. 相似文献
7.
《Physics letters. [Part B]》1988,212(2):153-157
We study the type-II superstrings in four dimensions by studying vacua where massless chiral multiplets transform as complex representations of the non-abelian gauge group. We show that the gauge group can only be SU(3) and that such fields transform as 3 of SU(3). However, attempts to obtain the theory with N=1 supergravity fail. It turns out that the “different” constructions via asymmetric orbifolds give the same massless spectrum with necessarily N=2 supergravity. 相似文献
8.
Starting from the Verma modules of the algebra sl(4, ?) we explicitly construct factor representations of the algebra su(2, 2) which are connected with unitary representation of group SU(2, 2). We find a full set of extremal vectors for this kind of representations, so we can solve explicitly the problem of irreducibility of these representations. 相似文献
9.
Henri Bacry 《Communications in Mathematical Physics》1993,153(2):359-390
Band representations are analyzed from a pure group theoretical point of view, with the aid of the dual of the crystallographic group (the set of equivalence classes of unitary irreducible representations). It is shown on the examples of the onedimensional crystallographic groups that we have to introduce a distinction between band and quasi-band representations, the wordband being reserved for induced representations.The dual of the groupF222 is explicitly constructed. It permits to show that two elementary band representations which have the same decompositions into unitary irreducible representations are not equivalent. 相似文献
10.
This paper describes Clebsch-Gordan coefficients (CGCs) for unitary irreducible representations (UIRs) of the extended quantum-mechanical Poincaré group . ‘Extended’ refers to the extension of the 10 parameter Lie group that is the Poincaré group by the discrete symmetries C, P, and T; ‘quantum mechanical’ refers to the fact that we consider projective representations of the group. The particular set of CGCs presented here is applicable to the problem of the reduction of the direct product of two massive, unitary irreducible representations (UIRs) of with positive energy to irreducible components. Of the 16 inequivalent representations of the discrete symmetries, the two standard representations with UCUP = ±1 are considered. Also included in the analysis are additive internal quantum numbers specifying the superselection sector. As an example, these CGCs are applied to the decay process of the ? (4S) meson. 相似文献
11.
《Physics letters. [Part B]》1986,173(3):284-288
Gauge invariant and gauge fixed BRS invariant actions are constructed in arbitrary dimensions for free massless integer spin fields carrying mixed representations of the Lorentz group described by Young tableaux (2, 1, 1, …, 1)n. The complete ghost spectrum is deduced by demanding nilpotency of the BRS transformations and leads to a correct count of the on-shell degrees of freedom. Dimensional reduction is used to study the corresponding gauge invariant massive theory. On-shell consistency is then ensured by the fact that the masses arise via a “telescopic Higgs effect”. 相似文献
12.
Adrien Brochier 《Communications in Mathematical Physics》2012,311(1):55-96
We compute explicitly the monodromy representations of “cyclotomic” analogs of the Knizhnik–Zamolodchikov differential system.
These are representations of the type B braid group Bn1{B_n^1} . We show how the representations of the braid group B
n
obtained using quantum groups and universal R-matrices may be enhanced to representations of Bn1{B_n^1} using dynamical twists. Then, we show how these “algebraic” representations may be identified with the above “analytic” monodromy
representations. 相似文献
13.
从李羣的一般理论,具体地讨论了SU4的数学处理,给出了羣的代数结构、不可约表示维数的公式、三个基本表示的明显形式及表示直积分解的主要结果。根据SU4对称,下列基本粒子的对称模型被构成:(1)Bacry和Van Hove模型,(2)Schwinger模型,(3)正反粒子对称的坂田模型,(4)正反粒子对称的八度法模型。在这些模型中,一些与实验一致的新的结果被得到。 相似文献
14.
G. Rideau 《Letters in Mathematical Physics》1990,20(1):1-10
A concept of linear covariance is defined for nonlinear formal representations of the Poincaré group. Then it is proved that the formal nonlinear representations previously built for 2+1 dimensions with irreducible unitary massless representations as free parts (cf. (1)) are nonlinearly equivalent to linearly covariant representations. 相似文献
15.
Governed by locality, we explore a connection between unitary braid group representations associated to a unitary R-matrix and to a simple object in a unitary braided fusion category. Unitary R-matrices, namely unitary solutions to the Yang-Baxter equation, afford explicitly local unitary representations of braid groups. Inspired by topological quantum computation, we study whether or not it is possible
to reassemble the irreducible summands appearing in the unitary braid group representations from a unitary braided fusion
category with possibly different positive multiplicities to get representations that are uniformly equivalent to the ones
from a unitary R-matrix. Such an equivalence will be called a localization of the unitary braid group representations. We show that the q = e
πi/6 specialization of the unitary Jones representation of the braid groups can be localized by a unitary 9 × 9 R-matrix. Actually this Jones representation is the first one in a family of theories (SO(N), 2) for an odd prime N > 1, which are conjectured to be localizable. We formulate several general conjectures and discuss possible connections to
physics and computer science. 相似文献
16.
Unitary representations of some infinite dimensional groups 总被引:12,自引:2,他引:10
Graeme Segal 《Communications in Mathematical Physics》1981,80(3):301-342
We construct projective unitary representations of (a) Map(S
1;G), the group of smooth maps from the circle into a compact Lie groupG, and (b) the group of diffeomorphisms of the circle. We show that a class of representations of Map(S
1;T), whereT is a maximal torus ofG, can be extended to representations of Map(S
1;G), 相似文献
17.
K. G. Klimenko 《Zeitschrift fur Physik C Particles and Fields》1990,48(3):511-518
Two quantum theories where scalar fields are transformed over 1) adjoint and vector representations of theO(N) group, and 2) adjoint and fundamental representations of theSU(N) group, are investigated with the aid of Gaussian effective potential method. It is shown, that there exist autonomous phases with spontaneous breaking of the initial symmetry. 相似文献
18.
M. Nakashima 《Communications in Mathematical Physics》1988,117(1):109-125
Indecomposable representations have been extensively used in the construction of conformal and de Sitter gauge theories. It is thus noteworthy that certain unitary highest weight representations have been given a geometric realization as the unitary quotient of an indecomposable representation using indefinite harmonic forms [RSW]. We apply this construction toSU (2,2) and the de Sitter group. The relation is established between these representations and the massless, positive energy representations ofSU (2,2) obtained in the physics literature. We investigate the extent to which this construction allows twistors to be viewed as a gauge theory ofSU (2,2). For the de Sitter group, on which the gauge theory of singletons is based, we find that this construction is not directly applicable. 相似文献
19.
Günther Hörmann 《Communications in Mathematical Physics》1997,184(1):51-63
We study representation theory of the Weyl relations for infinitely many degrees of freedom. Differentiability of regular
representations along rays in the parameter space E suggests to consider smooth structures on E. Switching from representations of CCR to group representations of the associated Heisenberg group over E we develop a framework for smooth representations of the Heisenberg group as an infinite dimensional Lie group. After careful
inspection and translation of the necessary differential geometric input for Kirillov's orbit method we are able to construct
a large class of smooth representations. These reproduce the Schr?dinger representation if E is finite dimensional.
Received: 10 May 1996 / Accepted: 30 July 1996 相似文献
20.
We present the (algebra) group contraction chain SU(1, 1) → P(1, 1) → G(1, 1), where P(1, 1) and G(1, 1) are the Poincaré and the Galilei groups, respectively, in (1 + 1) dimensions. We have paid attention to the contraction of the pseudo-extended Poincaré group to the central extended Galilei group. Objects like group laws, coadjoint orbits and representations of the contracted groups have been obtained in terms of their noncontracted counterparts. As an application we study the Moyal quantization of classical systems, having those groups as symmetry groups, by means of the contraction of the so called Stratonovich-Weyl kernels which provide such quantization. 相似文献