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1.
In this paper, we study the diagrammatic categorification of q-boson algebra and also q-fermion algebra. We construct a graphical category corresponding to q-boson algebra. q-Fock states correspond to some kind of 1-morphisms, and the graded dimension of the graded vector space of 2-morphisms is exactly the inner product of the corresponding q-Fock states. We also find that this graphical category can be used to categorify q-fermion algebra.  相似文献   

2.
In this paper we deal with q-commuting variables x and y satisfying the relation xy = qyx + (q – 1)y 2 with q complex, 0 < |q| < 1. We study various functional equations for q-exponentials and we deduce some identities for q-special functions involving q-commuting variab les.  相似文献   

3.
We consider a set of Hamiltonian circuits filling a Manhattan lattice, i.e., a square lattice with alternating traffic regulation. We show that the generating function (with fugacityz) of this set is identical to the critical partition function of aq-state Potts model on an unoriented square lattice withq 1/2 =z. The set of critical exponents governing correlations of Hamiltonian circuits is derived using a Coulomb gas technique. These exponents are also found to be those of an O(n) vector model in the low-temperature phase withn =q 1/2 =z. The critical exponents in the limitz = 0 are then those of spanning trees (q= 0) and of dense polymers (n=0,T < Tc), corresponding to a conformal theory with central chargeC = –2. This shows that the Manhattan orientation and the Hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of Hamiltonian walks.  相似文献   

4.
5.
In this paper we define a new q-special function A n (x, b, c; q). The new function is a generalization of the q-Laguerre function and the Stieltjes–Wigert function. We deduced all the properties of the function A n (x, b, c; q). Finally, lim q1 A n ((1 – q)x, –, 1;q) gives L n (,)(x,q), which is a -modification of the ordinary Laguerre function.  相似文献   

6.
We point out that the equivalent-photon approximation (EPA) for processes with massive spin-1 particles in the final state would have validity in a more restricted kinematic domain than for processes where it is commonly applied, viz., those with spin-1/2 or spin-0 particles in the final state. We obtain the criterion for the validity ofEPA for the two-photon production of a pair of charged, massive, point-like spin-1 particlesV ±, each of massM and with a standard magnetic moment (κ=1). In a process in which one of the photons is real and the other virtual with four-momentumq, the condition for the validity ofEPA is |q 2|≪M 2, in addition to the usual condition |q 2|≪W 2,W being theV + V invariant mass. In a process in which both photons are virtual (with four-momentaq andq′), our condition is |q 2||q2|W 4 ≪ 16M 8, in addition to |q 2| ≪M 2, |q2| ≪M 2 and |q 2| ≪W 2, |q2| ≪W 2. Even when these extra conditions permitting the use ofEPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q 2| ≪W 2 and |q2| ≪W 2. We also discuss how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge theory. Examples ofW boson production in Weinberg-Salam model are considered for which the condition |q 2||q2|W 4 ≪ 16M 8 is shown to be removed.  相似文献   

7.
In this paper, the completeness of the k orthonormalized eigenstates of the operator (a q f(N q )) k (k 3) is proved. We introduce a new kind of higher order squeezing and an antibunching. The properties of the Mth-order squeezing and the antibunching effect of the k states are investigated. The result shows that these states may form a complete Hilbert space, and the Mth order [M = (m + 1/2)k;m = 0,1,2,. . .] squeezing effects exist in all of the k states when k is even. There is the antibunching effect in all of the states.  相似文献   

8.
The differences among quon operators, q a-math oscillator operators and q-deformed oscillator operators are pointed out. The q-deformed ocsillator and q a-math oscillator are constructed in terms of q q = 0 quon.  相似文献   

9.
We establish a new Howe duality between a pair of two queer Lie superalgebras (q(m),q(n)). This gives a representation theoretic interpretation of a well-known combinatorial identity for Schur Q-functions. We further establish the equivalence between this new Howe duality and the Schur–Sergeev duality between q(n) and a central extension of the hyperoctahedral group H k. We show that the zero-weight space of a q(n)-module with highest weight given by a strict partition of n is an irreducible module over the finite group parameterized by . We also discuss some consequences of this Howe duality.  相似文献   

10.
本文利用新近建立的多模压缩态理论,详细研究了一种新型的多模复共轭虚偶相干态光场|Ψi,e*(2)>q的广义非线性等阶N次方Y压缩与等阶N次方H压缩特性.结果发现:1)当压缩阶数N为奇数时,态Ψi,e*(2)>q在一定条件下总可呈现出周期性变化的、任意阶的等阶N次方Y压缩效应;当腔模总数q与压缩阶数N两者之乘积q·N为奇数时,则在一定条件下态|Ψi,e*(2)>q又可呈现出周期性变化的、任意阶的等阶N次方H压缩效应.2)态|Ψi,e*(2)>q与多模偶相干态光场|Ψi,e*(2)>q与多模虚偶相干态光场|Ψi,e(2)>q的压缩幅度、压缩条件和压缩特征等完全相同.这一结果再次从理论上证实了多模压缩光中的确存在着“相反压缩”和“压缩简并”这两类新的物理现象.  相似文献   

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