Discrete series of unitary irreducible representations of the Uq(u(3, 1)) and Uq(u(n, 1)) noncompact quantum algebras

The structure of all discrete series of unitary irreducible representations of the U _q (u(3, 1)) and U _q (u(n, 1)) noncompact quantum algebras are investigated with the aid of extremal projection operators and the q-analog of the Mickelsson-Zhelobenko algebra Z(g, g′) _q . The orthonormal basis constructed in the infinite-dimensional space of irreducible representations of the U _q (u(n, 1)) ⊇ U _q (u(n)) algebra is the q-analog of the Gelfand-Graev basis in the space of the corresponding irreducible representations of the u(n, 1) ⊇ u(n) classical algebra.     

Super-WZNW with reductions to supersymmetric and fermionic integrable models

A systematic construction for an action describing a class of supersymmetric integrable models as well as for pure fermionic theories is discussed in terms of the gauged WZNW model associated to half integer graded affine Kac–Moody algebras. Explicit examples of the N=1,2 super-sinh(sine)-Gordon models are discussed in detail. Pure fermionic theories arises for cosets sl(p,1)/sl(p)u(1) when a maximal kernel condition is fulfilled. The integrability condition for such models is discussed and it is shown that the simplest example when p=2 leads to the constrained Bukhvostov–Lipatov, Thirring, scalar massive and pseudo-scalar massless Gross–Neveu models.     

From geometric quantization to conformal field theory

Investigation of 2d conformal field theory in terms of geometric quantization is given. We quantize the so-called model space of the compact Lie group, Virasoro group and Kac-Moody group. In particular, we give a geometrical interpretation of the Virasoro discrete series and explain that this type of geometric quantization reproduces the chiral part of CFT (minimal models, 2d-gravity, WZNW theory). In the appendix we discuss the relation between classical (constant)r-matrices and this geometrical approach.     

From chiral to two-dimensional Wess-Zumino-Novikov-Witten model via quantum gauge group

We study the canonical quantization of the SU(n) WZNW model. Decoupling the chiral dynamics requires an extended state space including left and right monodromies as independent variables. In the simplest (n = 2) case we explicitly show that the zero modes of the monodromy extended SU(2) WZNW model give rise to a quantum group gauge theory in a finite-dimensional Fock space. We define the subspace of U_q(sl(2)) ⊗ U_q(sl(2))-invariant vectors on which the monodromy invariance is also restored and construct the physical space applying a generalized cohomology condition.     

Free products of compact quantum groups

We construct and study compact quantum groups from free products ofC ^*-algebras. In this connection, we discover two mysterious classes of natural compact quantum groups,A _u (m) andA _o (m). TheA _u (m)'s (respectivelyA _o (m)'s) are non-isomorphic to each other for differentm's, and are not obtainable by the ordinary quantization method. We also clarify some basic concepts in the theory of compact quantum groups.     

On Quantization in Light-cone Variables Compatible with Wavelet Transform

Canonical quantization of quantum field theory models is inherently related to the Lorentz invariant partition of classical fields into the positive and the negative frequency parts u(x) = u⁺(x) + u^?(x), performed with the help of Fourier transform in Minkowski space. That is the commutation relations are being established between nonlocalized solutions of field equations. At the same time the construction of divergence free physical theory requires the separation of the contributions of different space-time scales. In present paper, using the light-cone variables, we propose a quantization procedure which is compatible with separation of scales using continuous wavelet transform, as described in our previous paper (Altaisky, M.V., Kaputkina, N.E.: Phys. Rev. D 88, 025015 2013).     

Comment on Vub from exclusive semileptonic B and D decays

The prospects for determining |V_ub| from exclusive B semileptonic decay are discussed. The double ratio of form factors (f^(B→ρ)/f^(B→K*))/(f^(D→ρ)/f^(D→K*)) is calculated using chiral perturbation theory. Its deviation from unity due to contributions that are non-analytic in the symmetry breaking parameters is very small. Combining experimental data obtainable from , and can lead to a model independent determination of |V_ub| with an uncertainty from theory of about 10%.     

Deformations of compact quantum groups via Rieffel's quantization

It is shown that compact quantum groups containing torus subgroups can be deformed into new compact quantum groups under Rieffel's quantization. This is applied to showing that the two classes of compact quantum groupsK _q ^u andK _q studied by Levendorkii and Soibelman are strict deformation quantization of each other, and that the quantum groupsA _u (m) have many deformations.     

Quaternionic-valued Gravitation in 8D, Grand Unification and Finsler Geometry

A unification model of 4D gravity and SU(3)×SU(2)×U(1) Yang-Mills theory is presented. It is obtained from a Kaluza-Klein compactification of 8D quaternionic gravity on an internal CP ²=SU(3)/U(2) symmetric space. We proceed to explore the nonlinear connection formalism used in Finsler geometry to show how ordinary gravity in D=4+2 dimensions has enough degrees of freedom to encode a 4D gravitational and SU(5) Yang-Mills theory. This occurs when the internal two-dim space is a sphere S ². This is an appealing result because SU(5) is one of the candidate GUT groups. We conclude by discussing how the nonlinear connection formalism of Finsler geometry provides an infinite hierarchical extension of the Standard Model within a six dimensional gravitational theory due to the embedding of SU(3)×SU(2)×U(1)⊂SU(5)⊂SU(∞).     

Supersymmetric anyon model coupled to the electromagnetic field

We construct a supersymmetric gauge model describing the electromagnetic interaction of anyons. This is done by means of the supersymmetric generalization of theU(1) ×U(1) gauge theory. The model contains the statisticalU(1) gauge field endowed with a Chern-Simons mass term and the electromagnetic field, both with the corresponding superpartners, coupled to matter fields. This constrained system is analyzed from the Hamiltonian point of view and the canonical quantization is found. The path-integral method is used to develop the perturbative formalism. We define suitable propagators and vertices and give the diagrammatics and the Feynman rules.     

The E(4) Πu state in K2 and its perturbations

The E(4) ¹Π_u←X ¹Σ⁺_g band system of the K₂ molecule is investigated by the technique of Doppler-free optical–optical double resonance polarization spectroscopy. The observed vibrational levels v=0 to 9 of the E state are subject to numerous rotational perturbations by the neighboring 4 ³Π_u, 4 ¹Σ⁺_u, and 5 ³Σ⁺_u electronic states. By using deperturbation methods, the potential curves of the 4 ¹Π_u and 4 ³Π_u states are determined as well as some properties of the 4 ¹Σ⁺_u and 5 ³Σ⁺_u state potentials. The results are compared with predictions of ab initio calculations.     

Doppler-free two-photon absorption spectroscopy of trans-glyoxal under magnetic fields up to 6T

In order to measure the Doppler-free two-photon absorption (DFTPA) spectrum in the presence of a strong magnetic field, a sample cell placed in an optical resonator was installed at the centre of the bore of a superconducting magnet capable of generating a magnetic field of up to 6T. Changes in spectra of the A ¹A_u ← X ¹A_g transition of trans-glyoxal were measured as a function of magnetic field strength. Level crossings induced by Zeeman energy shifts were observed. The perturbing level, which shows hyperfine splitting, was identified as the ³A_u(nπ?) state, because the hyperfine splitting is small in the ³B_u(^ππ?) state and large in the ³A_u(nπ?) state. The perturbation between the A ¹A_u(nπ?) and ³A_u(nπ?) states was shown to take place by either vibronic interaction or Zeeman interaction between the ³A_u(nπ?) state and the ³B_u(ππ?) component mixed to the A ¹A_u(nπ?) state by spin-orbit interaction. The magnetic moment of the A ¹A_u state was determined to be approximately 0.0028μ_B, and the magnitude of the mixing coefficients 〈1 ³B_u|H _so|1 ¹A_u〉/[E(1 ¹A_u) ? E(1 ³B_u)] was evaluated to be 0.026.     

Geometric Quantization¶and the Generalized Segal--Bargmann Transform¶for Lie Groups of Compact Type

Let K be a connected Lie group of compact type and let T ^*(K) be its cotangent bundle. This paper considers geometric quantization of T ^*(K), first using the vertical polarization and then using a natural K?hler polarization obtained by identifying T ^*(K) with the complexified group K _ℂ. The first main result is that the Hilbert space obtained by using the K?hler polarization is naturally identifiable with the generalized Segal–Bargmann space introduced by the author from a different point of view, namely that of heat kernels. The second main result is that the pairing map of geometric quantization coincides with the generalized Segal–Bargmann transform introduced by the author. This means that the pairing map, in this case, is a constant multiple of a unitary map. For both results it is essential that the half-form correction be included when using the K?hler polarization. These results should be understood in the context of results of K. Wren and of the author with B. Driver concerning the quantization of (1+1)-dimensional Yang–Mills theory. Together with those results the present paper may be seen as an instance of “quantization commuting with reduction”. Received: 28 June 2001 / Accepted: 17 September 2001     

NO2分子的光学-光学双色双共振多光子离化谱

以Nd:YAG激光器的二倍频输出光为抽运光,其三倍频输出抽运的光学参量发生/放大器输出光为探测光,利用光学-光学双色双共振多光子离化光谱技术(OODR-MPI),获得了NO₂分子在605—675nm探测光波长范围内的多光子离化激发谱. 通过对NO₂分子离化机理的分析,确定了在此波长区间,NO₂分子经1+3+1双共振多光子过程离化,离化通道为NO₂(X²A₁)hν 关键词： 2')" href="#">NO₂ 光学-光学双共振多光子离化谱 里德伯态 分子常数     

氢分子3pπ D1πu+和4pσ B″1Σu+态的预解离

运用量子亏损理论，并与参考系变换及本征通道R-矩阵法相结合，建立了描述氢分子里德伯态的预解离过程的理论方法．通过对氢分子的3pπD¹π_u⁺和4pσ B″¹Σ_u⁺电子态的预解离过程的研究，阐明其解离的机理，并给出预解离的线宽． 关键词：     

Fundamental Fermions Fit Inside One <Emphasis Type="Italic">su</Emphasis>(1|5) Irreducible Representation

The Lie superalgebra su(1|5) has irreducible representations of dimension 32, in which the 32 fundamental fermions of one generation (leptons and quarks, of left and right chirality, and their antiparticles) can be accommodated. The branching of these su(1|5) representations with respect to its subalgebra su(3)× su(2)× u(1) reproduces precisely the classification of these fundamental fermions according to the gauge group su(3)^c× su(2)^w× u(1)^w of the Standard Model. Furthermore, a simple construction of the relevant representations is given, and some consequences are discussed.     

Constant-cutoff approach to radiative decays of hyperons: E2/M1 transition ratios

We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then study the radiative decays ofJ ^π=3/2⁺ baryons using the constant-cutoff approach to theSU(3) collective treatment of the Skyrme model for hyperons. Thus we evaluate the widths and E2/M1 ratios, showing that there is a general qualitative agreement with the results obtained using the complete Skyrme model, as well as the nonrelativistic quark model and quenched lattice model, for the total widths.     

Quantum Field Formalism for the Electromagnetic Interaction of Composite Particles in a Nonrelativistic Gauge Model III

A classical nonrelativistic U(1)×U(1) gauge field model that describes the topologically massive electromagnetic interaction of composite particles in (2+1) dimensions is proposed. The model, generalization of a previously postulated one, contains a Chern-Simons U(1) field and the topologically massive electromagnetic U(1) field, and it uses both a composite boson system or a composite fermion one. The second case is considered explicitly. By using the Dirac Hamiltonian method for constrained systems, the canonical quantization is carried out. By means of the Faddeev-Senjanovic formalism, the path integral quantization is developed. Consequently, the Feynman rules are established and the diagrammatic structure is treated. The application of the Becchi-Rouet-Stora-Tyutin algorithm is discussed. The present and previous models are compared.