Coherent states associated with the groups SU(N) and SU(N, 1)

The coherent-state basis is constructed for symmetric representations of the groups SU(N) and SU(N, 1) and its properties are studied. The evolution of coherent states is considered. A relationship between the SU(N) coherent states and the Glauber coherent states is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 83–89, January, 1990.     

The Branching Rules for SU(2N)⊃(SU(N)⊃O(N)⊃O(3))⊗SU(2) and the Highest Weight States for SU(N) and O(N)

Simple analytical recurrent formulae of the branching rules for group chain SU(2N)⊃(SU(N)⊃O(N)⊃O(3))⊗SU(2) are obtained. The highest weight states for the irreducible representations [2^al^b] or {nS} of group SU(N) and for the irreducible representations (2^α1^β) or (υS) of group O(N) are constructed respectively     

TRIGONOMETRIC SU(N) GAUDIN MODEL

In this paper, we obtain the eigenstates and the eigenvalues of the Hamiltonians of the trigonometric SU(N) Gaudin model based on the quasi-classical limit of the trigonometric SU(N) chain with the periodic boundary condition. By using the quantum inverse scattering method, we also obtain the eigenvalues of the generating function of the trigonometric SU(N) Gaudin model.     

Geometric phase in SU(N) interferometry

An interferometric scheme to study Abelian geometric phase shift over the manifold SU(N)/U(N − 1) is presented. Presented by H. de Guise at the DI-CRM Workshop held in Prague, 18–21 June 2000. This work has been supported by two Macquarie University Research Grants and by an Australian Research Council Large Grant.     

Semi-fermionic representation of SU(N) Hamiltonians

We represent the generators of the SU(N) algebra as bilinear combinations of Fermi operators with imaginary chemical potential. The distribution function, consisting of a minimal set of discrete imaginary chemical potentials, is introduced to satisfy the local constraints. This representation leads to the conventional temperature diagram technique with standard Feynman codex, except that the Matsubara frequencies are determined by neither integer nor half-integer numbers. The real-time Schwinger-Keldysh formalism is formulated in the framework of complex equilibrium distribution functions for auxiliary semi-fermionic fields. We discuss the continuous large N and SU(2) large spin limits. We illustrate the application of this technique for magnetic and spin-liquid states of the Heisenberg model. Received 26 February 2001 and Received in final form 25 April 2001     

Emergent SU(N) symmetry in disordered SO(N) spin chains

The European Physical Journal B - We report the first observation of the low-frequency Raman spectra of 2-propanol from ambient to supercritical condition. Phenomenological analysis is applied to...     

SU(6)W and πN→ϱN revisited

We point out that the intersection of the Berkeley-SLAC and Saclay signs of πN→?N resonant amplitudes are consistent with ?-broken SU(6)_W if both the 70, L^P = 1^?and 56, L^P = 2⁺ multiplets choose anti-SU(6)_W solutions. The symmetry scheme still fails in that the πN→πΔ relative signs require an SU(6)_W-like solution for the 56, L^P = 2⁺. This failure however now rests on a single incorrect sign prediction among all N? and Δπ amplitudes.     

Mixing of meson isosinglets in SU(5) and an extension to SU(N)

The mixing angles of meson isosinglets belonging to the 24-dimensional and singlet representations of SU(5) are calculated under specific assumptions in the non-relativistic quark model. The procedure to extend the scheme to SU(N) has been outlined. The results have been compared with other earlier estimates.     

N = 4 supergravity theory with local SU(2) × SU(2) invariance

N = 4 supergravity theory has been formulated in two different equivalent forms, which may be expected to become inequivalent when the internal symmetry is gauged. The extension of the first form to include local SO(4) internal symmetry is known. In this paper the extension of the second form to local SU(2) × SU(2) invariance is given, and is indeed inequivalent to the first form. The second form is in general parity non-conserving, while both forms have scalar field potentials that are unbounded from below.     

ExactS-matrix of the adjoint SU(N) representation

We have calculated the exact factorisedS-matrices of the adjoint SU(N) representation in 1+1 space-time dimensions. Besides the trivial solution the only realised solution exhibits anO(N ²–1) symmetry.     

SU(N) gauge fields with spherical symmetry

A method to construct spherically symmetricSU(N) gauge fields and an invariant classification are presented. For the groupSU(3) the ansätze are completely elaborated. The corresponding sourcelessSU(3)-Yang-Mills equations are discussed.     

Bosonization of the SU(N) Thirring models

Bosonization is applied to the SU(N) Thirring models, and interesting relations between various two-dimensional field theories arise. In particular, we show that the SU(2) model is equivalent to a version of the Sine-Gordon equation plus a free massless field.     

Magnetic monopoles in SU(N) gauge theories

The potential $\text{A}\text{(}\text{r}\text{) ≡}\text{M}\text{(}\text{r}\text{?}\text{×}\text{n}\text{?}\text{)(r?}\text{r}\text{·}\text{n}\text{?}\text{)}{}^{\mathrm{?1}}$ is a static solution to the classical theory of non-abelian gauge fields coupled to a point magnetic source, for any matrix $\text{M}$ in the Lie algebra of the gauge group G. This solution is rotationally invariant if the eigenvalues of $\text{M}$ in the adjoint representation of G are quantized in half-integer units, but is stable to small perturbations only if all non-vanishing eigenvalues are $\text{±}\text{1}\text{2}$. In this paper, for the gauge groups G = SU(N), it is shown which sets of eigenvalues of $\text{M}$ are consistent with the group structure, which consistent sets are gauge inequivalent, and which consistent gauge inequivalent sets correspond to stable monopoles. It is found that there are N inequivalent stable monopoles, including the trivial case $\text{M}\text{=}\text{0}$. Equivalence here is with respect to non-singular gauge transformations—the symmetry transformations of the classical theory. Singular gauge transformations are, in contrast, not symmetries but they are nevertheless useful for classifying solutions and for relating the above concept of local stability to the global, or topological, stability associated with the Dirac strings. In this context, it is shown that there are N distinct topological classes of monopoles, with the group structure of the center $\text{Z}{}_{\mathrm{N}}\text{?Π}{}_1\text{(}\text{SU}\text{(N)/}\text{Z}{}_{\mathrm{N}}\text{)}$ of SU(N), that each class contains exactly one stable monopole, and that any other monopole in the same class has a strictly larger value of the magnetic charge magnitude $\text{tr}\text{M}{}^2$. This leads to an interesting physical picture of local stability as a consequence of the minimization of magnetic energy. The paper concludes with some comments on related topics: the empirical absence of magnetic charge, `t Hooft's calculation of magnetic energy, magnetic confinement, and spontaneously broken theories.     

Asymptotically finite SU(N) models of field theory

Models finite in the one-loop approximation are constructed for quantum field theory. In particular, a finite model with two Higgs multiplets is constructed on the basis of the SU(N) group. Violation of the conditions on the coupling constants induces ultraviolet or infrared-asymptotic finiteness. The behavior of the effective coupling constants in an external gravitational field is also investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 56–64, December, 1991.     

Face Algebras and Unitarity of SU(N)L-TQFT

A collisionless plasma is described by the Vlasov–Maxwell system. In many physical situations, a plasma is invariant under either rotations or translations. Many symmetric equilibria with nontrivial magnetic fields are critical points of an appropriate Liapunov functional, and their dynamical stability is studied among all symmetric perturbations. The set of all minimizers of the Liapunov functional are dynamically stable. Criteria for stability for general critical points are also established. A simpler sufficient condition for stability is derived for neutral equilibria. Received: 13 February 1998 / Accepted: 13 July 1998     

DMRG studies of critical SU(N) spin chains

The DMRG method is applied to integrable models of antiferromagnetic spin chains for fundamental and higher representations of SU(2), SU(3), and SU(4). From the low energy spectrum and the entanglement entropy, we compute the central charge and the primary field scaling dimensions. These parameters allow us to identify uniquely the Wess–Zumino–Witten models capturing the low energy sectors of the models we consider.