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Register a new userThe Batalin-Tyutin Formalism on the Collective Coordinates Quantisation of the SU(2) Skyrme Model
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We apply The Batalin-Tyutin constraint formalism of converting a second class system into a first class system for the rotational quantisation of the SU(2) Skyrme model. We obtain the first class constraint and the Hamiltonian in the extended phase space. The vacuum functional is constructed and evaluated in the unitary gauge and a multiplier dependent gauge. Finally, we discuss the spectrum of the extended theory. The use of the BT formalism on the collective coordinates quantisation of the SU(2) Skyrme model leads an additional term in the usual quantum Hamiltonian that can improve the phenomenology predicted by the Skyrme model.
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The quantisation of the Wess-Zumino-Witten model on a circle is discussed in the case of $SU(N)$ at level $k$. The quantum commutation of the chiral vertex operators is described by an exchange relation with a braiding matrix, $Q$. Using quantum consistency conditions, the braiding matrix is found explicitly in the fundamental representation. This matrix is shown to be related to the Racah matrix for $U_t(SL(N))$. From calculating the four-point functions with the Knizhnik-Zamolodchikov equations, the deformation parameter $t$ is shown to be $t=exp({ipi /(k+N)})$ when the level $kge 2$. For $k=1$, there are two possible types of braiding, $t=exp({ipi /(1+N)})$ or $t=exp(ipi)$. In the latter case, the chiral vertex operators are constructed explicitly by extending the free field realisation a la Frenkel-Kac and Segal. This construction gives an explicit description of how to chirally factorise the $SU(N)_{k=1}$ WZW model.
We study an equivariant extension of the Batalin-Vilkovisky formalism for quantizing gauge theories. Namely, we introduce a general framework to encompass failures of the quantum master equation, and we apply it to the natural equivariant extension of AKSZ solutions of the classical master equation (CME). As examples of the construction, we recover the equivariant extension of supersymmetric Yang-Mills in 2d and of Donaldson-Witten theory.
We present novel analytic hairy black holes with a flat base manifold in the (3+1)-dimensional Einstein SU(2)-Skyrme system with negative cosmological constant. We also construct (3+1)-dimensional black strings in the Einstein $SU(2)$-non linear sigma model theory with negative cosmological constant. The geometry of these black strings is a three-dimensional charged BTZ black hole times a line, without any warp factor. The thermodynamics of these configurations (and its dependence on the discrete hairy parameter) is analyzed in details. A very rich phase diagram emerges.
The Becchi-Rouet-Stora-Tyutin (BRST) method is applied to the quantization of the solitons of the non-linear $O(3)$ model in $2+1$ dimensions. We show that this method allows for a simple and systematic treatment of zero-modes with a non-commuting algebra. We obtain the expression of the BRST hamiltonian and show that the residual interaction can be perturbatively treated in an IR-divergence-free way. As an application of the formalism we explicitly evaluate the two-loop correction to the soliton mass.
In this talk, we describe recent developments in the Skyrme model. Our main focus is on discussing various effects which need to be taken into account, when calculating the properties of light atomic nuclei in the Skyrme model. We argue that an important step is to understand spinning Skyrmions and discuss the theory of relative equilibria in this context.
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