Related papers: A Canonical Approach to Duality Transformations
In these lectures a general introduction to T-duality is given. In the abelian case the approaches of Buscher, and Ro\u{c}ek and Verlinde are reviewed. Buscher's prescription for the dilaton transformation is recovered from a careful…
We construct explicit canonical transformations producing non-abelian duals in principal chiral models with arbitrary group G. Some comments concerning the extension to more general $\sigma$-models, like WZW models, are given.
We exploit a new theory of duality transformations to construct dual representations of models incompatible with traditional duality transformations. Hence we obtain a solution to the long-standing problem of non-Abelian dualities that…
We present a brief review on the canonical transformation description of some duality symmetries in string and gauge theories. In particular, we consider abelian and non-abelian T-dualities in closed and open string theories as well as…
We apply the method of differential renormalization to two and three dimensional abelian gauge theories. The method is especially well suited for these theories as the problems of defining the antisymmetric tensor are avoided and the…
For non-Abelian tensor gauge fields we have found an alternative form of duality transformation, which has the property that the direct and the inverse transformations coincide. This duality transformation has the desired property that the…
This paper presents a canonical dual approach for solving nonconvex quadratic minimization problem. By using the canonical duality theory, nonconvex primal minimization problems over n-dimensional Lorentz cone can be transformed into…
Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous…
A modification of the Abelian Duality transformations is proposed guaranteeing that a (not necessarily conformally invariant) $\sigma$-model be quantum equivalent (at least up to two loops in perturbation theory) to its dual. This requires…
In this paper, we revisit foundations of umbral calculus using a straightforward approach based on an explicit matrix realization of binomial convolution. We construct an umbral duality of Wronskian type for rational curves in echelon form,…
We examine the electric-magnetic duality for a U(1) gauge theory on a general 4-manifold. The partition function for such a theory transforms as a modular form of specific weight. However, in the canonical approach, we show that S-duality,…
Canonical duality-triality is a breakthrough methodological theory, which can be used not only for modeling complex systems within a unified framework, but also for solving a wide class of challenging problems from real-world applications.…
We demonstrate that the technique of abelian bosonization through duality transformations can be extended to gauging anomalous symmetries. The example of a Dirac fermion theory is first illustrated. This idea is then also applied to…
Applying the techniques of nonabelian duality to a system of Majorana fermions in 1+1 dimensions we obtain the level-one Wess-Zumino-Witten model as the dual theory. This makes nonabelian bosonization a particular case of a nonabelian…
We study T-duality with non-zero components of NSNS two form field along directions we dualize with the help of canonical formalism. As a result of this procedure we determine generalized Buscher's rules. We also apply the same procedure to…
We show that the recently developed soldering formalism in the Lagrangian approach and canonical transformations in the Hamiltonian approach are complementary. The examples of gauged chiral bosons in two dimensions and self-dual models in…
We show that S-duality in four dimensional non-supersymmetric abelian gauge theories can be formulated as a canonical transformation in the phase space of the theory. This transformation is the usual interchange between electric and…
We provide a natural duality that matches, in reverse order, the coefficients of the characteristic polynomial of the Maurer-Cartan of the Wronskian matrix with the coefficients of the original differential equation. Abel's identity is…
An irreducible canonical approach to second-class constraints reducible of an arbitrary order is given. This method generalizes our previous results from [Europhys. Lett. 50 (2000) 169, J. Phys. A: Math. Theor. 40 (2007) 14537] for first-…
A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality…