Gautam Bhattacharya

ALGEBRAIC BETHE ANSATZ SCHEME FOR RELATIVISTIC INTEGRABLE FIELD THEORIES IN CONTINUUM-: SINE-GORDON MODEL

The linear problem associated with the Lax operator of the classical sine-Gordon theory can be recast into the monodromy matrix form that can be extended to quantum theory as well. Product of the quantum monodromy matrices will have contributions from the singularities arising out of the operator product expansions of sine-Gordon field. This enables one to find the star-triangle relations. This is a generalization of the method used by Thacker for the non-relativistic nonlinear Schrodinger field theory. In the infinite volume limit, it leads to an unambiguous description of the algebra involving the scattering data operators. Starting from a vacuum the module of physical states are constructed by the application of chains of the scattering operators and they turn out to have definite eigenvalues of energy and momentum. The mass-spectra and two-particle S matrix elements can be calculated straightforwardly and they coincide with the well-known results of Zamolodchikov and Zamolodchikov. It is also shown that the particle states can be created by a generalized Jordon-Wigner transformation of the free fermionic creation operators — thus establishing a link between the S matrix element and certain co-cycles.

Solving a conformal invariant two-dimensional field theory by the bethe ansatz

Abstract The Yang-Baxter relation among the monodromy matrices of the SU(2) Wess-Zumino-Witten model is derived using the operator product expansion of currents guided by the conformal invariance of the theory. This is subsequently used to solve for the S -matrix and mass spectra by the algebraic Bethe ansatz. The particle states describe free massless fermions.

Yang-Baxter relation from operator product singularities

Abstract Leading singular behavior of the product of scalar fields at short distance is exploited to obtain the Yang-Baxter relation involving the direct product of monodromy matrices of quantum sine-Gordon field theory. No lattice regularisation is necessary and hence the space-time symmetries are manifest. Correctness is checked by comparing the classical limit, mass spectra and S -matrix.

Invariance of fermion determinant under large gauge transformations

Abstract We argue that in the perturbative framework the natural symmetry of the fermionic determinant is the perturbative gauge transformation (p.g.t.) which differs from the usual gauge transformation of the effective action through the absence of terms independent of the coupling constant. Calculated in a non-perturbative framework appropriate for large gauge function, the sum of these latter terms vanish. In three dimensions the invariance of the full fermion determinant under large gauge transformations is thus ensured due to the invariance under p.g.t. of the Chern-Simons term arising in some perturbative regularisations.

A COVARIANT APPROACH TO THE GENERALIZED MULTI-INFLATON COSMOLOGICAL PERTURBATION

Following the formalism developed in Astrophys. J.375, 443 (1991), differential equations for the gauge invariant scalar part of the metric perturbation in the Friedmann–Robertson–Walker background with multiple inflatons with arbitrary field metric are obtained without any specific choice of gauge. Subsequently, an algorithm for the solution of these equations in the slow-roll approximation is given without any prior choice of the basis system in the field manifold. Vector and tensor perturbations are also briefly reviewed.