A Variational Approach to Bound States in Quantum Field Theory

We consider here in a toy model an approach to bound state problem in a nonperturbative manner using equal time algebra for the interacting field operators. Potential is replaced by offshell bosonic quanta inside the bound state of nonrelativistic particles. The bosonic dressing is determined through energy minimisation, and mass renormalisation is carried out in a nonperturbative manner. Since the interaction is through a scalar field, it does not include spin effects. The model however nicely incorporates an intuitive picture of hadronic bound states in which the gluon fields dress the quarks providing the binding between them and also simulate the gluonic content of hadrons in deep inelastic collisions.Comment: latex, revtex, 22 page

Vacuum structure and effective potential at finite temperature: a variational approach

We compute the effective potential for $\phi^4$ theory with a squeezed coherent state type of construct for the ground state. The method essentially consists in optimising the basis at zero and finite temperatures. The gap equation becomes identical to resumming the infinite series of daisy and super daisy graphs while the effective potential includes multiloop effects and agrees with that obtained through composite operator formalism at finite temperature.Comment: 15 pages, Revtex, No figures, to appear in Jou. of Phys.G(Nucl. and Part. Phys.

Chiral Symmetry Breaking and Pion Wave Function

We consider here chiral symmetry breaking through nontrivial vacuum structure with quark antiquark condensates. We then relate the condensate function to the wave function of pion as a Goldstone mode. This simultaneously yields the pion also as a quark antiquark bound state as a localised zero mode in vacuum. We illustrate the above with Nambu Jona-Lasinio model to calculate different pionic properties in terms of the vacuum structure for breaking of exact or approximate chiral symmetry, as well as the condensate fluctuations giving rise to $\sigma$ mesons.Comment: latex, revtex, 16 page

BCS BEC crossover and phase structure of relativistic system: a variational approach

We investigate here the BCS BEC crossover in relativistic systems using a variational construct for the ground state and the minimization of the thermodynamic potential. This is first studied in a four fermion point interaction model and with a BCS type ansatz for the ground state with fermion pairs. It is shown that the antiparticle degrees of freedom play an important role in the BCS BEC crossover physics, even when the ratio of fermi momentum to the mass of the fermion is small. We also consider the phase structure for the case of fermion pairing with imbalanced populations. Within the ansatz, thermodynamically stable gapless modes for both fermions and anti fermions are seen for strong coupling in the BEC regime. We further investigate the effect of fluctuations of the condensate field by treating it as a dynamical field and generalize the BCS ansatz to include quanta of the condensate field also in a boson fermion model with quartic self interaction of the condensate field. It is seen that the critical temperature decreases with inclusion of fluctuations.Comment: 18 pages, 13 figures, one more section added, title modified, version to appear in Phys Rev