Thermodynamic calculations in relativistic finite-temperature quantum field theories

A Minkowski space formalism of finite-temperature quantum field theory is used to compute static thermodynamic quantities in the one- and two-loop approximation in an elegant and straightforward way using a generalization of Weinberg's tadpole method of calculating effective potentials. Systematic diagrammatic techniques for low- and high-temperature expansions are developed. Renormalizability by zero-temperature symmetric counterterms is proven for all orders in the loop expansion and demonstrated explicitly to two loops. Many useful computational techniques applicable to general finite temperature calculations are explained.     

Secret supersymmetry and the fractional charges of quantum solitons

Supersymmetry generators are constructed from the physical operators in a quantum field theory of interacting Bose and Fermi fields where a soliton is present. These supersymmetry generators obey a standard supersymmetry algebra with a central charge and can be used to give an algebraic proof of charge fractionalization of the soliton ground state.     

Lorentz invariant exact solution of the anomalous chiral Schwinger model

We present an exact solution of the anomalous chiral Schwinger model using Fermionic variables. We implement infrared regularization by considering the model on a spatial circleS ¹. Quantum effects modify the gauge constraints through the appearance of Schwinger terms in the gauge algebra. We perform a careful analysis of the resulting second class gauge constraints by implementing Dirac's method at the quantum level and obtain the spectrum of the theory. We get a consistent unitary Lorentz invariant theory for particular values of the counterterms. We find that when we regulate the fermionic sector of the model without reference to the gauge fields Lorentz invariance requires that we add both Lorentz variant and gauge variant counterterms.