Narrow Results

Changes of field variables may lead to multivalued fields which do not satisfy the Schwarz integrability conditions. Their quantum field theory needs special care as is illustrated here in applications to superfluid and superconducting phase transitions. Extending the notions that first qantization governs fluctuating orbits while second quantization deals with fluctuating field, the theory of multivalued fields may be considered as a theory of third quantization. The lecture is an introduction to my new book on this subject.

Recent experiments by Kim and Chan on solid ⁴He have been interpreted as discovery of a supersolid phase of matter. Arguments based on wavefunctions have shown that such a phase exists, but do not necessarily apply to solid ⁴He. Imaginary time path integrals, implemented using Monte Carlo methods, provide a definitive answer; a clean system of solid ⁴He should be a normal quantum solid, not one with superfluid properties. The Kim-Chan phenomena must be due to defects introduced when the solid is formed.