Phase transitions in quantum field theory. I. Phases of the Thirring model

Journal Article · Thu Nov 01 04:00:00 EST 1979 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(79)90263-X· OSTI ID:5483715

Sharatchandra, H S; Mitra, P

In this series of papers we exhibit and analyse phase transitions in quantum field theory. In this paper we consider the Thirring model. We show that when the interaction becomes sufficiently attractive there is a transition to a vacuum that is 'dead' in the sense there are no finite energy excitations. Nevertheless the corresponding continuum Green's functions exist. We make this demonstration precise by considering the model on a lattice and constructing the continuum limit explicitly on either side of the critical point. For this we extensively use the connection between the spin-1/2 x-y-z chain and the lattice model. We also show a new continuum theory with four fermion interactions exists in 1 + 1 dimensions. This theory corresponds to taking the continuum limit of the spin chain in absence of any external magnetic field. Its Hamiltonian differs from that of the Thirring model by addition of fermion number operator with an infinite coefficient and is not renormalizable in the conventional sense. It has more interesting critical properties and a different spectrum.

• Research Organization: Theoretical Physics Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
• OSTI ID: 5483715
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 123:1; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
FIELD THEORIES
FUNCTIONS
GREEN FUNCTION
PARTICLE PROPERTIES
PHASE TRANSFORMATIONS
QUANTUM FIELD THEORY
RENORMALIZATION
SPIN
THIRRING MODEL
VACUUM POLARIZATION