A class of conformally invariant quantum field theories

Poincaré invariant quantum field theories can be formulated on noncommutative planes if the statistics of fields is twisted. This is equivalent to state that the coproduct on the Poincaré group is suitably twisted. In the present work we present a twisted Poincaré invariant quantum field theory at finite temperature. For that we use the formalism of thermofield dynamics (TFD). This TFD formalism is extend to incorporate interacting fields. This is a nontrivial step, since the separation in positive and negative frequency terms is no longer valid in TFD. In particular, we prove the validity of Wick's theorem for twisted scalar quantum field at finite temperature.

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Superselection Structure of Massive Quantum Field Theories in 1+1 Dimensions

Reviews in Mathematical Physics ◽

10.1142/s0129055x98000380 ◽

1998 ◽

Vol 10 (08) ◽

pp. 1147-1170 ◽

Cited By ~ 17

Author(s):

Michael Müger

Keyword(s):

Large Class ◽

Field Theories ◽

Positive Energy ◽

Quantum Field Theories ◽

Quantum Field ◽

Haag Duality ◽

Conformally Invariant ◽

Split Property

We show that a large class of massive quantum field theories in 1+1 dimensions, characterized by Haag duality and the split property for wedges, does not admit locally generated superselection sectors in the sense of Doplicher, Haag and Roberts. Thereby the extension of DHR theory to 1+1 dimensions due to Fredenhagen, Rehren and Schroer is vacuous for such theories. Even charged representations which are localizable only in wedge regions are ruled out. Furthermore, Haag duality holds in all locally normal representations. These results are applied to the theory of soliton sectors. Furthermore, the extension of localized representations of a non-Haag dual net to the dual net is reconsidered. It must be emphasized that these statements do not apply to massless theories since they do not satisfy the above split property. In particular, it is known that positive energy representations of conformally invariant theories are DHR representations.

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GALILEI-INVARIANT QUANTUM FIELD THEORIES WITH PAIR INTERACTIONS: A REVIEW

International Journal of Modern Physics A ◽

10.1142/s0217751x91001453 ◽

1991 ◽

Vol 06 (17) ◽

pp. 2937-2970 ◽

Cited By ~ 12

Author(s):

HEiDE NARNHOFER ◽

WALTER THIRRING

Keyword(s):

Ergodic Theory ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Mixing Properties ◽

Essential Condition ◽

Classical Systems ◽

Pair Potentials ◽

Heisenberg Representation ◽

Invariant Quantum

We exhibit a class of quantum field theories where particles interact with pair potentials and for which the time evolution exists in the Heisenberg representation. The essential condition for existence is stability in the thermodynamic sense and this is achieved by having the interaction fall off with the relative momenta of the particles. This can be done in a Galilei-invariant manner. We show that these systems have some mixing properties which one postulates in ergodic theory but which are difficult to prove for classical systems.

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