Multilocal Fermionization

@article{Rehren2013MultilocalF,
  title={Multilocal Fermionization},
  author={Karl-Henning Rehren and Gennaro Tedesco},
  journal={Letters in Mathematical Physics},
  year={2013},
  volume={103},
  pages={19-36}
}
We present a simple isomorphism between the algebra of one real chiral Fermi field and the algebra of n real chiral Fermi fields. The isomorphism preserves the vacuum state. This is possible by a “change of localization”, and gives rise to new multilocal symmetries generated by the corresponding multilocal current and stress–energy tensor. The result gives a common underlying explanation of several remarkable recent results on the representation of the free Bose field in terms of free Fermi… 
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References

SHOWING 1-10 OF 16 REFERENCES
Extensions of Conformal Nets¶and Superselection Structures
Abstract:Starting with a conformal Quantum Field Theory on the real line, we show that the dual net is still conformal with respect to a new representation of the Möbius group. We infer from this
Modular structure and duality in conformal quantum field theory
Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories, i.e. the Tomita-Takesaki modular group associated with
The CPT-theorem in two-dimensional theories of local observables
Let ℳ be a von Neumann algebra with cyclic and separating vector Ω, and letU(a) be a continuous unitary representation ofR with positive generator and Ω as fixed point. If these unitaries induce for
ON THE DUALITY CONDITION FOR QUANTUM FIELDS
A general quantum field theory is considered in which the fields are assumed to be operator‐valued tempered distributions. The system of fields may include any number of boson fields and fermion
Affine Lie algebras and quantum groups
Let g be a finite dimensional simple Lie algebra of simply laced type. Drinfeld has shown that the tensor category of finite-dimensional representations of the corresponding quantized enveloping
The massless Thirring model: Positivity of Klaiber'sn-point functions
We present a simple solution to the problem of proving positivity of Klaiber'sn-point functions for the massless Thirring model. The corresponding fields are obtained as strong limits of explicitly
Reduced density matrix and internal dynamics for multicomponent regions
We find the density matrix corresponding to the vacuum state of a massless Dirac field in two dimensions reduced to a region of the space formed by several disjoint intervals. We calculate explicitly
On the equilibrium states in quantum statistical mechanics
AbstractRepresentations of theC*-algebra $$\mathfrak{A}$$ of observables corresponding to thermal equilibrium of a system at given temperatureT and chemical potential μ are studied. Both for finite
Soliton Operators for the Quantized Sine-Gordon Equation
Operators for the creation and annihilation of quantum sine-Gordon solitons are constructed. The operators satisfy the anticommutation relations and field equations of the massive Thirring model. The
TRANSFORMATION GROUPS FOR SOLITON EQUATIONS
A printing blanket and method of making same is provided wherein such blanket comprises a base structure, a surface layer made of a fluorocarbon elastomer, and a binder layer comprised of a
...
1
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