arXiv subjects

M. R. Niedermaier

Publications and source records attributed to M. R. Niedermaier.

7 recordsLinked to original sources

arXiv1998

Varying the Unruh Temperature in Integrable Quantum Field Theories

A computational scheme is developed to determine the response of a quantum field theory (QFT) with a factorized scattering operator under a variation of the Unruh temperature. To this end a new family of integrable systems is introduced, obtained by deforming such QFTs in a way that preserves the bootstrap S-matrix. The deformation parameter βplays the role of an inverse temperature for the thermal equilibrium states associated with the Rindler wedge, β= 2πbeing the QFT value. The form factor approach provides an explicit computational scheme for the β\neq 2πsystems, enforcing in particular a modification of the underlying kinematical arena. As examples deformed counterparts of the Ising model and the Sinh-Gordon model are considered.

hep-th↗

arXiv1998

Form Factors, Thermal States and Modular Structures

Form factor sequences of an integrable QFT can be defined axiomatically as solutions of a system of recursive functional equations, known as ``form factor equations''. We show that their solution can be replaced with the study of the representation theory of a novel algebra F(S). It is associated with a given two-particle S-matrix and has the following features: (i) It contains a double TTS algebra as a subalgebra. (ii) Form factors arise as thermal vector states over F(S) of temperature 1/2π. The thermal ground states are in correspondence to the local operators of the QFT. (iii) The underlying `finite temperature structure' is indirectly related to the ``Unruh effect'' in Rindler spacetime. In F(S) it is manifest through modular structures (j,δ) in the sense of algebraic QFT, which can be implemented explicitly in terms of the TTS generators.

hep-th↗

arXiv1997

A Derivation of the Cyclic Form Factor Equation

A derivation of the cyclic form factor equation from quantum field theoretical principles is given; form factors being the matrix elements of a field operator between scattering states. The scattering states are constructed from Haag-Ruelle type interpolating fields with support in a `comoving' Rindler spacetime. The cyclic form factor equation then arises from the KMS property of the modular operators Delta associated with the field algebras of these Rindler wedges. The derivation in particular shows that the equation holds in any massive 1+1 dim. relativistic QFT, regardless of its integrability.

hep-th↗

arXiv1995

On the Free Field Realization of Form Factors

A method to construct free field realizations for the form factors of diagonal factorized scattering theories is described. Form factors are constructed from linear functionals over an associative `form factor algebra', which in particular generate solutions of the deformed Knizhnik-Zamolodchikov equations with parameter $2π$. We show that there exists a unique deformation off the (`Rindler') value $2π$ that preserves the original $S$-matrix and which allows one to realize form factors as vector functionals over an algebra of generalized vertex operators.

hep-th↗

arXiv1995

An Algebraic Approach to Form Factors

An associative $*$-algebra is introduced (containing a $TTR$-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each $T$-invariant linear functional over the algebra automatically satisfies all the form factor axioms. It is argued that this answers the question (posed in the functional Bethe ansatz) how to select the dynamically correct representations of the $TTR$-algebra. Applied to the case of integrable QFTs with diagonal factorized scattering theory a universal formula for the eigenvalues of the conserved charges emerges.

hep-th↗

arXiv1994

Infinite Abelian Subalgebras in Quantum W-Algebras: An Elementary Proof

An elementary proof is given for the existence of infinite dimensional abelian subalgebras in quantum W-algebras. In suitable realizations these subalgebras define the conserved charges of various quantum integrable systems. We consider all principle W-algebras associated with the simple Lie algebras. The proof is based on the more general result that for a class of vertex operators the quantum operators are related to their classical counterparts by an equivalence transformation.

hep-th↗

arXiv1994

The Quantum Spectrum of the Conserved Charges in Affine Toda Theories

The exact eigenvalues of the infinite set of conserved charges on the multi-particle states in affine Toda theories are determined. This is done by constructing a free field realization of the Zamolodchikov-Faddeev algebra in which the conserved charges are realized as derivative operators. The resulting eigenvalues are renormalization group (RG) invariant, have the correct classical limit and pass checks in first order perturbation theory. For $n=1$ one recovers the (RG invariant form of the) quantum masses of Destri and DeVega.

hep-th↗