Quantum Massless Field in 1+1 Dimensions

Abstract:We study the Sine-Gordon model with Minkowski signature in the framework of perturbative algebraic quantum field theory. We calculate the vertex operator algebra braiding property. We prove that in the finite regime of the model, the expectation valuewith respect to the vacuum or a Hadamard state-of the Epstein Glaser S-matrix and the interacting current or the field respectively converge, both given as formal power series.

“…Such Hadamard states were given, for example, in [Sch12,DM06]. The choice of the Hadamard state is not unique, but different choices lead to isomorphic algebraic structures.…”

Section: Introductionmentioning

confidence: 99%

The Quantum Sine-Gordon Model in Perturbative AQFT

Bahns

Rejzner²

2017

“…We are aware of only two places where such states were explicitly constructed: one is the diploma thesis of Sebastian Schubert [29], where he found a surprisingly simple example of a Hadamard 2-point function. The other place is a paper of Derezinski and Meissner [12], where they explicitly construct a representation on a separable Hilbert space. Actually, Schubert's states are vector states in this representation.…”

Section: Free Massless Scalar Field In 2 Dimensionsmentioning

confidence: 99%

“…Observe that we have changed the notation compared to [12]. Our q corresponds to the p of [12], and our p to their −χ .…”

Section: Derezinski-meissner Representation Inspired By a Constructimentioning

confidence: 99%

“…Observe that we have changed the notation compared to [12]. Our q corresponds to the p of [12], and our p to their −χ . Moreover, the functions σ R,L of DM are obtained from Schubert's ψ in terms of their Fourier transforms bŷ…”

Section: Derezinski-meissner Representation Inspired By a Constructimentioning

confidence: 99%

“…In this paper, we extend these results in the following way. Since the vacuum state of the massless free scalar field is not a regular state on the Weyl algebra of the field, we use a representation introduced by Derezinski and Meissner [12], quite similar to the representation used in early day string theory. We show that in this representation the S-matrix (as a generating functional for time ordered products of the interaction Lagrangian) is unitary and satisfies Bogoliubov's causal factorization condition.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Local Nets of Von Neumann Algebras in the Sine–Gordon Model

Bahns

Fredenhagen

Rejzner

2021

The Haag–Kastler net of local von Neumann algebras is constructed in the ultraviolet finite regime of the Sine–Gordon model, and its equivalence with the massive Thirring model is proved. In contrast to other authors, we do not add an auxiliary mass term, and we work completely in Lorentzian signature. The construction is based on the functional formalism for perturbative Algebraic Quantum Field Theory together with estimates originally derived within Constructive Quantum Field Theory and adapted to Lorentzian signature. The paper extends previous work by two of us.

Asymptotic Morphisms and Superselection Theory in the Scaling Limit II: Analysis of Some Models

Conti

Morsella

2019

We introduced in a previous paper a general notion of asymptotic morphism of a given local net of observables, which allows to describe the sectors of a corresponding scaling limit net. Here, as an application, we illustrate the general framework by analyzing the Schwinger model, which features confined charges. In particular, we explicitly construct asymptotic morphisms for these sectors in restriction to the subnet generated by the derivatives of the field and momentum at time zero. As a consequence, the confined charges of the Schwinger model are in principle accessible to observation. We also study the obstructions, that can be traced back to the infrared singular nature of the massless free field in d = 2, to perform the same construction for the complete Schwinger model net. Finally, we exhibit asymptotic morphisms for the net generated by the massive free charged scalar field in four dimensions, where no infrared problems appear in the scaling limit.