scholarly journals Construction of Kink Sectors for Two-Dimensional Quantum Field Theory Models – An Algebraic Approach

1998 ◽  
Vol 10 (06) ◽  
pp. 851-891 ◽  
Author(s):  
Dirk Schlingemann
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Algebraic Approach ◽  
Vacuum State ◽  
Quantum Field ◽  
Two Dimensional ◽  
Algebraic Quantum ◽  
Free Scalar ◽  
Split Property ◽  
Text Model

Several two-dimensional quantum field theory models have more than one vacuum state. Familiar examples are the Sine-Gordon and the [Formula: see text]-model. It is known that in these models there are also states, called kink states, which interpolate different vacua. A general construction scheme for kink states in the framework of algebraic quantum field theory is developed in a previous paper. However, for the application of this method, the crucial condition is the split property for wedge algebras in the vacuum representations of the considered models. It is believed that the vacuum representations of P(ϕ)2-models fulfill this condition, but a rigorous proof is only known for the massive free scalar field. Therefore, we investigate in a construction of kink states which can directly be applied to a large class of quantum field theory models, by making use of the properties of the dynamics of a P(ϕ)2 and Yukawa2 models.

scholarly journals ON THE EXISTENCE OF KINK (SOLITON) STATES

1996 ◽  
Vol 08 (08) ◽  
pp. 1187-1203 ◽  
Author(s):  
DIRK SCHLINGEMANN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vacuum State ◽  
Quantum Field ◽  
Algebraic Quantum Field Theory ◽  
Algebraic Quantum ◽  
Vacuum States ◽  
Text Model ◽  
Kink Soliton ◽  
Natural Way

Several two-dimensional quantum field theory models have more than one vacuum state. Familiar examples are the Sine-Gordon and the [Formula: see text]-model. It is known that in these models there are also states, called soliton or kink states, which interpolate different vacua. We investigate the following question: Which are the properties a pair of vacuum states must have, such that an interpolating kink state can be constructed? We discuss the problem in the framework of algebraic quantum field theory which includes, for example, the P(ϕ)2-models. We identify a large class of vacuum states, including the vacua of the P(ϕ)2-models, for which there is a natural way to construct an interpolating kink state.

scholarly journals Locality and General Vacua in Quantum Field Theory

2021 ◽  
Author(s):  
Daniele Colosi ◽  
◽  
Robert Oeckl ◽  
◽  
◽  
...  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Vacuum State ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Algebraic Quantum ◽  
Particle Pairs ◽  
The One ◽  
Gns Construction

We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-Kähler polarizations which occur generically on timelike hypersurfaces in Lorentzian spacetimes as has been shown recently. We achieve this in two ways: On the one hand we replace Hilbert space states by observables localized on hypersurfaces, in the spirit of algebraic quantum field theory. On the other hand we apply the GNS construction to twisted star-structures to obtain Hilbert spaces, motivated by the notion of reflection positivity of the Euclidean approach to quantum field theory. As one consequence, the well-known representation of a vacuum state in terms of a sea of particle pairs in the Hilbert space of another vacuum admits a vast generalization to non-Kähler vacua, particularly relevant on timelike hypersurfaces.

scholarly journals BRAID GROUP STATISTICS IN TWO-DIMENSIONAL QUANTUM FIELD THEORY

1996 ◽  
Vol 08 (07) ◽  
pp. 907-924 ◽  
Author(s):  
C. ADLER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Braid Group ◽  
Scattering Theory ◽  
Quantum Field ◽  
Two Dimensional ◽  
Algebraic Quantum Field Theory ◽  
Algebraic Quantum ◽  
Dimensional Minkowski Space ◽  
Braid Group Statistics

Within the framework of algebraic quantum field theory, we construct explicitly localized morphisms of a Haag-Kastler net in 1+1-dimensional Minkowski space showing abelian braid group statistics. Moreover, we investigate the scattering theory of the corresponding quantum fields.

scholarly journals A microlocal approach to renormalization in stochastic PDEs

2021 ◽  
pp. 2150075
Author(s):  
Claudio Dappiaggi ◽  
Nicolò Drago ◽  
Paolo Rinaldi ◽  
Lorenzo Zambotti
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Large Class ◽  
Random Fields ◽  
Stochastic Partial Differential Equations ◽  
Algebraic Approach ◽  
Stochastic Pdes ◽  
Quantum Field ◽  
Regularization Scheme ◽  
Text Model

We present a novel framework for the study of a large class of nonlinear stochastic partial differential equations (PDEs), which is inspired by the algebraic approach to quantum field theory. The main merit is that, by realizing random fields within a suitable algebra of functional-valued distributions, we are able to use techniques proper of microlocal analysis which allow us to discuss renormalization and its associated freedom without resorting to any regularization scheme and to the subtraction of infinities. As an example of the effectiveness of the approach we apply it to the perturbative analysis of the stochastic [Formula: see text] model.

CAUSAL SPACES, CAUSAL COMPLEMENTS AND THEIR RELATIONS TO QUANTUM FIELD THEORY

1996 ◽  
Vol 08 (02) ◽  
pp. 229-270 ◽  
Author(s):  
MICHAEL KEYL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Causal Structure ◽  
Space Time ◽  
Quantum Field ◽  
Algebraic Quantum ◽  
Space Time Structure ◽  
Klein Gordon ◽  
Free Scalar ◽  
Local Observables

In this paper the question is analyzed, how it is possilble to reconstruct classical spacetime from the net of local observables of a quantum field theory. To this end different aspects of space-time structure are considered separately. Special attention is drawn to the topological and the causal structure of space-time. Within the scope of causality the differences between causal spaces introduced by Kronheimer and Penrose and causal disjointness relations used in algebraic quantum field theory are considered. Finally we show that the free scalar field on a globally hyperbolic space-time is a special example for our scheme, even if the corresponding Klein-Gordon operator is a Huygens operator.

scholarly journals Algebraic Quantum Field Theory on Spacetimes with Timelike Boundary

2018 ◽  
Vol 19 (8) ◽  
pp. 2401-2433 ◽  
Author(s):  
Marco Benini ◽  
Claudio Dappiaggi ◽  
Alexander Schenkel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Algebraic Quantum Field Theory ◽  
Algebraic Quantum

scholarly journals Beyond Combination: How Cosmic Consciousness Grounds Ordinary Experience

2018 ◽  
Vol 4 (3) ◽  
pp. 390-410 ◽  
Author(s):  
ITAY SHANI ◽  
JOACHIM KEPPLER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vacuum State ◽  
Present Approach ◽  
Quantum Field ◽  
Eastern Philosophy ◽  
Stochastic Electrodynamics ◽  
Ordinary Experience ◽  
Wisdom Traditions ◽  
Ordinary Consciousness

AbstractThe aim of this paper is twofold. First, our purpose is to propose and motivate a novel and scientifically informed variant of cosmopsychism, namely, the view that the experiences of ordinary subjects are ultimately grounded in an all-pervading cosmic consciousness. Second, we will demonstrate that this approach generates promising avenues for addressing familiar problems of phenomenal constitution. We use stochastic electrodynamics (SED) as the physical bedrock of our approach, supplementing it with key insights about the nature of consciousness long emphasized in eastern philosophy and other wisdom traditions. We proceed to show that our approach substantiates an intriguing way of thinking about the dynamical emergence of ordinary consciousness from cosmic consciousness, identifying the latter with the vacuum state of quantum field theory. Finally, we argue that the present approach is well suited to address problems of phenomenal constitution, in particular as they pertain to the qualities and structure of experience and to the generation of subjects.

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