scholarly journals A C*-algebra approach to the Schwinger model

1981 ◽  
Vol 80 (1) ◽  
pp. 1-21 ◽  
Author(s):  
A. L. Carey ◽  
C. A. Hurst
Keyword(s):  
C Algebra ◽  
Schwinger Model ◽  
Algebra Approach

scholarly journals Projective Modules Over Quantum Projective Line

2017 ◽  
Vol 28 (03) ◽  
pp. 1750022 ◽  
Author(s):  
Albert Jeu-Liang Sheu
Keyword(s):  
Projective Line ◽  
Complete Classification ◽  
Projective Modules ◽  
C Algebra ◽  
Isomorphism Classes ◽  
Complex Projective Spaces ◽  
Algebra Approach ◽  
Quantum Spheres ◽  
Complex Projective

Taking a groupoid C*-algebra approach to the study of the quantum complex projective spaces [Formula: see text] constructed from the multipullback quantum spheres introduced by Hajac and collaborators, we analyze the structure of the C*-algebra [Formula: see text] realized as a concrete groupoid C*-algebra, and find its [Formula: see text]-groups. Furthermore, after a complete classification of the unitary equivalence classes of projections or equivalently the isomorphism classes of finitely generated projective modules over the C*-algebra [Formula: see text], we identify those quantum principal [Formula: see text]-bundles introduced by Hajac and collaborators among the projections classified.

C*-Algebra Approach in Quantum Field Theory

1981 ◽  
Vol 24 (5) ◽  
pp. 881-885 ◽  
Author(s):  
Huzihiro Araki
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
C Algebra ◽  
Algebra Approach

scholarly journals ASPECTS OF NONCOMMUTATIVE LORENTZIAN GEOMETRY FOR GLOBALLY HYPERBOLIC SPACETIMES

2003 ◽  
Vol 15 (10) ◽  
pp. 1171-1217 ◽  
Author(s):  
VALTER MORETTI
Keyword(s):  
Causal Structure ◽  
Order Relation ◽  
Partial Ordering ◽  
Lorentzian Geometry ◽  
Causal Order ◽  
C Algebra ◽  
Globally Hyperbolic ◽  
C Algebras ◽  
Hyperbolic Spacetime ◽  
Algebra Approach

Connes' functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d'Alembert operator and the causal functions of a globally-hyperbolic spacetime. As a step of the presented machinery, a proof of the almost-everywhere smoothness of the Lorentzian distance considered as a function of one of the two arguments is given. Afterwards, using a C*-algebra approach, the spacetime causal structure and the Lorentzian distance are generalized into noncommutative structures giving rise to a Lorentzian version of part of Connes' noncommutative geometry. The generalized noncommutative spacetime consists of a direct set of Hilbert spaces and a related class of C*-algebras of operators. In each algebra a convex cone made of self-adjoint elements is selected which generalizes the class of causal functions. The generalized events, called loci, are realized as the elements of the inductive limit of the spaces of the algebraic states on the C*-algebras. A partial-ordering relation between pairs of loci generalizes the causal order relation in spacetime. A generalized Lorentz distance of loci is defined by means of a class of densely-defined operators which play the role of a Lorentzian metric. Specializing back the formalism to the usual globally-hyperbolic spacetime, it is found that compactly-supported probability measures give rise to a non-pointwise extension of the concept of events.

A C*-ALGEBRA APPROACH TO THE IRREDUCIBILITY OF COWEN-DOUGLAS OPERATORS

1999 ◽  
Vol 20 (03) ◽  
pp. 305-308
Author(s):  
YIFENG XUE ◽  
ZONGYAO WANG
Keyword(s):  
C Algebra ◽  
Algebra Approach

scholarly journals A $C^*$-algebra approach to complex symmetric operators

2015 ◽  
Vol 367 (10) ◽  
pp. 6903-6942 ◽  
Author(s):  
Kunyu Guo ◽  
Youqing Ji ◽  
Sen Zhu
Keyword(s):  
C Algebra ◽  
Algebra Approach ◽  
Complex Symmetric ◽  
Symmetric Operators

Light front field theory: An advanced Primer

2007 ◽  
Vol 57 (3) ◽  
Author(s):  
L'ubomír Martinovič
Keyword(s):  
Field Theory ◽  
Detailed Comparison ◽  
Light Front ◽  
Two Dimensional ◽  
Schwinger Model ◽  
Initial Space ◽  
Model Hamiltonian ◽  
Spatial Volume ◽  
Hamiltonian Perturbation Theory ◽  
Light Front Quantization

Light front field theory: An advanced PrimerWe present an elementary introduction to quantum field theory formulated in terms of Dirac's light front variables. In addition to general principles and methods, a few more specific topics and approaches based on the author's work will be discussed. Most of the discussion deals with massive two-dimensional models formulated in a finite spatial volume starting with a detailed comparison between quantization of massive free fields in the usual field theory and the light front (LF) quantization. We discuss basic properties such as relativistic invariance and causality. After the LF treatment of the soluble Federbush model, a LF approach to spontaneous symmetry breaking is explained and a simple gauge theory - the massive Schwinger model in various gauges is studied. A LF version of bosonization and the massive Thirring model are also discussed. A special chapter is devoted to the method of discretized light cone quantization and its application to calculations of the properties of quantum solitons. The problem of LF zero modes is illustrated with the example of the two-dimensional Yukawa model. Hamiltonian perturbation theory in the LF formulation is derived and applied to a few simple processes to demonstrate its advantages. As a byproduct, it is shown that the LF theory cannot be obtained as a "light-like" limit of the usual field theory quantized on an initial space-like surface. A simple LF formulation of the Higgs mechanism is then given. Since our intention was to provide a treatment of the light front quantization accessible to postgradual students, an effort was made to discuss most of the topics pedagogically and a number of technical details and derivations are contained in the appendices.

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