Algebraic structures of the quantum projective [sl(2,C)‐invariant] field theory: The commutative version of Elie Cartan’s exterior differential calculus

The aim of the tutorial is to help students to master the basic concepts and methods of the study of calculus. In volume 2 we study analytic geometry in space; differential calculus of functions of several variables; local, conditional, global extrema of functions of several variables; multiple, curvilinear and surface integrals; elements of field theory; numerical, power series, Taylor series and Maclaurin, and Fourier series; applications to the analysis and solution of applied problems. Great attention is paid to comparison of these methods, the proper choice of study design tasks, analyze complex situations that arise in the study of these branches of mathematical analysis. For self-training and quality control knowledge given test questions. For teachers, students and postgraduate students studying mathematical analysis.

Download Full-text

Topological Quantum Field Theory and Algebraic Structures*

Quantum Field Theory and Noncommutative Geometry - Lecture Notes in Physics ◽

10.1007/11342786_14 ◽

2008 ◽

pp. 255-287

Author(s):

T. Kimura

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Topological Quantum Field Theory ◽

Quantum Field ◽

Algebraic Structures ◽

Topological Quantum

Download Full-text

LOCAL SYMPLECTIC FIELD THEORY

International Journal of Mathematics ◽

10.1142/s0129167x13500419 ◽

2013 ◽

Vol 24 (05) ◽

pp. 1350041 ◽

Cited By ~ 1

Author(s):

OLIVER FABERT

Keyword(s):

Field Theory ◽

Symplectic Manifold ◽

Local Version ◽

Algebraic Structures ◽

Witten Theory ◽

Symplectic Field Theory

Generalizing local Gromov–Witten theory, in this paper we define a local version of symplectic field theory. When the symplectic manifold with cylindrical ends is four-dimensional and the underlying simple curve is regular by automatic transversality, we establish a transversality result for all its multiple covers and discuss the resulting algebraic structures.

Download Full-text

GAUGE FIELD THEORY ON THE Eq(2)-COVARIANT PLANE

International Journal of Modern Physics A ◽

10.1142/s0217751x04019512 ◽

2004 ◽

Vol 19 (20) ◽

pp. 3349-3375 ◽

Cited By ~ 2

Author(s):

FRANK MEYER ◽

HAROLD STEINACKER

Keyword(s):

Field Theory ◽

Gauge Theory ◽

Differential Calculus ◽

Euclidean Plane ◽

Star Product ◽

Gauge Field Theory ◽

Two Dimensional ◽

Suitable Measure ◽

Natural Way ◽

Invariant Integration

Gauge theory on the q-deformed two-dimensional Euclidean plane [Formula: see text] is studied using two different approaches. We first formulate the theory using the natural algebraic structures on [Formula: see text], such as a covariant differential calculus, a frame of one-forms and invariant integration. We then consider a suitable star product, and introduce a natural way to implement the Seiberg–Witten map. In both approaches, gauge invariance requires a suitable "measure" in the action, breaking the Eq(2)-invariance. Some possibilities to avoid this conclusion using additional terms in the action are proposed.

Download Full-text