scholarly journals Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 620
Author(s):  
Tijana Radenković ◽  
Marko Vojinović
Keyword(s):  
Field Theory ◽  
Category Theory ◽  
Degrees Of Freedom ◽  
Canonical Quantization ◽  
Topological Field Theory ◽  
Dynamic Constraints ◽  
Specific Choice ◽  
Higher Category Theory ◽  
Topological Field ◽  
Hamiltonian Analysis

The higher category theory can be employed to generalize the B F action to the so-called 3 B F action, by passing from the notion of a gauge group to the notion of a gauge 3-group. The theory of scalar electrodynamics coupled to Einstein–Cartan gravity can be formulated as a constrained 3 B F theory for a specific choice of the gauge 3-group. The complete Hamiltonian analysis of the 3 B F action for the choice of a Lie 3-group corresponding to scalar electrodynamics is performed. This analysis is the first step towards a canonical quantization of a 3 B F theory, an important stepping stone for the quantization of the complete scalar electrodynamics coupled to Einstein–Cartan gravity formulated as a 3 B F action with suitable simplicity constraints. It is shown that the resulting dynamic constraints eliminate all propagating degrees of freedom, i.e., the 3 B F theory for this choice of a 3-group is a topological field theory, as expected.

scholarly journals PARTICLE CONTENT IN TOPOLOGICAL FIELD THEORIES

1994 ◽  
Vol 09 (01) ◽  
pp. 29-39 ◽  
Author(s):  
ANDREW TOON
Keyword(s):  
Field Theory ◽  
Topological Field Theories ◽  
Path Integral ◽  
Degrees Of Freedom ◽  
Field Theories ◽  
Topological Field Theory ◽  
Particle Content ◽  
Integral Measure ◽  
Topological Field ◽  
Dimensionality Of Space

By demanding that the path-integral measure of the topological field theories be metric-independent, we can derive powerful constraints on the particle content of a topological field theory as well as on the dimensionality of space-time. We also relate this metric independence to the number of degrees of freedom in the theory.

A COMMENT ON TOPOLOGICAL FIELD THEORY QUANTIZATION AND STOCHASTIC PROCESSES

1990 ◽  
Vol 05 (19) ◽  
pp. 3777-3786 ◽  
Author(s):  
L.F. CUGLIANDOLO ◽  
G. LOZANO ◽  
H. MONTANI ◽  
F.A. SCHAPOSNIK
Keyword(s):  
Field Theory ◽  
Equilibrium State ◽  
Stochastic Processes ◽  
Topological Field Theories ◽  
Topological Charge ◽  
Field Theories ◽  
Langevin Equations ◽  
Topological Field Theory ◽  
Topological Field

We discuss the relation between different quantization approaches to topological field theories by deriving a connection between Bogomol’nyi and Langevin equations for stochastic processes which evolve towards an equilibrium state governed by the topological charge.

TETRAHEDRA AND POLYNOMIAL EQUATIONS IN TOPOLOGICAL FIELD THEORY

1991 ◽  
Vol 06 (20) ◽  
pp. 3571-3598 ◽  
Author(s):  
NOUREDDINE CHAIR ◽  
CHUAN-JIE ZHU
Keyword(s):  
Field Theory ◽  
Topological Field Theory ◽  
Fundamental Representation ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Witten Theory ◽  
Topological Field ◽  
General Program ◽  
The One ◽  
Chern Simons

Some tetrahedra in SUk(2) Chern-Simons-Witten theory are computed. The results can be used to compute an arbitrary tetrahedron inductively by fusing with the fundamental representation. The results obtained are in agreement with those of quantum groups. By associating a (finite) topological field theory (FTFT) to every rational conformal field theory (RCFT), we show that the pentagon and hexagon equations in RCFT follow directly from some skein relations in FTFT. By generalizing the operation of surgery on links in FTFT, we also derive an explicit expression for the modular transformation matrix S(k) of the one-point conformal blocks on a torus in RCFT and the equations satisfied by S(k), in agreement with those required in RCFT. The implication of our results on the general program of classifying RCFT is also discussed.

scholarly journals Chern–Simons–Rozansky–Witten topological field theory

2009 ◽  
Vol 823 (3) ◽  
pp. 403-427 ◽  
Author(s):  
Anton Kapustin ◽  
Natalia Saulina
Keyword(s):  
Field Theory ◽  
Topological Field Theory ◽  
Topological Field ◽  
Chern Simons

scholarly journals Topological Field Theory and Computing with Instantons

2017 ◽  
Vol 529 (12) ◽  
pp. 1700123 ◽  
Author(s):  
Massimiliano Di Ventra ◽  
Fabio L. Traversa ◽  
Igor V. Ovchinnikov
Keyword(s):  
Field Theory ◽  
Topological Field Theory ◽  
Topological Field

scholarly journals TOPOLOGICAL FIELD THEORY OF VORTICES OVER CLOSED KÄHLER MANIFOLD

1995 ◽  
Vol 10 (30) ◽  
pp. 4371-4385
Author(s):  
HYUK-JAE LEE
Keyword(s):  
Field Theory ◽  
Vortex Pair ◽  
Kähler Manifolds ◽  
Topological Field Theory ◽  
Kahler Manifolds ◽  
Topological Theory ◽  
Vortex Equations ◽  
Pair Model ◽  
Topological Field ◽  
Component Direction

We show that the vortex equations of the n-dimensional closed Kähler manifolds can be derived from Einstein-Hermitian equations of the (n+1)-dimensional closed Kähler manifolds by setting invariance under translation in the (n+1)th component direction. We construct the topological theory about the vortex pair model through the dimensional reduction of the topological BRST structure.

scholarly journals BRST-FIXED POINTS AND TOPOLOGICAL CONFORMAL SYMMETRY

1992 ◽  
Vol 07 (24) ◽  
pp. 2215-2222 ◽  
Author(s):  
TOSHIO NAKATSU ◽  
YUJI SUGAWARA
Keyword(s):  
Field Theory ◽  
Fixed Points ◽  
Conformal Symmetry ◽  
Topological Field Theory ◽  
Two Dimensional ◽  
Brst Transformation ◽  
Dimensional Gravity ◽  
Matter System ◽  
Topological Field ◽  
Topological Matter

We study the twisted version of the supersymmetric G/T = SU (n)/ U (1)⊗(n−1) gauged Wess-Zumino-Witten model. By studying its fixed points under BRST transformation this model is shown to be reduced to a simple topological Field theory, that is, the topological matter system in the K. Li's theory of two-dimensional gravity for the case of n = 2, and its generalization for n ≥ 3.

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