scholarly journals BRST QUANTIZATION AND THE PRODUCT FORMULA FOR THE RAY-SINGER TORSION

1995 ◽  
Vol 10 (12) ◽  
pp. 1779-1805 ◽  
Author(s):  
CHARLES NASH ◽  
DENJOE O’CONNOR
Keyword(s):  
Finite Elements ◽  
Topological Field Theories ◽  
Brst Quantization ◽  
Product Formula ◽  
Field Theories ◽  
Analytic Torsion ◽  
Quantum Field ◽  
Infinite Dimensional ◽  
New Class ◽  
Topological Field

We give a quantum field theoretic derivation of the formula obeyed by the Ray-Singer torsion on product manifolds. Such a derivation has proved elusive up to now. We use a BRST formalism which introduces the idea of an infinite dimensional Universal Gauge Fermion, and is of independent interest, being applicable to situations other than the ones considered here. We are led to a new class of Fermionic topological field theories. Our methods are also applicable to combinatorially defined manifolds and methods of discrete approximation, such as the use of a simplicial lattice or finite elements. The topological field theories discussed provide a natural link between the combinatorial and analytic torsion.

BRST quantization of topological field theories

1989 ◽  
Vol 315 (3) ◽  
pp. 577-605 ◽  
Author(s):  
Danny Birmingham ◽  
Mark Rakowski ◽  
George Thompson
Keyword(s):  
Topological Field Theories ◽  
Brst Quantization ◽  
Field Theories ◽  
Topological Field

scholarly journals DIFF(Σ) AND METRICS FROM HAMILTONIAN-TQFT'S IN 2+1 DIMENSIONS

1993 ◽  
Vol 08 (24) ◽  
pp. 2277-2283 ◽  
Author(s):  
ROGER BROOKS
Keyword(s):  
Topological Field Theories ◽  
Gauge Theories ◽  
Dimensional Space ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Canonical Gravity ◽  
Topological Quantum ◽  
Topological Field

The constraints of BF topological gauge theories are used to construct Hamiltonians which are anti-commutators of the BRST and anti-BRST operators. Such Hamiltonians are a signature of topological quantum field theories (TQFTs). By construction, both classes of topological field theories share the same phase spaces and constraints. We find that, for (2+1)- and (1+1)-dimensional space-times foliated as M=Σ × ℝ, a homomorphism exists between the constraint algebras of our TQFT and those of canonical gravity. The metrics on the two-dimensional hypersurfaces are also obtained.

TOPOLOGICAL FIELD THEORIES ON THE COMPACT KÄHLER COMPLEX SURFACES

1994 ◽  
Vol 09 (10) ◽  
pp. 903-911
Author(s):  
HYUK-JAE LEE
Keyword(s):  
Topological Field Theories ◽  
Chern Class ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Complex Surfaces ◽  
Topological Quantum ◽  
Topological Field ◽  
Universal Bundle ◽  
Compact Kähler Manifold

The structure of topological quantum field theories on the compact Kähler manifold is interpreted. The BRST transformations of fields are derived from universal bundle and the observables are found from the second Chern class of universal bundle.

Hamiltonian BRST quantization of topological field theories

1989 ◽  
Vol 227 (2) ◽  
pp. 239-244 ◽  
Author(s):  
Y. Igarashi ◽  
H. Imai ◽  
S. Kitakado ◽  
H. So
Keyword(s):  
Topological Field Theories ◽  
Brst Quantization ◽  
Field Theories ◽  
Topological Field

Topological field theories, Nicolai maps and BRST quantization

1988 ◽  
Vol 214 (3) ◽  
pp. 381-386 ◽  
Author(s):  
Danny Birmingham ◽  
Mark Rakowski ◽  
George Thompson
Keyword(s):  
Topological Field Theories ◽  
Brst Quantization ◽  
Field Theories ◽  
Topological Field

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.

scholarly journals Topological field theories on manifolds with Wu structures

2017 ◽  
Vol 29 (05) ◽  
pp. 1750015 ◽  
Author(s):  
Samuel Monnier
Keyword(s):  
Topological Field Theories ◽  
Geometric Quantization ◽  
Discrete Symmetry ◽  
Local System ◽  
Field Theories ◽  
Simons Theory ◽  
General Point ◽  
Topological Field ◽  
Generalized Cohomology ◽  
Chern Simons

We construct invertible field theories generalizing abelian prequantum spin Chern–Simons theory to manifolds of dimension [Formula: see text] endowed with a Wu structure of degree [Formula: see text]. After analyzing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf–Witten theories. We take a general point of view where the Chern–Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern–Simons action. In the 3-dimensional spin case, the latter provides a definition of the “fermionic correction” introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing. The physical motivation for this work comes from the fact that in the [Formula: see text] case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with [Formula: see text] supersymmetry, as will be discussed elsewhere.

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