FUSION RULES, TOPOLOGICAL QUANTUM MECHANICS AND THREE-MANIFOLDS

1993 ◽  
Vol 08 (31) ◽  
pp. 3001-3010 ◽  
Author(s):  
JUAN MATEOS GUILARTE
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Path Integral ◽  
Hamiltonian Formalism ◽  
Fusion Rules ◽  
Path Integral Quantization ◽  
Topological Quantum ◽  
Verlinde Algebra ◽  
Chern Simons

Path-integral quantization of Chern-Simons field theory in the Hamiltonian formalism is developed. A derivation of Verlinde algebra in topological quantum mechanics arises and three-manifold invariants are recovered.

scholarly journals On a gravity dual to flavored topological quantum mechanics

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Andrey Feldman
Keyword(s):  
Quantum Mechanics ◽  
Effective Field ◽  
Abjm Theory ◽  
Yang Mills ◽  
Topological Quantum ◽  
Higher Derivatives ◽  
Structure Constants ◽  
Holographic Description ◽  
M Theory ◽  
Chern Simons

Abstract In this paper, we propose a generalization of the AdS2/CFT1 correspondence constructed by Mezei, Pufu and Wang in [1], which is the duality between 2d Yang-Mills theory with higher derivatives in the AdS2 background, and 1d topological quantum mechanics of two adjoint and two fundamental U(N ) fields, governing certain protected sector of operators in 3d ABJM theory at the Chern-Simons level k = 1. We construct a holographic dual to a flavored generalization of the 1d quantum mechanics considered in [1], which arises as the effective field theory living on the intersection of stacks of N D2-branes and k D6-branes in the Ω-background in Type IIA string theory, and describes the dynamics of the protected sector of operators in $$ \mathcal{N} $$ N = 4 theory with k fundamental hypermultiplets, having a holographic description as M-theory in the AdS4× S7/ℤk background. We compute the structure constants of the bulk theory gauge group, and construct a map between the observables of the boundary theory and the fields of the bulk theory.

PHYSICAL STATES OF THE TOPOLOGICAL SCHWINGER MODEL

1992 ◽  
Vol 07 (03) ◽  
pp. 259-266 ◽  
Author(s):  
CHIGAK ITOI ◽  
HISAMITSU MUKAIDA
Keyword(s):  
Field Theory ◽  
Path Integral ◽  
Correlation Functions ◽  
Hamiltonian Formalism ◽  
Topological Field Theory ◽  
Schwinger Model ◽  
Physical Operator ◽  
Topological Field ◽  
The Relationship ◽  
Large Gauge Transformation

The Schwinger model with the strong coupling limit is studied as a topological field theory both in the path-integral and in the Hamiltonian formalism. The correlation functions between arbitrary numbers of physical operators are obtained. All the physical states in this model are completely determined in the Hamiltonian formalism. The relationship between a physical operator and the generator of a large gauge transformation is clarified. The chiral condensation is also calculated.

scholarly journals CHERN–SIMONS APPROACH TO THREE-MANIFOLD INVARIANTS

1995 ◽  
Vol 10 (06) ◽  
pp. 487-493
Author(s):  
BOGUSŁAW BRODA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Lie Group ◽  
Three Dimensional ◽  
Simons Theory ◽  
Quantum Field ◽  
Topological Quantum ◽  
Chern Simons ◽  
Direct Implementation ◽  
Chern Simons Theory

A new, formal, noncombinatorial approach to invariants of three-dimensional manifolds of Reshetikhin, Turaev and Witten in the framework of nonperturbative topological quantum Chern–Simons theory, corresponding to an arbitrary compact simple Lie group, is presented. A direct implementation of surgery instructions in the context of quantum field theory is proposed. An explicit form of the specialization of the invariant to the group SU(2) is shown.

A METHOD TO CALCULATE $Q_{\rm BRST}^2$ IN THE PATH-INTEGRAL QUANTIZATION

1991 ◽  
Vol 06 (24) ◽  
pp. 2229-2236 ◽  
Author(s):  
Y. IGARASHI ◽  
J. KUBO ◽  
S. SAKAKIBARA
Keyword(s):  
Path Integral ◽  
Finite Time ◽  
Hamiltonian Formalism ◽  
Time Development ◽  
Brst Transformation ◽  
Yang Mills ◽  
Path Integral Quantization ◽  
Time Path ◽  
Brst Charge

The BRST transformation of wave functional represented in a finite-time path-integral is analyzed in the generalized Hamiltonian formalism of Batalin, Fradkin, and Vilkovisky, and it is shown that the anomalous Schwinger terms that appear in the nilpotency condition and the time development of BRST charge Q BRST can be directly calculated in the path-integral quantization. We explicitly compute [Formula: see text] in a chiral Yang–Mills theory. The method is general in character, and can easily be applied to other theories.

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