Results 1 to 10 of about 316 (182)
Journal of High Energy PhysicsWe provide a formulation of quantum mechanics based on the cohomology of the Batalin-Vilkovisky (BV) algebra. Focusing on quantum-mechanical systems without gauge symmetry we introduce a homotopy retract from the chain complex of the harmonic oscillator ...
Christoph Chiaffrino +2 more
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Towards quantum black hole microstates
Journal of High Energy Physics, 2023 We study the cohomology of local BPS operators in N $$ \mathcal{N} $$ = 4 Yang-Mills theory. The finite N cohomologies consist of the graviton part (subject to the stringy exclusion principle) and the rest which may describe black hole microstates in ...
Sunjin Choi +4 more
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From Gauge Anomalies to Gerbes and Gerbal Representations: Group Cocycles in Quantum Theory
Acta Polytechnica, 2010 In this paper I shall discuss the role of group cohomology in quantum mechanics and quantum field theory. First, I recall how cocycles of degree 1 and 2 appear naturally in the context of gauge anomalies.
J. Mickelsson
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Quantum Algorithm for Estimating Betti Numbers Using Cohomology Approach [PDF]
QuantumTopological data analysis has emerged as a powerful tool for analyzing large-scale data. An abstract simplicial complex, in principle, can be built from data points, and by using tools from homology, topological features could be identified.
Nhat A. Nghiem +2 more
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A rigorous definition of fiberwise quantum cohomology and equivariant quantum cohomology [PDF]
Communications in Analysis and Geometry, 1998 Since the proposal of the notion of quantum cohomology by the physicist \textit{C. Vafa} [in: `Essays on mirror manifolds', 96-119 (1992; Zbl 0827.58073)] and its mathematical foundation by \textit{Y. Ruan} and \textit{G. Tian} [J. Differ. Geom. 42, 259-367 (1995; Zbl 0860.58005)] for semi-positive symplectic manifolds, the quantum cohomology has ...
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Virasoro constraints for quantum cohomology
Journal of Differential Geometry, 1998 Eguchi-Hori-Xiong and S. Katz proposed a conjecture that the partition function of topological sigma model coupled to gravity is annihilated by infinitely many differential operators which form half branch of the Virasoro algebra. In this paper, we give a proof to this conjecture for the genus 0 part.
Liu, Xiaobo, Tian, Gang
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Symplectic singularities, color confinement, and the quantum Dirac sheaf
Journal of High Energy PhysicsA singularity ℂ2r /G, with G a split symplectic reflection group, may or may not be crepant. Then the total space 𝒳 of the Donagi-Witten integrable system is crepant for some 4d N = 2 $$ \mathcal{N}=2 $$ SCFT and non-crepant for others.
Sergio Cecotti
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Relative quantum cohomology of the Chiang Lagrangian
Forum of Mathematics, SigmaWe compute the open Gromov-Witten disk invariants and the relative quantum cohomology of the Chiang Lagrangian $L_\triangle \subset \mathbb {C}P^3$ .
Anna Hollands +4 more
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COHOMOLOGICAL QUANTUM MECHANICS AND CALCULABILITY OF OBSERVABLES [PDF]
Modern Physics Letters A, 1996 We reconsider quantum mechanical systems based on the classical action being the period of a one-form over a cycle and elucidate three main points. First we show that the prepotential V is no longer completely arbitrary but obeys a consistency integral equation. That is the one-form dV defines the same period as the classical action.
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Peterson-Lam-Shimozono’s theorem is an affine analogue of quantum Chevalley formula
Forum of Mathematics, SigmaWe give a new proof of an unpublished result of Dale Peterson, proved by Lam and Shimozono, which identifies explicitly the structure constants, with respect to the quantum Schubert basis, for the T-equivariant quantum cohomology $QH^{\bullet }_T(G/P)
Chi Hong Chow
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