Representations of fermionic star product algebras and the projectively flat connection

AbstractAfter reviewing geometric quantisation of linear bosonic and fermionic systems, we study the holonomy of the projectively flat connection on the bundle of Hilbert spaces over the space of compatible complex structures and relate it to the Maslov index and its various generalisations. We also consider bosonic and fermionic harmonic oscillators parametrised by compatible complex structures and compare Berry’s phase with the above holonomy.

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A `xi`-projectively flat connection on Kenmotsu manifolds

Mathematical Analysis and Convex Optimization ◽

10.29252/maco.1.1.2 ◽

2020 ◽

Vol 1 (1) ◽

pp. 0-0

Author(s):

Vahid Pirhadi ◽

Keyword(s):

Flat Connection ◽

Projectively Flat ◽

Kenmotsu Manifolds

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ON A PERFECT FLUID KÂ¨ AHLER SPACETIME

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v12i3.44 ◽

2016 ◽

Vol 12 (3) ◽

pp. 4350-4355

Author(s):

VIBHA SRIVASTAVA ◽

P. N. PANDEY

Keyword(s):

Field Equation ◽

Perfect Fluid ◽

Sectional Curvature ◽

Einstein Field Equation ◽

Cosmological Term ◽

Conformal Killing ◽

Killing Vectors ◽

Projectively Flat ◽

Conformal Killing Vectors

The object of the present paper is to study a perfect fluid KÂ¨ahlerspacetime. A perfect fluid KÂ¨ahler spacetime satisfying the Einstein field equation with a cosmological term has been studied and the existence of killingand conformal killing vectors have been discussed. Certain results related to sectional curvature for pseudo projectively flat perfect fluid KÂ¨ahler spacetime have been obtained. Dust model for perfect fluid KÂ¨ahler spacetime has also been studied.

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Correction to: Star-Product Formalism for the Probability and Mean-Value Representations of Qudits

Journal of Russian Laser Research ◽

10.1007/s10946-020-09937-y ◽

2021 ◽

Author(s):

Peter Adam ◽

Vladimir A. Andreev ◽

Margarita A. Man’ko ◽

Vladimir I. Man’ko ◽

Matyas Mechler

Keyword(s):

Star Product ◽

Mean Value

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Topological correlators and surface defects from equivariant cohomology

Journal of High Energy Physics ◽

10.1007/jhep09(2020)185 ◽

2020 ◽

Vol 2020 (9) ◽

Author(s):

Rodolfo Panerai ◽

Antonio Pittelli ◽

Konstantina Polydorou

Keyword(s):

Quantum Mechanics ◽

Equivariant Cohomology ◽

Surface Defects ◽

Star Product ◽

Three Dimensional ◽

Three Dimensions ◽

Dimensional System ◽

The Novel ◽

One Dimensional ◽

Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

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