The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions

Experimental quantum Hamiltonian learning

Nature Physics ◽

10.1038/nphys4074 ◽

2017 ◽

Vol 13 (6) ◽

pp. 551-555 ◽

Cited By ~ 58

Author(s):

Jianwei Wang ◽

Stefano Paesani ◽

Raffaele Santagati ◽

Sebastian Knauer ◽

Antonio A. Gentile ◽

...

Keyword(s):

Quantum Hamiltonian

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THE FUNCTIONAL INTEGRAL ON THE HALF-LINE

International Journal of Modern Physics A ◽

10.1142/s0217751x90001422 ◽

1990 ◽

Vol 05 (15) ◽

pp. 3029-3051 ◽

Cited By ~ 38

Author(s):

EDWARD FARHI ◽

SAM GUTMANN

Keyword(s):

Time Evolution ◽

Wide Class ◽

Green's Functions ◽

Green’S Functions ◽

Functional Integral ◽

Half Line ◽

Functional Integrals ◽

Quantum Hamiltonian ◽

Do So

A quantum Hamiltonian, defined on the half-line, will typically not lead to unitary time evolution unless the domain of the Hamiltonian is carefully specified. Different choices of the domain result in different Green’s functions. For a wide class of non-relativistic Hamiltonians we show how to define the functional integral on the half-line in a way which matches the various Green’s functions. To do so we analytically continue, in time, functional integrals constructed with real measures that give weight to paths on the half-line according to how much time they spend near the origin.

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ERRATA: COMMENTS ON GENERALIZED QUANTUM HAMILTONIAN REDUCTIONS

Modern Physics Letters A ◽

10.1142/s0217732392003232 ◽

1992 ◽

Vol 07 (03) ◽

pp. 267-267 ◽

Cited By ~ 1

Author(s):

Toshiya Kawai ◽

Toshio Nakatsu

Keyword(s):

Quantum Hamiltonian

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QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA

International Journal of Modern Physics A ◽

10.1142/s0217751x92002210 ◽

1992 ◽

Vol 07 (20) ◽

pp. 4885-4898 ◽

Cited By ~ 11

Author(s):

KATSUSHI ITO

Keyword(s):

Lie Algebras ◽

Free Field ◽

Lie Superalgebra ◽

Lie Superalgebras ◽

Hamiltonian Reduction ◽

Affine Lie Algebras ◽

Quantum Hamiltonian Reduction ◽

Free Field Realization ◽

Coset Construction ◽

Quantum Hamiltonian

We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

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